MachineLearning.ipynb

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    "<a id=\"top\"></a>\n",
    "\n",
    "# Machine Learning\n",
    "\n",
    "<br>\n",
    "\n",
    "## Coursera Machine Learning with Andrew Ng\n",
    "[https://www.coursera.org/learn/machine-learning/home/welcome](https://www.coursera.org/learn/machine-learning/home/welcome)\n",
    "- [Unit 1 - Linear Regression](#unit1)\n",
    "- [Unit 2 - Multivariate Linear Regression](#unit2)\n",
    "- [Unit 3 - Logistic Regression](#unit3)\n",
    "- [Unit 7 - SVM](#unit7)\n",
    "- [Unit 8 - Unsupervised Learning & Dimension Reduction](#unit8)\n",
    "- [Unit 9 - Anomaly Detection](#unit9)\n",
    "___\n",
    "\n",
    "## Python Machine Learning\n",
    "[https://www.packtpub.com/big-data-and-business-intelligence/python-machine-learning](https://www.packtpub.com/big-data-and-business-intelligence/python-machine-learning)\n",
    "- [Decision Trees and Ensemble Methods](#dt)\n",
    "- [Natural Language Processing (NLP)](#nlp)\n",
    "- [Feature Selection](#fs)\n",
    "___\n",
    "\n",
    "## Analytics Vidhyra\n",
    "https://www.analyticsvidhya.com/blog/\n",
    "- [Regularization](#reg)\n",
    "\n",
    "---\n",
    "\n",
    "## Other\n",
    "- [Encoding categorical features](#enccat)\n",
    "\n",
    "---\n",
    "\n",
    "## General Assembly\n",
    "- [Pros and Cons of basic machine learning algorithms](#procon)\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Coursera Machine Learning\n",
    "\n",
    "*\"A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P, if its performance at tasks in T, as measured by P, improves with experience E.\" - Tom Mitchell*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"unit1\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Unit 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Supervised vs unsupervised learning\n",
    "\n",
    "- **Supervised learning:** given an input dataset and corresponding output, train computer to make predictions. Two types:\n",
    " 1. *Regression* - predicts a continuous output\n",
    " 1. *Classification* - predicts a discrete output\n",
    " <br><br>\n",
    "- **Unsupervised learning:** given dataset with no output, derive structure from data, typically done with clustering."
   ]
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   "source": [
    "## Linear regression with one variable\n",
    "\n",
    "Univariate linear regression is a type of supervised learning used to predict a single output value $y$ from a single input value $x$, with a given number of examples $m$. The $i^{th}$ training example is represented by $(x^{(i)}, y^{(i)})$.\n",
    "\n",
    "We model the dataset/system with a ***hypothesis function*** $h$ that maps the input variable $x$ to the output variable $y$. For univariate linear regression,\n",
    "\n",
    "$$h_{\\theta}(x) = \\theta_{0} + \\theta_{1}x$$\n",
    "\n",
    "To calculate the ***parameters*** $\\theta s$ in the hypothesis function, choose values for the parameters so that $h_{\\theta}(x)$ is close to the given actual output values $y$. This can be achieved by minimizing the quantity,\n",
    "\n",
    "$$\\min_{\\theta_{0}, \\ \\theta_{1}} \\ \\frac{1}{2m} \\sum_{i=1}^{m} \\ [h_{\\theta}(x^{(i)}) - y^{(i)}]^{2}$$\n",
    "where,\n",
    "$$ h_{\\theta}(x^{(i)}) = \\theta_{0} + \\theta_{1}x^{(i)} $$\n",
    "\n",
    "The term inside the summation is called the ***squared error cost function*** and is typically written,\n",
    "\n",
    "$$ J(\\theta_{0}, \\theta_{1}) = \\frac{1}{2m} \\sum_{i=1}^{m} \\ [h_{\\theta}(x^{(i)}) - y^{(i)}]^{2} $$\n",
    "\n",
    "So the idea is to use an algorithm that can select values for the parameters that minimize the value of the cost function."
   ]
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   "source": [
    "## Gradient descent\n",
    "\n",
    "Algorithm used for function minimization, for univariate linear regression, this method will calculate values for $\\theta_{0}$ and $\\theta_{1}$ that minimize $J$.\n",
    "\n",
    "**Basic procedure:**\n",
    "1. Start with a guess for the value of $\\theta_{0}$ and $\\theta_{1}$.\n",
    "1. Calculate $J$, then select new values of $\\theta_{0}$ and $\\theta_{1}$ until $J$ is minimized.\n",
    "\n",
    "**Definition:**\n",
    "$$ repeat \\ until \\ convergence: \\  \\theta_{j} := \\theta_{j} - \\alpha \\frac{\\partial}{\\partial \\theta_{j}} J(\\theta_{0}, \\theta_{1}) \\ \\ for \\ j=0 \\ and \\  j=1  $$\n",
    "\n",
    "**Notes:**\n",
    "\n",
    "Gradient descent uses ***simultaneous update*** where the right hand side of the equation is calculated for all $js$ then all $js$ are updated at the same time before performing the next iteration of gradient descent. The parameter $\\alpha$ is defined as the ***learning rate***.\n",
    "\n",
    "After each iteration, the current value of $\\theta$ moves close to the minimum of $J$ as a function of $\\theta$.\n",
    "\n",
    "Selecting $\\alpha$ is important because if the value is too large, the update at each step may pass over the actual minimum $J$ and fail to find the minimum. If $\\alpha$ is too small, the process will take a long time to complete.\n",
    "\n",
    "When all training examples are used in each step, the process is called ***batch gradient descent***.\n",
    "\n",
    "**For univariate linear regression:**\n",
    "\n",
    "The derivative of the cost function $J$ relative to the parameters $\\theta$ yields ( remember $h_{\\theta}(x^{(i)}) = \\theta_{0} + \\theta_{1}x^{(i)}$ ),\n",
    "$$ \\theta_{0} := \\theta_{0} - \\alpha  \\frac{1}{m} \\sum_{i=1}^{m} \\ [h_{\\theta}(x^{(i)}) - y^{(i)}] $$\n",
    "$$ \\theta_{1} := \\theta_{1} - \\alpha  \\frac{1}{m} \\sum_{i=1}^{m} \\ [h_{\\theta}(x^{(i)}) - y^{(i)}] \\cdot x^{(i)} $$"
   ]
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   "cell_type": "markdown",
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   "source": [
    "<a id=\"unit2\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Unit 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multivariate linear regression\n",
    "\n",
    "Instead of one input variable $x$ there are now $n$ input variables or features, $x_{0}, x_{1}, ..., x_{n}$. Thus the hypothesis function becomes,\n",
    "\n",
    "$$ h_{\\theta}(x) = \\theta_{0} + \\theta_{1} x_{1} + \\theta_{2} x_{2} + ... + \\theta_{n} x_{n} $$\n",
    "\n",
    "where by convention, $x_{0} = 1$. This expression can be simplified by using column vectors to represent $x$ and $\\theta$ in which case,\n",
    "\n",
    "$$ x = \\begin{pmatrix}x_{0}\\\\x_{1}\\\\.\\\\x_{n}\\end{pmatrix} , \\qquad \\theta = \\begin{pmatrix}\\theta_{0}\\\\\\theta_{1}\\\\.\\\\\\theta_{n}\\end{pmatrix} , \\qquad h_{\\theta}(x) = \\theta^{T} x \\ = (\\theta_{0} \\ \\theta_{1} \\ ... \\ \\theta_{n})\\begin{pmatrix}x_{0}\\\\x_{1}\\\\.\\\\x_{n}\\end{pmatrix}$$"
   ]
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   "source": [
    "## Multivariate gradient descent\n",
    "\n",
    "Instead of two update rules for $\\theta_{0}$ and $\\theta_{1}$ there are now $n$ update rules for each feature which can be written,\n",
    "\n",
    "$$ \\theta_{j} := \\theta_{j} - \\alpha  \\frac{1}{m} \\sum_{i=1}^{m} \\ [h_{\\theta}(x^{(i)}) - y^{(i)}] \\cdot x_{j}^{(i)} $$\n",
    "\n",
    "It is import to make sure the features are on a similar scale so that they converge at a similar rate. One means of doing this is to use ***feature scaling***; subtract the mean value then divide by the maximum minum minimum value or the standard deviation of the feature. Ideally, features should be in the range [-1,1].\n",
    "\n",
    "**How to choose learning rate:**\n",
    "\n",
    "First, to ensure gradient descent is working correctly, plot the minimum value of $J(\\theta)$ as a function of the number of iterations of gradient descent. The curve should be decreasing with a slope that flattens out at higher iterations to indicate it is approaching convergence.\n",
    "\n",
    "If the plot does not decrease monotonically, then it is likely that $\\alpha$ is set too large and should be decreased. Typical range of values to try: \n",
    "\n",
    "$$ \\alpha = \\ ..., 0.001, 0.003, 0.01, 0.03, 0.1, 0.3, 1, ... $$\n",
    "\n",
    "If convergence takes a long time, it is likely that $\\alpha$ is set too small and must be increased."
   ]
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   "source": [
    "## Polynomial regression\n",
    "\n",
    "The hypothesis function becomes,\n",
    "\n",
    "$$ h_{\\theta}(x) = \\theta_{0} + \\theta_{1} x + \\theta_{2} x^{2} + ... + \\theta_{n} x^{n} $$\n",
    "\n",
    "where $n$ can also take on values between 0 and 1.\n",
    "\n",
    "Here, feature scaling becomes very important because of the power variation between features in the hypothesis function."
   ]
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"unit3\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Unit 3"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Logistic regression\n",
    "\n",
    "In classification problems it often occurs that the output variable $y \\in \\{0,1\\}$, i.e., there is a positive or negative outcome this is called a ***binary classification problem***.\n",
    "\n",
    "If using linear regression to predict either 0 or 1 values it may seem reasonable to select predictions greater than 0.5 equal to 1 and those below equal to 0. However data points that may not be expected to change the prediction mechanism can alter the linear regression of the data and significantly change the output of the hypothesis function.\n",
    "\n",
    "Instead it is better to use a ***sigmoid function*** rather than a linear function to represent the hypothesis,\n",
    "$$ h_{\\theta}(x) = g(\\theta^{T} x) = \\frac{1}{1 + e^{-\\theta^{T} x}} $$\n",
    "\n",
    "<img src=\"images/sigmoid.png\" width=\"300\">\n",
    "\n",
    "\n",
    "Logistic regression returns a probability that the hypothesis function outputs to 0 or 1 such that,\n",
    "\n",
    "$$ P(y = 0  \\ | \\ x; \\theta) + P(y = 1 \\ | \\ x; \\theta) = 1 $$\n",
    "\n",
    "The reasonable choice for returning an output of 1 is then, $ h_{\\theta}(x) \\ge 0.5 $ or $\\theta^{T} x \\ge 0$, and an output of 0 when $ h_{\\theta}(x) \\lt 0.5 $ or $\\theta^{T} x \\lt 0$.\n",
    "\n",
    "Thus the ***decision boundary***, the line that separates $y=0$ and $y=1$, occurs where $\\theta^{T} x = 0$.\n",
    "\n",
    "This method works well for linearly-separable classes. It can be thought of as returning the log-odds ratio predicting the conditional probability of a particular event, i.e., given the data in $x$, what are the log-odds of output $y=0$ or output $y=1$ occurring."
   ]
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   "source": [
    "## Cost function for logistic regression\n",
    "\n",
    "The cost function for linear regression (based on the sum of the squared error) cannot be used here as it would be non-convex and not guaranteed to converge to the global minima when using gradient descent.\n",
    "\n",
    "Instead we want a function that behaves appropriately,\n",
    "\n",
    "$$ if \\ h_{\\theta} (x) = 0, \\ predict \\ P(y=1 \\ | \\ x;\\theta) = 0, so \\ Cost \\rightarrow \\infty $$\n",
    "$$ if \\ h_{\\theta} (x) = 1, \\ predict \\ P(y=1 \\ | \\ x;\\theta) = 1, so \\ Cost \\rightarrow 0 $$\n",
    "$$ if \\ h_{\\theta} (x) = 1, \\ predict \\ P(y=0 \\ | \\ x;\\theta) = 0, so \\ Cost \\rightarrow \\infty $$\n",
    "$$ if \\ h_{\\theta} (x) = 0, \\ predict \\ P(y=0 \\ | \\ x;\\theta) = 1, so \\ Cost \\rightarrow 0 $$\n",
    "\n",
    "The logitistic/sigmoid function has this behavior,\n",
    "$$ h_{\\theta}(x) = \\frac{1}{1+e^{-\\theta^Tx}} $$\n",
    "\n",
    "A good selection then given the sigmoid shape of the hypothesis function is,\n",
    "\n",
    "$$ Cost \\ (h_{\\theta} (x), y) = \\begin{cases} -\\log[h_{\\theta} (x)]  & \\mbox{if } y = 1 \\\\ -\\log[1 - h_{\\theta} (x)] & \\mbox{if } y = 0 \\end{cases} $$\n",
    "\n",
    "Since $y = 0$ or $1$ always, this multipart definition can be written as a single expression,\n",
    "\n",
    "$$ Cost \\ (h_{\\theta} (x), y) = -y \\log[h_{\\theta} (x)] - (1-y) \\log[1 - h_{\\theta} (x)] $$\n",
    "\n",
    "And,\n",
    "\n",
    "$$ J(\\theta) = - \\frac{1}{m} \\sum_{i=1}^{m} y^{(i)} \\log{h_{\\theta} (x^{(i)})} + (1-y^{(i)}) \\log{(1 - h_{\\theta} (x^{(i)}))} $$\n",
    "\n",
    "This expression can be derived from maximum likelihood estimation theory."
   ]
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   "source": [
    "## Gradient descent for logistic regression\n",
    "\n",
    "To minimize $J(\\theta)$ by calculating the partial derivative gives,\n",
    "\n",
    "$$ \\theta_{j} := \\theta_{j} - \\alpha  \\frac{1}{m} \\sum_{i=1}^{m} \\ [h_{\\theta}(x^{(i)}) - y^{(i)}] \\cdot x_{j}^{(i)} $$\n",
    "\n",
    "which is identical to linear regression, the only difference being the form of the hypothesis function $h_{\\theta}(x)$."
   ]
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   "source": [
    "## Multiclass logistic regression\n",
    "\n",
    "For systems that have more output options than 0 and 1 as in binary classification. It is possible to iteratively apply binary classification using a ***one-vs-all*** procedure,\n",
    "\n",
    "$$ h_{\\theta}^{(i)} (x) = P(y=i \\ | \\ x;\\theta) \\qquad (i=1,2,3,...) $$\n",
    "\n",
    "Each iteration returns the probability that $y=i$. So for each example, the predicted output is,\n",
    "\n",
    "$$ \\max_{i} h_{\\theta}^{(i)} (x) $$"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "## Regularization to address overfitting\n",
    "\n",
    "One method to reduce variance and overfitting is to penalize certain features and make the corresponding parameters very small so that they have little influence in determining the value of the cost function. This can be achieved by adding the product of the square of the features with a large number,\n",
    "\n",
    "$$ \\min_{\\theta} \\frac{1}{2m} \\sum_{i=1}^{m} \\ [h_{\\theta}(x^{(i)}) - y^{(i)}]^{2} + \\lambda \\sum_{j=1}^{n} \\theta_{j}^{2} $$\n",
    "\n",
    "If the ***regularization parameter*** $\\lambda$ is set too high, the solution may end up underfitting.\n",
    "\n",
    "Note that for linear regression, $\\theta_{0}$ is not regularized, i.e., it is not included in the summation."
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regularization and linear regression\n",
    "\n",
    "The gradient descent formula becomes,\n",
    "\n",
    "$$ \\theta_{j} := \\theta_{j} (1 - \\alpha \\frac{\\lambda}{m}) - \\alpha \\frac{1}{m} \\sum_{i=1}^{m} \\ [h_{\\theta}(x^{(i)}) - y^{(i)}] \\cdot x_{j}^{(i)} $$"
   ]
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   "source": [
    "## Regularization and logistic regression\n",
    "\n",
    "The cost function is,\n",
    "\n",
    "$$ J(\\theta) = - \\frac{1}{m} \\sum_{i=1}^{m} [-y^{(i)} \\log{h_{\\theta} (x^{(i)})} - (1-y^{(i)}) \\log{(1 - h_{\\theta} (x^{(i)}))}] + \\frac{\\lambda}{2m} \\sum_{j=1}^{n} \\theta_{j}^{2} $$\n",
    "\n",
    "And the gradient descent formula is identical to that for linear regression with the exception that the hypothesis function $h_{\\theta}(x)$ is different,\n",
    "\n",
    "$$ \\theta_{j} := \\theta_{j}  - \\alpha \\Big[ \\Big( \\frac{1}{m} \\sum_{i=1}^{m} \\ [h_{\\theta}(x^{(i)}) - y^{(i)}] \\cdot x_{j}^{(i)} \\Big) + \\frac{\\lambda}{m} \\theta_{j} \\Big] $$"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "<a id=\"unit7\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Unit 7"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Support vector machines\n",
    "\n",
    "In SVMs, the optimization objective is to maximize the ***margin***. The margin is defined as the distance between the separating hyperplane (decision boundary) and the training samples that are closest to this hyperplane, which are the so-called ***support vectors***. The rationale behind having decision boundaries with large margins is that they tend to have a lower generalization error whereas models with small margins are more prone to overfitting.\n",
    "\n",
    "SVM can be derived by modifying logistic regression. Consider the cost function written as,\n",
    "\n",
    "$$ \\min_{\\theta} \\frac{1}{m} \\sum_{i=1}^{m} y^{(i)} {cost}_{(y=1)} \\Big( \\theta^{T} x^{(i)} \\Big) + \n",
    "(1-y^{(i)}) {cost}_{(y=0)} \\Big( \\theta^{T} x^{(i)} \\Big) + \\frac{\\lambda}{2m} \\sum_{j=0}^{n} \\theta_{j}^{2} $$\n",
    "\n",
    "Drop the use of $m$ and define regularization as $C\\cdot A + B$ instead of $A + \\lambda \\cdot B$ such that $C = 1/\\lambda$,\n",
    "\n",
    "$$ \\min_{\\theta} C \\sum_{i=1}^{m} y^{(i)} {cost}_{(y=1)} \\Big( \\theta^{T} x^{(i)} \\Big) + \n",
    "(1-y^{(i)}) {cost}_{(y=0)} \\Big( \\theta^{T} x^{(i)} \\Big) + \\frac{1}{2} \\sum_{j=0}^{n} \\theta_{j}^{2} $$\n",
    "\n",
    "The portions of the cost function $cost \\ ( \\theta^{T} x^{(i)} )$ require,\n",
    "$$ If \\ y=1, \\ \\theta^{T} x^{(i)} \\ge 1 $$\n",
    "$$ If \\ y=0, \\ \\theta^{T} x^{(i)} \\le -1 $$\n",
    "\n",
    "To simplify the derivation, assume a large regularization parameter $C$ which simplifies the optimization objective to,\n",
    "\n",
    "$$ \\min_{\\theta} \\frac{1}{2} \\sum_{j=0}^{n} \\theta_{j}^{2} $$\n",
    "\n",
    "The dot product of two vectors can be written as the product of the projection of one vector on to the other times its norm,\n",
    "\n",
    "$$ \\theta^{T} x^{(i)} = p^{(i)} \\cdot \\| \\theta \\| $$\n",
    "\n",
    "Thus minimizing $\\theta$ is equivalent to choosing $\\theta$ that maximizes $p^{(i)}$. This is why SVM is called *large margin optimization* or why SVM selects hyperplanes that maximize the separation between classes."
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Kernels\n",
    "\n",
    "To solve a nonlinear problem using an SVM, transform the training data onto a higher dimensional feature space via a mapping function, then train a linear SVM model to classify the data in this new feature space. \n",
    "\n",
    "Create landmarks in feature space and define a similarity function $f$ that relates how similar example $x$ is to each landmark $l$. A function that works well to describe this relationship is the *Gaussian or radial basis function*,\n",
    "\n",
    "$$ f_{i}(x) = \\exp{\\Bigg( - \\frac{\\|x - l^{(i)} \\|^{2}}{2\\sigma^{2}} \\Bigg)} $$\n",
    "\n",
    "The hypothesis function for *three* features becomes,\n",
    "\n",
    "$$ h_{\\theta}(x) = \\theta_{0} + \\theta_{1} f_{1} + \\theta_{2} f_{2} + \\theta_{3} f_{3} $$\n",
    "\n",
    "And we predict $y=1$ if,\n",
    "\n",
    "$$ h_{\\theta}(x) = \\theta^{T} f = \\theta_{0} + \\theta_{1} f_{1} + \\theta_{2} f_{2} + \\theta_{3} f_{3} \\ge 0 $$\n",
    "\n",
    "How are the landmarks determined? For each example in the training set, set landmarks at the location of the training examples so in the end there are $m$ total examples.\n",
    "\n",
    "Now the cost function becomes,\n",
    "\n",
    "$$ \\min_{\\theta} C \\sum_{i=1}^{m} y^{(i)} {cost}_{(y=1)} \\Big( \\theta^{T} f^{(i)} \\Big) + \n",
    "(1-y^{(i)}) {cost}_{(y=0)} \\Big( \\theta^{T} f^{(i)} \\Big) + \\frac{1}{2} \\sum_{j=1}^{m} \\theta_{j}^{2} $$\n",
    "\n",
    "Remember that there are $m$ features and thus $m$ parameters $\\theta$,\n",
    "\n",
    "$$ \\theta^{T} f = \\theta_{0} + \\theta_{1} f_{1} + \\theta_{2} f_{2} + ... + \\theta_{m} f_{m} $$\n",
    "\n",
    "The value of $\\sigma$ used in the similarity function require tuning. Smaller values increase the influence or reach of the training examples leading to a softer boundary. Larger values will cause the boundary to tightly trace all but 1 of the classes, which can lead to generalization error on test data.\n",
    "\n",
    "In the end the **support vectors** or landmarks are the datapoints that lie on the hyperplanes. They are found by checking each and every data point against the SVM constraints and those that have the smallest distance from the data point to the support vector are the support vectors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"unit8\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Unit 8"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unsupervised learning: K-means clustering\n",
    "\n",
    "Two step algorithm that is repeated until convergence:\n",
    "1. Cluster assignment\n",
    "1. Centroid calculation\n",
    "\n",
    "Cluster centroids are randomly initialized before the algorithm begins. Cluster assignment of each example is based on Euclidean distance between example and cluster centroids. This is reflected in the cost function of the optimization objective also called the ***inertia***,\n",
    "\n",
    "$$ \\min_{c, \\ \\mu} \\ \\frac{1}{m} \\sum_{i=1}^{m} \\| x^{(i)} - \\mu_{c^{(i)}} \\|^{2} $$\n",
    "\n",
    "where $c$ is the cluster index and $\\mu$ is the location of the cluster centroid.\n",
    "\n",
    "### Initializing cluster centroids:\n",
    "\n",
    "Different choices of initialization can yield different results, the solution of k-means may converge to a local optima. To prevent this from occurring:\n",
    "\n",
    "1. Randomly select centroids to be specific training examples. \n",
    "1. Run k-means (optimization objective) and minimize cost function.\n",
    "1. Repeat steps 1 and 2 (perhaps 100) and select the k-means results that have the lowest cost.\n",
    "\n",
    "### Choosing number of clusters:\n",
    "\n",
    "Most common method is to select number of clusters manually based on some downstream purpose (i.e., market segmentation such as t-shirt sizing).\n",
    "\n",
    "**Elbow method**: Plot the cost function for various number of clusters. Select the solution that corresponds to the location where the plot flattens out. It is possible that this method may not work.\n",
    "\n"
   ]
  },
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   "source": [
    "## Dimensionality reduction: Principal component analysis\n",
    "\n",
    "It may be possible to reduce the number of features in the training set without sacrificing significant model performance.\n",
    "\n",
    "**Algorithm:**\n",
    "1. Compute covariance matrix from the standardized dataset,\n",
    "$$ \\Sigma = \\frac{1}{m} \\sum_{i=1}{n} (x^{(i)})(x^{(i)})^{T} $$\n",
    "1. Compute eigenvectors of $\\Sigma$ using singular value decomposition,\n",
    "$$ U, \\ S, \\ V = svd(\\Sigma) $$ <br>\n",
    "\n",
    "Here the first $k$ column vectors of $U$ will transform the $n$ dimensional space data to the reduced $k$ dimensional space, $z = U^{T} x.$\n",
    "\n",
    "To recover approximate representations of the original data from the compressed/transformed data, $x_{approx} = U z.$\n",
    "\n",
    "The basis of the transformed datasets are then the eigenvectors of the covariance matrix, which are called *principal components*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Notes on singular value decomposition (SVD)\n",
    "\n",
    "Reference:<br>\n",
    "https://en.wikipedia.org/wiki/Singular_value_decomposition\n",
    "\n",
    "The singular value decomposition of a *real-valued* $m \\times n$ matrix $M$ is given by,\n",
    "$$ M = USV^{T} $$\n",
    "where,\n",
    "- $U$ is an $m \\times m$ unitary matrix\n",
    "- $S$ is a diagonal $m \\times n$ matrix with non-negative numbers on the diagonal (these entries are the **singular values**)\n",
    "- $V$ is an $n \\times n$ unitary matrix\n",
    "\n",
    "If the original, real matrix $M$ is *normal* (square) then,\n",
    "- the columns of $U$ (left-singular vectors) are **eigenvectors** of $MM^T$\n",
    "- the columns of $V$ (right-singular vectors) are **eigenvectors** of $M^TM$\n",
    "- the diagonal values of $S$ are the **eigenvalues** of $M^TM$ or $MM^T$\n",
    "\n",
    "Thus the eigenvalue decomposition and SVD differ except for positive semi-definite normal matrices. The eigenvalue decomposition is $M=UDU^{-1}$ and SVD is $M=USV^T$.\n",
    "\n",
    "#### Eigenvalue decomposition\n",
    "\n",
    "It is possible to build a square matrix from the dataset by calculating the **covariance matrix** $C$ (i.e., the covariance of the dataset with itself). For $m \\times n$ matrix $M$,\n",
    "$$ C = \\frac{1}{m-1} M^T \\cdot M $$\n",
    "\n",
    "Singular value decomposition is then applied to matrix $C$, the resulting principal components are then the eigenvectors of the covariance matrix."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"unit9\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Unit 9"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Anomaly detection\n",
    "\n",
    "Assume an unlabeled dataset that contains clean and anomalous data where each example $x^{(i)}$ is $x \\in \\mathbb{R}^{n}$. Then apply multivariate density estimation to each example (assuming features are independent),\n",
    "\n",
    "$$ p(x) = p(x_{1}; \\ \\mu_{1}, \\sigma_{1}^{2}) \\cdot p(x_{2}; \\ \\mu_{2}, \\sigma_{2}^{2}) \\cdot \\ldots \\cdot p(x_{n}; \\ \\mu, \\sigma_{n}^{2}) = \\prod_{j=1}^{n} \\ p(x_{j}; \\mu_{j} \\sigma_{j}^{2}) $$\n",
    "\n",
    "### Algorithm:\n",
    "\n",
    "1. Choose features that may be indicative of anomalous examples.\n",
    "1. Fit parameters for all $n$ features $\\mu_{n}$, $\\sigma_{n}^{2}$,\n",
    "$$ \\mu_{j} = \\frac{1}{m} \\sum_{i=1}^{m} x_{j}^{(i)}, \\quad \\sigma_{j}^{2} = \\frac{1}{m} \\sum_{i=1}^{m} \\big(x_{j}^{(i)} - \\mu \\big)^{2} $$\n",
    "1. Given new example $x$, compute multivariate density estimate of all the relevant features of this example $p(x)$,\n",
    "$$ p(x) = \\prod_{j=1}^{n} \\ p(x_{j}; \\mu_{j} \\sigma_{j}^{2}) = \\prod_{j=1}^{n} \\frac{1}{\\sqrt{2 \\pi} \\sigma_{j}} \\exp - \\Big( \\frac{(x_{j} - \\mu_{j})^2}{2 \\sigma_{j}^{2}} \\Big) $$\n",
    "1. Compare $p(x) < \\epsilon$, if true then this example $x$ is an anomaly.\n",
    "\n",
    "<br>\n",
    "### Pseudo-supervised learning approach:\n",
    "\n",
    "Create dataset with labeled anomalous examples ($y=0$ if normal, $y=1$ If anomalous) and divide into CV and test sets.\n",
    "\n",
    "1. Fit parameters for all $n$ features $\\mu_{n}$, $\\sigma_{n}^{2}$ for training set.\n",
    "1. Evaluate $p(x)$ for each training example and predict $y=1$ if $p(x) < \\epsilon$ and $y=0$ if $p(x) \\ge \\epsilon$.\n",
    "1. Use a good unbalanced class metric such as F1-score to evaluate model on CV/test set.\n",
    "1. Can use CV set to select appropriate $\\epsilon$ and features to include in model before running on test set.\n",
    "\n",
    "<br>\n",
    "### Feature selection:\n",
    "\n",
    "1. ***Check if features are Gaussian*** (not strictly necessary) by plotting distribution. If feature has log-normal distribution, replace feature $x$ with $\\log{x}$ or $\\log{x + c}$. If the feature has an exponential distribution, can adjust feature distribution with power: $x^{1/p}$.\n",
    "1. ***Use error analysis*** so that $p(x)$ is small for anomalous examples and large for normal examples. Choose quick algorithm, run it, refine it so that anomalous values that are predicted to be normal are no long misclassified.\n",
    "\n",
    "<br>\n",
    "### Multivariate gaussian distribution:\n",
    "\n",
    "1. Fit model $p(x)$ by calculating mean average $\\mu$ and covariance $\\Sigma$,\n",
    "$$ \\mu_{j} = \\frac{1}{m} \\sum_{i=1}^{m} x_{j}^{(i)}, \\quad \\Sigma = \\frac{1}{m} \\sum_{i=1}^{m} \\big(x^{(i)} - \\mu \\big) \\big(x^{(i)} - \\mu \\big)^{T} $$\n",
    "1. Given a new example $x$, compute,\n",
    "$$ p(x) = \\frac{1}{(2\\pi)^{n/2} |\\Sigma|^{1/2}} \\ \\exp{\\Big( -\\frac{1}{2}(x-\\mu)^{T} \\Sigma^{-1} (x-\\mu) \\Big)} $$\n",
    "1. Classify as an anomaly if $p(x) < \\epsilon$.\n",
    "\n",
    "This method does not assume the features are independent (i.e., the axes of the multivariate Gaussian distribution are orthogonal, for 2D this means the Gaussian top view is an ellipse) as was done with the original model. Another way of describing this relationship is to say the original model is the special case where the covariance matrix is diagonal.\n",
    "\n",
    "### Separable model vs multivariate:\n",
    "\n",
    "1. Multivariate will capture correlations between features where separable model would new features to capture these relationships.\n",
    "1. Separable model is computationally cheaper since the matrix inversion $\\Sigma^{-1}$ is not needed.\n",
    "1. If number of examples $m$ is small, separable model can be used where as multivariate approach requires $m>n$ so that covariance matrix $\\Sigma$ is invertible. Also if there are linearly-dependent features then $\\Sigma$ is non-invertible, so remove the feature causing the redundancy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "<br><br>\n",
    "___\n",
    "\n",
    "# Python Machine Learning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Parametric vs Nonparameteric classifiers\n",
    "\n",
    "Using parametric models, we estimate parameters from the training dataset to learn a function that can classify new data points without requiring the original training dataset anymore. In contrast, nonparametric models can't be characterized by a set of parameters, and the number of parameters grows with the training data.\n",
    "\n",
    "### Parametric\n",
    "- Perceptron\n",
    "- Logistic regression\n",
    "- Linear SVM\n",
    "\n",
    "### Nonparametric\n",
    "- Decision trees/random forests\n",
    "- Kernel SVM\n",
    "- KNN"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"dt\"></a>\n",
    "<br>\n",
    "\n",
    "# Decision Trees and Ensemble Methods\n",
    "\n",
    "Additional reference:<br>\n",
    "[http://stackoverflow.com/questions/1859554/what-is-entropy-and-information-gain](http://stackoverflow.com/questions/1859554/what-is-entropy-and-information-gain)\n",
    "\n",
    "Decision tree classifiers make predictions by asking a series of questions. The questions to ask are determined by data features. The idea is to find the feature that best splits the target class into the purest possible children nodes (ie: nodes that don't contain a mix of both classes, rather pure nodes with only one class). This is achieved by splitting the data at each node in order to maximize the ***information gain ratio***,\n",
    "\n",
    "$$ \\max \\ IG(D_{p}, f) = I(D_{p}) - \\sum_{j=1}^{m} \\frac{N_{j}}{N_{p}} I(D_{j}) $$\n",
    "\n",
    "Here $f$ is the feature to perform the split, $D_{p}$ and $D_{j}$ are the dataset of the parent and $j$th child node, $N_{p}$ and $N_{j}$ are the number of examples of the parent and $j$th child node, $I$ is the impurity measure. Impurity is the \"opposite\" of information.\n",
    "\n",
    "Information gain ratio biases the decision tree against considering attributes with a large number of distinct values. So it solves the drawback of information gain—namely, information gain applied to attributes that can take on a large number of distinct values might learn the training set too well.\n",
    "\n",
    "The information gain is simply the difference between the impurity of the parent node and the normalized sum of the child node impurities. The lower the impurity of the child nodes, the larger the information gain.\n",
    "\n",
    "To improve computational performance, scikit-learn uses binary decision trees,\n",
    "\n",
    "$$ IG(D_{p}, f) = I(D_{p}) - \\sum_{j=1}^{m} \\frac{N_{left}}{N_{p}} I(D_{left}) - \\frac{N_{right}}{N_{p}} I(D_{right})$$\n",
    "\n",
    "The common ***impurity measures*** are ***Gini impurity***, ***entropy***, and the ***classification error***.\n",
    "1. Entropy maximizes the mutual information in a tree. If $p(i|t)$ is the proportion of examples that belong to class $i$  for node $t$, entropy is 0 if $p(i=1|t)=1$ or $p(i=0|t)=0$ and entropy is 1 if $p(i=1|t)=0.5$ and $p(i=0|t)=0.5$.\n",
    "1. Gini impurity can be understood as a criterion to minimize the probability of misclassification. Similar to entropy, Gini is maximized if the classes are perfectly mixed.\n",
    "1. In practice, both Gini and entropy produce similar results.\n",
    "1. Classification error is a useful criterion for pruning but not recommended for learning.\n",
    "\n",
    "*Feature scaling is not necessary for building decision trees.*\n",
    "\n",
    "### Prediction probability\n",
    "\n",
    "Probabilities are calculated from a frequency vector that is created for each node at training time. The vector collects the frequency values of each class label computed from the class label distribution at that node. Then the frequencies are normalized so that they sum up to 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Random forest\n",
    "\n",
    "Random forests are an *ensemble* of decision trees, *weak learners* that are combined together to form a strong learner.\n",
    "\n",
    "### Algorithm:\n",
    "1. Draw a random ***bootstrap*** sample of $n$ examples.\n",
    "1. Grow a decision tree from the bootstrap sample,\n",
    " 1. Randomly select $d$ features without replacement.\n",
    " 1. Split the node using the $d$ feature that provides according to the optimization objective, i.e., maximizing the information gain ratio.\n",
    "1. Repeat steps 1 and 2 $k$ times.\n",
    "1. Aggregrate the predictions be each of the $k$ decision trees by returning a ***majority vote*** (i.e., the class predicted by the most estimators).\n",
    "\n",
    "Typically, the hyperparameter most in need of tuning is the number of trees to use, $k$. Additionally, the parameters $n$ and $d$ can also be tuned."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bagging - building an ensemble from bootstrap samples\n",
    "\n",
    "Rather than using the same training set and taking a majority vote to predict a class, bagging draws bootstrap examples (random samples with replacement) from the training set. One example is random forests (with the exception that random forests also select a random number of features to fit the individual trees)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Boosting of weak learners (Adaboost)\n",
    "\n",
    "Here, the ensemble consists of weak learners that have only a slight performance advantage over random guessing such as a decision tree stump. To improve performance of the ensemble, weak learners are applied to misclassified training examples, boosting the performance for examples that are difficult to classify.\n",
    "\n",
    "### Algorithm summary:\n",
    "1. Draw a random subset of training samples $d_{1}$ without replacement from the training set and train a weak learner $c_{1}$.\n",
    "1. Draw a second random subset without replacement $d_{2}$ and add 50% of the misclassified examples from $d_{1}$ to train a new weak learner $c_{2}$.\n",
    "1. Find the training examples $d_{3}$ on which $c_{1}$ and $c_{2}$ disagree to train a new weak learner $c_{3}$.\n",
    "1. Combine the output of $c_{1}$, $c_{2}$, and $c_{3}$ via majority voting."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gradient boosting\n",
    "\n",
    "Gradient tree boosting is a generalization of boosting to apply an arbitrary differentiable loss function. Like other boosting approaches it combines weak learners to form a strong learner in iterative fashion.\n",
    "\n",
    "Typically, the process begins with a weak model that predicts the mean of $y$. At successive stage of boosting $1 \\le m \\le M$, the model $F_m(x)$ is replaced with a better model $F_{m+1}(x) = F_{m}(x) + h(x)$. The estimator $h(x)$ is calculated from the residual,\n",
    "\n",
    "$$ h(x) = y - F_{m}(x) $$\n",
    "\n",
    "Here the objective function is to minimize $h(x)$, i.e., the new weak learner introduced will fit $h(x)$ to $y - F_{m}(x)$. Instead of calculating the gradient of the loss function $L(y,F_{m}(x)-h(x))$ to find the parameters to minimize $h(x)$, we fit a decision tree. So all the parameters of the decision tree must be computed. Typically one tree at a time is introduced.\n",
    "\n",
    "### Algorithm overview\n",
    "1. Fit an initial ensemble model\n",
    "$$ F(x) = \\sum_{m=1}^{M} \\gamma_{m} h_{m}(x) $$ \n",
    "1. In each stage, introduce a weak learner to compensate the shortcomings of existing weak learners.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"nlp\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Natural Language Processing (NLP)\n",
    "\n",
    "### Bag-of-words\n",
    "\n",
    "This technique represents text as numerical feature vectors.\n",
    "\n",
    "1. Create a ***vocabulary*** of unique ***tokens*** (such as words) from the documents (examples).\n",
    "1. Construct a ***feature vector*** from each document that contains the counts of how often each token (word) appears in each document (example). These feature vectors tend to be sparse.\n",
    "\n",
    "One examples in scikit-learn is the `CountVectorizer`, each index in the feature vector corresponds to an integer count in the dictionary. These values are called ***raw term frequencies***, $tf(t,d)$ - the number of times a term $t$ occurs in document $d$.\n",
    "\n",
    "Another example is the `HashingVectorizer` which uses a hashing function with a specified number of bins that represent tokens. This approach can result in smaller and easier to compute models due to the use of hashing for token lookup and restricting the total number of tokens. However it is not possible to invert to return importance of individual terms and there is no idf.\n",
    "\n",
    "Typically, words are used as tokens however it also possible to generate ***n-grams***, a contiguous sequence of 1 or more words, letters, or symbols.\n",
    "\n",
    "Term frequency of appearance is often not the most useful information. It is often necessary to downweight frequently occurring terms in the feature vectors with a technique called ***term frequency-inverse document frequency***, \n",
    "\n",
    "$$ tf\\mbox{-}idf(t,d) = tf(t,d) \\times idf(t,d) $$\n",
    "\n",
    "The inverse document frequency is,\n",
    "\n",
    "$$ idf(t,d) = \\log{\\frac{n_d}{1+df(t,d)}} $$\n",
    "\n",
    "Where $n_d$ is the number of documents and $df(t,d)$ is the number of documents $d$ that contain term $t$. Using 1 in the denominator assigns a non-zero value to terms that appear in all examples (documents) and the $\\log$ function ensures that low document frequencies are not given too much weight.\n",
    "\n",
    "The implementation of `TfidfTransformer` in scikit-learn uses $1+n_d$ in the numerator of the idf term and the full tf-idf equation is $ tf\\mbox{-}idf(t,d) = tf(t,d) \\times \\big( idf(t,d) + 1 \\big) $. In addition, each feature vector is normalized by its L2-norm to have length 1.\n",
    "\n",
    "It is possible to apply dimensionality reduction of the sparse matrices generated by vectorization using `TruncatedSVD` which is applied to the training data directly rather than the covariance matrix. When used on term-count or tf-idf data, this technique is known as Latent Semantic Analysis (LSA)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Processing documents into tokens\n",
    "\n",
    "One common method to *tokenize* a document is to split it into words based on whitespace characters.\n",
    "\n",
    "***Stemming*** involves breaking down a word into its root form so that similar words can be mapped to the same stem. This is implemented with the Natural Language Toolkit (NLTK) for Python.\n",
    "\n",
    "***Lemmatization*** aims to obtain the canonical (grammatically correct) forms of individual words. However this process is more computationally intense and it has been observed that stemming and lemmatization have little impact on the performance of text classification.\n",
    "\n",
    "***Stop-words*** are very common words that appear frequently in texts but are unlikely to have any useful information, such as *is*, *and*, *has*, etc. These words can be removed with the NLTK and removing them can be useful especially when working with raw or normalized term frequencies rather than tf-idf."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"reg\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"fs\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Feature Selection\n",
    "\n",
    "Additional references:<br>\n",
    "[http://scikit-learn.org/stable/modules/feature_selection.html](http://scikit-learn.org/stable/modules/feature_selection.html)<br>\n",
    "[http://blog.datadive.net/selecting-good-features-part-i-univariate-selection/](http://blog.datadive.net/selecting-good-features-part-i-univariate-selection/)<br>\n",
    "[http://blog.datadive.net/selecting-good-features-part-ii-linear-models-and-regularization/](http://blog.datadive.net/selecting-good-features-part-ii-linear-models-and-regularization/)<br>\n",
    "[http://blog.datadive.net/selecting-good-features-part-iii-random-forests/](http://blog.datadive.net/selecting-good-features-part-iii-random-forests/)<br>\n",
    "[http://blog.datadive.net/selecting-good-features-part-iv-stability-selection-rfe-and-everything-side-by-side/](http://blog.datadive.net/selecting-good-features-part-iv-stability-selection-rfe-and-everything-side-by-side/)\n",
    "\n",
    "**Feature selection** is the process by which features are selected or generated to be input into a predictive model. \n",
    "\n",
    "## Approaches\n",
    "1. **Filter methods** - use statistical tests to determine if the null hypothesis (that the feature is not important) should be rejected. This univariate approach does not take into account interactive models (assumes additive models where features are linearly separable). One example is calculating correlation between feature and output.\n",
    "1. **Wrapper methods** - use a learning algorithm to report optimal subset of features. Examples include feature importance from random forest models or weights/parameters from linear regression, logistic regression, or SVM.\n",
    "1. **Embedded methods** - perform feature selection and model tuning simultaneously. Examples include using LASSO (L1 penalty) and Elastic Net (L1+L2).\n",
    "\n",
    "*Note: when using model-based methods to estimate the importance of features, it is important to remove any collinearity/multicollinearity otherwise the true effect on model performance may be obscured.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Univariate feature selection\n",
    "\n",
    "Apply univariate statistical tests to determine importance of feature.\n",
    "\n",
    "### Correlation\n",
    "\n",
    "The most straightforward method to measure the relationship between an individual feature and output is to calculate Pearson's correlation coefficient. Here values range from [-1,+1] where 0 indicates no correlation and extreme values strong correlation.\n",
    "\n",
    "This can be implemented in Python with:\n",
    "```\n",
    "from scipy.stats import pearsonr\n",
    "```\n",
    "\n",
    "Also, `sklearn` contains `f_regression` which can compute the F-score between output and feature for several features.\n",
    "\n",
    "The main drawback to this method is that it does not work well for data that are not linearly related. For example, the correlation between $x$ and $x_2$ is close to zero even though the values have a very strong relationship.\n",
    "\n",
    "### Mutual information and maximal information coefficient (MIC)\n",
    "\n",
    "Mutual information measures the mutual dependence between variables however it is not a metric and not normalized. Maximal information coefficient can overcome these shortcomings, it searches for optimal value binning and turn mutual information score into a [0,1] metric.\n",
    "\n",
    "MIC is available in Python with [minepy](http://minepy.readthedocs.io/en/latest/):\n",
    "```\n",
    "from minepy import MINE\n",
    "```\n",
    "\n",
    "However there are some concerns about the statistical power of this metric, it may not reject the null hypothesis that there is no relationship, when the null hypothesis is false (i.e., there is a relationship). In other words, it may fail to properly identify a relationship between variables.\n",
    "\n",
    "### Variance threshold\n",
    "\n",
    "If categorical or continuous features have very low variance (or all examples have the same values) then they are unlikely to have much predictive power. If the variance of a feature does not exceed some threshold, then it can be ignored. For example, if a Bernolli (binary) feature contains the same value for more than 80% of the examples ($p=0.8$), the variance can be calculated from $ \\sigma_B^2 = p(1-p) $ and used as a threshold.\n",
    "\n",
    "To implement this in `sklearn`:\n",
    "```\n",
    "from sklearn.feature_selection import VarianceThreshold\n",
    "```\n",
    "\n",
    "Before removing a feature with this method, it should be checked for a strong correlation with the output."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Recursive Feature Elimination (RFE)\n",
    "\n",
    "In **recursive feature elimination**, an external estimator that assigns weights to features (e.g., linear parametric model or ensemble non-parametric model) is used to select features by recursively considering smaller feature sets. First, the estimator is trained on the set of all features and weights are assigned to each. The features with the smallest weights are removed from the model and the estimator is refit to the pruned data. This process is repeated until the desired number of features is reached. \n",
    "\n",
    "This process can be combined with cross-validation, features are eliminated based on estimator weight and cross-validation is used to find the stopping point (i.e., the optimal number of features) by assessing performance of the pruned model.\n",
    "\n",
    "In `sklearn`,\n",
    "```\n",
    "from sklearn.feature_selection import RFE, RFECV\n",
    "```\n",
    "\n",
    "A similar process called **sequential backword selection (SBS)** eliminates features based on their effect on model performance. Features are removed if they do not cause a significant drop in model performance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Assessing feature importance with random forests\n",
    "\n",
    "\n",
    "There are two prominent feature selection methods: **mean decrease impurity** and **mean decrease accuracy**. \n",
    "\n",
    "### Background\n",
    "\n",
    "Random forests consist of a number of decision trees. Every node in the decision tree is a condition on a single feature designed to split the dataset into two so that similar response values end up in the same set/branch. The measure based on which the (locally) optimal condition is chosen is called impurity. For classification, impurity is typically ***Gini impurity*** or ***information gain/entropy*** and for regression trees it is ***variance***. \n",
    "\n",
    "### Mean decrease impurity\n",
    "\n",
    "When training a tree, it can be computed from how much each feature decreases the weighted impurity in the tree. For a forest of trees, the impurity decrease from each feature can be averaged and ranked. This is the **feature importance**.\n",
    "\n",
    "There are a few drawbacks. First, feature selection based on decrease in impurity is biased towards variables with more categories. Second, when there is collinearity, the incorporation of a feature in the tree causes a dramatic reduction in the importance of other correlated features. This is not necessarily problematic when building a prediction since when two or more variables correlated a valid strategy is to simply drop all except one, which is effectively what the random forest model is doing. However this can be an issue when interpreting the data and assessing individual feature importance.\n",
    "\n",
    "### Mean decrease accuracy\n",
    "\n",
    "The impact of each feature on the accuracy of the model is directly measured. First, a random forest model is fit on the data. Second, the values of each feature are iteratively shuffled at random(i.e., the order of rows is rearranged but the order of output values are kept constant). Finally, the training set with the shuffled feature is used to make predictions. If shuffling the values causes a significant drop in accuracy then it is clear that this feature is very important in determining the output.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stability selection\n",
    "\n",
    "A feature selection algorithm is applied to different subsets of data and with different subsets of features. After repeating the process several times, the results are aggregated by comparing how frequently an evaluated feature was marked as important. Strong features should have scores near 100% while irrelevant features will have scores close to zero.\n",
    "\n",
    "In `sklearn` this process is available for linear models with **randomized lasso (regression)** and **randomized logistic regression (classification)**,\n",
    "```\n",
    "from sklearn.linear_model import RandomizedLasso\n",
    "from sklearn.linear_model import RandomizedLogisticRegression\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "____\n",
    "# Regularization\n",
    "\n",
    "References:<br>\n",
    "http://www.analyticsvidhya.com/blog/2016/01/complete-tutorial-ridge-lasso-regression-python/\n",
    "____"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Overview\n",
    "\n",
    "Given a dataset, fit a polynomial function using linear regression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# import libraries\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import random\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "from matplotlib.pylab import rcParams\n",
    "rcParams['figure.figsize'] = 12, 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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mc9uJXemBrqoXZ5gL88FV9aYk12a4HHFrrT0/ydOq6msyTOj+gSRfuhvHBQCA/bZbs3B8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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117be8da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Define input array with angles from 60deg to 300deg converted to radians\n",
    "x = np.array([i*np.pi/180 for i in range(60,300,4)])\n",
    "np.random.seed(10)  #Setting seed for reproducibility\n",
    "y = np.sin(x) + np.random.normal(0,0.15,len(x))\n",
    "data = pd.DataFrame(np.column_stack([x,y]),columns=['x','y'])\n",
    "_ = plt.plot(data['x'],data['y'],'.')\n",
    "_ = plt.title('Data from randomized degree to radian conversion')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(60, 16)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>x_2</th>\n",
       "      <th>x_3</th>\n",
       "      <th>x_4</th>\n",
       "      <th>x_5</th>\n",
       "      <th>x_6</th>\n",
       "      <th>x_7</th>\n",
       "      <th>x_8</th>\n",
       "      <th>x_9</th>\n",
       "      <th>x_10</th>\n",
       "      <th>x_11</th>\n",
       "      <th>x_12</th>\n",
       "      <th>x_13</th>\n",
       "      <th>x_14</th>\n",
       "      <th>x_15</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1.1</td>\n",
       "      <td>1.1</td>\n",
       "      <td>1.1</td>\n",
       "      <td>1.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>1.3</td>\n",
       "      <td>1.4</td>\n",
       "      <td>1.4</td>\n",
       "      <td>1.5</td>\n",
       "      <td>1.6</td>\n",
       "      <td>1.7</td>\n",
       "      <td>1.7</td>\n",
       "      <td>1.8</td>\n",
       "      <td>1.9</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.1</td>\n",
       "      <td>1</td>\n",
       "      <td>1.2</td>\n",
       "      <td>1.4</td>\n",
       "      <td>1.6</td>\n",
       "      <td>1.7</td>\n",
       "      <td>1.9</td>\n",
       "      <td>2.2</td>\n",
       "      <td>2.4</td>\n",
       "      <td>2.7</td>\n",
       "      <td>3</td>\n",
       "      <td>3.4</td>\n",
       "      <td>3.8</td>\n",
       "      <td>4.2</td>\n",
       "      <td>4.7</td>\n",
       "      <td>5.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.2</td>\n",
       "      <td>0.7</td>\n",
       "      <td>1.4</td>\n",
       "      <td>1.7</td>\n",
       "      <td>2</td>\n",
       "      <td>2.4</td>\n",
       "      <td>2.8</td>\n",
       "      <td>3.3</td>\n",
       "      <td>3.9</td>\n",
       "      <td>4.7</td>\n",
       "      <td>5.5</td>\n",
       "      <td>6.6</td>\n",
       "      <td>7.8</td>\n",
       "      <td>9.3</td>\n",
       "      <td>11</td>\n",
       "      <td>13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.3</td>\n",
       "      <td>0.95</td>\n",
       "      <td>1.6</td>\n",
       "      <td>2</td>\n",
       "      <td>2.5</td>\n",
       "      <td>3.1</td>\n",
       "      <td>3.9</td>\n",
       "      <td>4.9</td>\n",
       "      <td>6.2</td>\n",
       "      <td>7.8</td>\n",
       "      <td>9.8</td>\n",
       "      <td>12</td>\n",
       "      <td>16</td>\n",
       "      <td>19</td>\n",
       "      <td>24</td>\n",
       "      <td>31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.3</td>\n",
       "      <td>1.1</td>\n",
       "      <td>1.8</td>\n",
       "      <td>2.3</td>\n",
       "      <td>3.1</td>\n",
       "      <td>4.1</td>\n",
       "      <td>5.4</td>\n",
       "      <td>7.2</td>\n",
       "      <td>9.6</td>\n",
       "      <td>13</td>\n",
       "      <td>17</td>\n",
       "      <td>22</td>\n",
       "      <td>30</td>\n",
       "      <td>39</td>\n",
       "      <td>52</td>\n",
       "      <td>69</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    x    y  x_2  x_3  x_4  x_5  x_6  x_7  x_8  x_9  x_10  x_11  x_12  x_13  \\\n",
       "0   1  1.1  1.1  1.1  1.2  1.3  1.3  1.4  1.4  1.5   1.6   1.7   1.7   1.8   \n",
       "1 1.1    1  1.2  1.4  1.6  1.7  1.9  2.2  2.4  2.7     3   3.4   3.8   4.2   \n",
       "2 1.2  0.7  1.4  1.7    2  2.4  2.8  3.3  3.9  4.7   5.5   6.6   7.8   9.3   \n",
       "3 1.3 0.95  1.6    2  2.5  3.1  3.9  4.9  6.2  7.8   9.8    12    16    19   \n",
       "4 1.3  1.1  1.8  2.3  3.1  4.1  5.4  7.2  9.6   13    17    22    30    39   \n",
       "\n",
       "   x_14  x_15  \n",
       "0   1.9     2  \n",
       "1   4.7   5.3  \n",
       "2    11    13  \n",
       "3    24    31  \n",
       "4    52    69  "
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# estimate data using polynomial regression\n",
    "\n",
    "for i in range(2,16):  #power of 1 is already there\n",
    "    colname = 'x_%d'%i      #new var will be x_power\n",
    "    data[colname] = data['x']**i\n",
    "print(data.shape)\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "def linear_regression(data, power, models_to_plot):\n",
    "    #initialize predictors:\n",
    "    predictors=['x']\n",
    "    if power>=2:\n",
    "        predictors.extend(['x_%d'%i for i in range(2,power+1)])\n",
    "    \n",
    "    #Fit the model\n",
    "    linreg = LinearRegression(normalize=True)\n",
    "    linreg.fit(data[predictors],data['y'])\n",
    "    y_pred = linreg.predict(data[predictors])\n",
    "    \n",
    "    #Check if a plot is to be made for the entered power\n",
    "    if power in models_to_plot:\n",
    "        plt.subplot(models_to_plot[power])\n",
    "        plt.tight_layout()\n",
    "        plt.plot(data['x'],y_pred)\n",
    "        plt.plot(data['x'],data['y'],'.')\n",
    "        plt.title('Plot for power: %d'%power)\n",
    "    \n",
    "    #Return the result in pre-defined format\n",
    "    rss = sum((y_pred-data['y'])**2)\n",
    "    ret = [rss]\n",
    "    ret.extend([linreg.intercept_])\n",
    "    ret.extend(linreg.coef_)\n",
    "    return ret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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JtvJGxENpmzf1RVufFcoNNWtES20cEfe5ssmF4zhvAb/EeEs/asPJcZx5wGbGmK2ae303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gS23hpmzYLNN/e7GkmXLnikEPz6K3TtCv/6F+ywg9/VSLqUN5LPRo1yHawXX/S7EvGCFrmQgrTe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\nRBpWVQVde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/KAL4GeQD4wB+jbyDmtSDqo/KXSli0ts5W/VCb83urV1l59tbUdOlh7yCHW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\nPPL/SEG0PQGfL0EAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11786e710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Initialize a dataframe to store the results\n",
    "\n",
    "col = ['rss','intercept'] + ['coef_x_%d'%i for i in range(1,16)]\n",
    "ind = ['model_power_%d'%i for i in range(1,16)]\n",
    "coef_matrix_simple = pd.DataFrame(index=ind, columns=col)\n",
    "\n",
    "#Define the powers for which a plot is required:\n",
    "models_to_plot = {1:231,3:232,6:233,9:234,12:235,15:236}\n",
    "\n",
    "#Iterate through all powers and assimilate results\n",
    "for i in range(1,16):\n",
    "    coef_matrix_simple.iloc[i-1,0:i+2] = linear_regression(data, power=i, models_to_plot=models_to_plot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>rss</th>\n",
       "      <th>intercept</th>\n",
       "      <th>coef_x_1</th>\n",
       "      <th>coef_x_2</th>\n",
       "      <th>coef_x_3</th>\n",
       "      <th>coef_x_4</th>\n",
       "      <th>coef_x_5</th>\n",
       "      <th>coef_x_6</th>\n",
       "      <th>coef_x_7</th>\n",
       "      <th>coef_x_8</th>\n",
       "      <th>coef_x_9</th>\n",
       "      <th>coef_x_10</th>\n",
       "      <th>coef_x_11</th>\n",
       "      <th>coef_x_12</th>\n",
       "      <th>coef_x_13</th>\n",
       "      <th>coef_x_14</th>\n",
       "      <th>coef_x_15</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>model_power_1</th>\n",
       "      <td>3.3</td>\n",
       "      <td>2</td>\n",
       "      <td>-0.62</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_power_2</th>\n",
       "      <td>3.3</td>\n",
       "      <td>1.9</td>\n",
       "      <td>-0.58</td>\n",
       "      <td>-0.006</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_power_3</th>\n",
       "      <td>1.1</td>\n",
       "      <td>-1.1</td>\n",
       "      <td>3</td>\n",
       "      <td>-1.3</td>\n",
       "      <td>0.14</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_power_4</th>\n",
       "      <td>1.1</td>\n",
       "      <td>-0.27</td>\n",
       "      <td>1.7</td>\n",
       "      <td>-0.53</td>\n",
       "      <td>-0.036</td>\n",
       "      <td>0.014</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_power_5</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>-5.1</td>\n",
       "      <td>4.7</td>\n",
       "      <td>-1.9</td>\n",
       "      <td>0.33</td>\n",
       "      <td>-0.021</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_power_6</th>\n",
       "      <td>0.99</td>\n",
       "      <td>-2.8</td>\n",
       "      <td>9.5</td>\n",
       "      <td>-9.7</td>\n",
       "      <td>5.2</td>\n",
       "      <td>-1.6</td>\n",
       "      <td>0.23</td>\n",
       "      <td>-0.014</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_power_7</th>\n",
       "      <td>0.93</td>\n",
       "      <td>19</td>\n",
       "      <td>-56</td>\n",
       "      <td>69</td>\n",
       "      <td>-45</td>\n",
       "      <td>17</td>\n",
       "      <td>-3.5</td>\n",
       "      <td>0.4</td>\n",
       "      <td>-0.019</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_power_8</th>\n",
       "      <td>0.92</td>\n",
       "      <td>43</td>\n",
       "      <td>-1.4e+02</td>\n",
       "      <td>1.8e+02</td>\n",
       "      <td>-1.3e+02</td>\n",
       "      <td>58</td>\n",
       "      <td>-15</td>\n",
       "      <td>2.4</td>\n",
       "      <td>-0.21</td>\n",
       "      <td>0.0077</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_power_9</th>\n",
       "      <td>0.87</td>\n",
       "      <td>1.7e+02</td>\n",
       "      <td>-6.1e+02</td>\n",
       "      <td>9.6e+02</td>\n",
       "      <td>-8.5e+02</td>\n",
       "      <td>4.6e+02</td>\n",
       "      <td>-1.6e+02</td>\n",
       "      <td>37</td>\n",
       "      <td>-5.2</td>\n",
       "      <td>0.42</td>\n",
       "      <td>-0.015</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_power_10</th>\n",
       "      <td>0.87</td>\n",
       "      <td>1.4e+02</td>\n",
       "      <td>-4.9e+02</td>\n",
       "      <td>7.3e+02</td>\n",
       "      <td>-6e+02</td>\n",
       "      <td>2.9e+02</td>\n",
       "      <td>-87</td>\n",
       "      <td>15</td>\n",
       "      <td>-0.81</td>\n",
       "      <td>-0.14</td>\n",
       "      <td>0.026</td>\n",
       "      <td>-0.0013</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_power_11</th>\n",
       "      <td>0.87</td>\n",
       "      <td>-75</td>\n",
       "      <td>5.1e+02</td>\n",
       "      <td>-1.3e+03</td>\n",
       "      <td>1.9e+03</td>\n",
       "      <td>-1.6e+03</td>\n",
       "      <td>9.1e+02</td>\n",
       "      <td>-3.5e+02</td>\n",
       "      <td>91</td>\n",
       "      <td>-16</td>\n",
       "      <td>1.8</td>\n",
       "      <td>-0.12</td>\n",
       "      <td>0.0034</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_power_12</th>\n",
       "      <td>0.87</td>\n",
       "      <td>-3.4e+02</td>\n",
       "      <td>1.9e+03</td>\n",
       "      <td>-4.4e+03</td>\n",
       "      <td>6e+03</td>\n",
       "      <td>-5.2e+03</td>\n",
       "      <td>3.1e+03</td>\n",
       "      <td>-1.3e+03</td>\n",
       "      <td>3.8e+02</td>\n",
       "      <td>-80</td>\n",
       "      <td>12</td>\n",
       "      <td>-1.1</td>\n",
       "      <td>0.062</td>\n",
       "      <td>-0.0016</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_power_13</th>\n",
       "      <td>0.86</td>\n",
       "      <td>3.2e+03</td>\n",
       "      <td>-1.8e+04</td>\n",
       "      <td>4.5e+04</td>\n",
       "      <td>-6.7e+04</td>\n",
       "      <td>6.6e+04</td>\n",
       "      <td>-4.6e+04</td>\n",
       "      <td>2.3e+04</td>\n",
       "      <td>-8.5e+03</td>\n",
       "      <td>2.3e+03</td>\n",
       "      <td>-4.5e+02</td>\n",
       "      <td>62</td>\n",
       "      <td>-5.7</td>\n",
       "      <td>0.31</td>\n",
       "      <td>-0.0078</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_power_14</th>\n",
       "      <td>0.79</td>\n",
       "      <td>2.4e+04</td>\n",
       "      <td>-1.4e+05</td>\n",
       "      <td>3.8e+05</td>\n",
       "      <td>-6.1e+05</td>\n",
       "      <td>6.6e+05</td>\n",
       "      <td>-5e+05</td>\n",
       "      <td>2.8e+05</td>\n",
       "      <td>-1.2e+05</td>\n",
       "      <td>3.7e+04</td>\n",
       "      <td>-8.5e+03</td>\n",
       "      <td>1.5e+03</td>\n",
       "      <td>-1.8e+02</td>\n",
       "      <td>15</td>\n",
       "      <td>-0.73</td>\n",
       "      <td>0.017</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_power_15</th>\n",
       "      <td>0.7</td>\n",
       "      <td>-3.6e+04</td>\n",
       "      <td>2.4e+05</td>\n",
       "      <td>-7.5e+05</td>\n",
       "      <td>1.4e+06</td>\n",
       "      <td>-1.7e+06</td>\n",
       "      <td>1.5e+06</td>\n",
       "      <td>-1e+06</td>\n",
       "      <td>5e+05</td>\n",
       "      <td>-1.9e+05</td>\n",
       "      <td>5.4e+04</td>\n",
       "      <td>-1.2e+04</td>\n",
       "      <td>1.9e+03</td>\n",
       "      <td>-2.2e+02</td>\n",
       "      <td>17</td>\n",
       "      <td>-0.81</td>\n",
       "      <td>0.018</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                rss intercept coef_x_1 coef_x_2 coef_x_3 coef_x_4 coef_x_5  \\\n",
       "model_power_1   3.3         2    -0.62      NaN      NaN      NaN      NaN   \n",
       "model_power_2   3.3       1.9    -0.58   -0.006      NaN      NaN      NaN   \n",
       "model_power_3   1.1      -1.1        3     -1.3     0.14      NaN      NaN   \n",
       "model_power_4   1.1     -0.27      1.7    -0.53   -0.036    0.014      NaN   \n",
       "model_power_5     1         3     -5.1      4.7     -1.9     0.33   -0.021   \n",
       "model_power_6  0.99      -2.8      9.5     -9.7      5.2     -1.6     0.23   \n",
       "model_power_7  0.93        19      -56       69      -45       17     -3.5   \n",
       "model_power_8  0.92        43 -1.4e+02  1.8e+02 -1.3e+02       58      -15   \n",
       "model_power_9  0.87   1.7e+02 -6.1e+02  9.6e+02 -8.5e+02  4.6e+02 -1.6e+02   \n",
       "model_power_10 0.87   1.4e+02 -4.9e+02  7.3e+02   -6e+02  2.9e+02      -87   \n",
       "model_power_11 0.87       -75  5.1e+02 -1.3e+03  1.9e+03 -1.6e+03  9.1e+02   \n",
       "model_power_12 0.87  -3.4e+02  1.9e+03 -4.4e+03    6e+03 -5.2e+03  3.1e+03   \n",
       "model_power_13 0.86   3.2e+03 -1.8e+04  4.5e+04 -6.7e+04  6.6e+04 -4.6e+04   \n",
       "model_power_14 0.79   2.4e+04 -1.4e+05  3.8e+05 -6.1e+05  6.6e+05   -5e+05   \n",
       "model_power_15  0.7  -3.6e+04  2.4e+05 -7.5e+05  1.4e+06 -1.7e+06  1.5e+06   \n",
       "\n",
       "               coef_x_6 coef_x_7 coef_x_8 coef_x_9 coef_x_10 coef_x_11  \\\n",
       "model_power_1       NaN      NaN      NaN      NaN       NaN       NaN   \n",
       "model_power_2       NaN      NaN      NaN      NaN       NaN       NaN   \n",
       "model_power_3       NaN      NaN      NaN      NaN       NaN       NaN   \n",
       "model_power_4       NaN      NaN      NaN      NaN       NaN       NaN   \n",
       "model_power_5       NaN      NaN      NaN      NaN       NaN       NaN   \n",
       "model_power_6    -0.014      NaN      NaN      NaN       NaN       NaN   \n",
       "model_power_7       0.4   -0.019      NaN      NaN       NaN       NaN   \n",
       "model_power_8       2.4    -0.21   0.0077      NaN       NaN       NaN   \n",
       "model_power_9        37     -5.2     0.42   -0.015       NaN       NaN   \n",
       "model_power_10       15    -0.81    -0.14    0.026   -0.0013       NaN   \n",
       "model_power_11 -3.5e+02       91      -16      1.8     -0.12    0.0034   \n",
       "model_power_12 -1.3e+03  3.8e+02      -80       12      -1.1     0.062   \n",
       "model_power_13  2.3e+04 -8.5e+03  2.3e+03 -4.5e+02        62      -5.7   \n",
       "model_power_14  2.8e+05 -1.2e+05  3.7e+04 -8.5e+03   1.5e+03  -1.8e+02   \n",
       "model_power_15   -1e+06    5e+05 -1.9e+05  5.4e+04  -1.2e+04   1.9e+03   \n",
       "\n",
       "               coef_x_12 coef_x_13 coef_x_14 coef_x_15  \n",
       "model_power_1        NaN       NaN       NaN       NaN  \n",
       "model_power_2        NaN       NaN       NaN       NaN  \n",
       "model_power_3        NaN       NaN       NaN       NaN  \n",
       "model_power_4        NaN       NaN       NaN       NaN  \n",
       "model_power_5        NaN       NaN       NaN       NaN  \n",
       "model_power_6        NaN       NaN       NaN       NaN  \n",
       "model_power_7        NaN       NaN       NaN       NaN  \n",
       "model_power_8        NaN       NaN       NaN       NaN  \n",
       "model_power_9        NaN       NaN       NaN       NaN  \n",
       "model_power_10       NaN       NaN       NaN       NaN  \n",
       "model_power_11       NaN       NaN       NaN       NaN  \n",
       "model_power_12   -0.0016       NaN       NaN       NaN  \n",
       "model_power_13      0.31   -0.0078       NaN       NaN  \n",
       "model_power_14        15     -0.73     0.017       NaN  \n",
       "model_power_15  -2.2e+02        17     -0.81     0.018  "
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Set the display format to be scientific for ease of analysis\n",
    "\n",
    "pd.options.display.float_format = '{:,.2g}'.format\n",
    "coef_matrix_simple"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Clearly the **size of the parameters increases dramatically with model complexity**. Larger parameters put more emphasis on those features, i.e., that particular features becomes a good predictor for the outcome. The large parameters on the higher order features force the estimator to closely match small deviations from the general trend which increases model complexity but decreases generalizability."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ridge regression\n",
    "\n",
    "The objective function (to be minimized) is modified to prevent the higher order features from acquiring inappropriately large parameters (during minimization) that can lead to overfitting and overly-complex estimators.\n",
    "\n",
    "*Min Objective = Residual sum of squares + $\\alpha$ $\\cdot$ Sum of square of parameters*\n",
    "\n",
    "Note: residual sum of squares is the same as the sum of squared residuals.\n",
    "\n",
    "This method forces model coefficients/parameters to adopt values that are not too extreme. For example, consider a model $y = \\beta_1 x_1 + \\beta_2 x_2$ and assume that the independent variables are highly correlated so $x_1 \\approx x_2$.\n",
    "\n",
    "Now consider two possible outcomes for the learned model,\n",
    "$$ y = 1 * x_1 + 1 * x_2 \\quad OR \\quad y = 2 * x_1 + 0 * x_2 $$\n",
    "\n",
    "The resulting penalties ($\\alpha \\sum_{i=1}^{n} \\beta_i^2$) are,\n",
    "$$ 1^2+1^2 = 2\\alpha \\quad OR \\quad 2^2 + 0^2 = 4\\alpha $$\n",
    "\n",
    "Thus the first outcome is prefered by the algorithm. So even if collinearity/multicollinearity is present, it is possible to use the value of the coefficients to more accurately interpret feature importance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "\n",
    "def ridge_regression(data, predictors, alpha, models_to_plot={}):\n",
    "    #Fit the model\n",
    "    ridgereg = Ridge(alpha=alpha,normalize=True)\n",
    "    ridgereg.fit(data[predictors],data['y'])\n",
    "    y_pred = ridgereg.predict(data[predictors])\n",
    "    \n",
    "    #Check if a plot is to be made for the entered alpha\n",
    "    if alpha in models_to_plot:\n",
    "        plt.subplot(models_to_plot[alpha])\n",
    "        plt.tight_layout()\n",
    "        plt.plot(data['x'],y_pred)\n",
    "        plt.plot(data['x'],data['y'],'.')\n",
    "        plt.title('Plot for alpha: %.3g'%alpha)\n",
    "    \n",
    "    #Return the result in pre-defined format\n",
    "    rss = sum((y_pred-data['y'])**2)\n",
    "    ret = [rss]\n",
    "    ret.extend([ridgereg.intercept_])\n",
    "    ret.extend(ridgereg.coef_)\n",
    "    return ret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PPOHOipgxw+9qRHJLLmZOXJcu8PDDcOqpbuqOiKRWLucNQPfuMHkynHUWfP65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5ILWsqbXDF/PpSVwb/+BfvsE3Rt/KcnWJJTYjUxykeVM3D0QMpHlROria15rU8f90esVb1ExCuJ\nMqdehw5w1VVw6aUBVFBEQiOZvMkVPXvCP//phgt++WXQtcktamCJ7yoXVRKtjlJbV0tVdRXR6ug6\nr19+Ofz971BTE1AFRSRUWsqcesOHw+efw+uv+1xBEQmNZPMmV+y3H1x4IQwdCqtWBV2b3KEGlviu\ntGspkeIIhQWFlBSXECmOrPP6TjtBSb8Y1zw0Jad7fkQkO7SUObGaGFMWTOGXuhg33giXXAJ1dQFV\nVkRyWkt5A2szJ1fucS6+GDp2hCuvDLomuUNzsCQQsZoY0eookeLIr8Ynx2pi7HR3OZ8ti7LD5hHe\nOa0ip8cwh53mREguaC5z6ofz1L82+dQKDt63iDPOgFNOCbDC0iTljeSClu5xGmZOxbDcuMf5/nvX\nAX7//TBkSNC18YfmYEnOKWpXRFn3siZDpXJRJV/8HIU2tUQX5f7jdREJXnOZ03g4T9X3UW65xc3H\n+vnngCorIjmtpXucXBxC2KWLW+zi97932+pIYmpgSdapf7zelkLaLilhu86/frzeUK49av//9u48\nTIrqUP/494wsER0NYVMR0fgTdWbcCLKIg0OMuYpXYxSD+otRVCLRoDciohKVaxSNC141JlETQUG9\nxF2EmwgiOioBvWBwmkUjAUEERmVpFUaWc/+oGadpeqnprq7qqn4/z8PjzHR1nVN29/uc03UWESke\nqYbz9O8PvXqlXp5YeSMi+XAzhDBRMWXO8cfDlVc6i15s3x50bYqbhghKUXKWOI0x/KxKrrsOuvdK\nvdxpWG+1R4mG7EjYJQ/niTfEmfZOHZefXcX775XToUPzccqbYClvJAoSMwdIu6R7MWbOjh1w0knw\ngx84i5JFmYYISuSUty2nX7e+XD0SLqpNv9xpWG+1i0jxSBzO09SgOX/WAMxF1dx4S3PmKG9ExAtN\nmQNkXNK9GDOnrAwmTIDx42HBgqBrU7zUwZKidlDfOjbvmT5cWnqrXUQkk8QGzaa2i5j8coxly5zH\nlDci4qVsHahizZwDDoB77oGf/hS2bAm6NsVJQwSlqMUb4lTeXc2qLYs4cr+KlLfHM63WI4WnITsS\nJU13sBbVL6KiUwX/vq6WDxeX8+STzY8rb4KjvJEoSc6bMLVxrIUhQ2D//Z27WVGUT96ogyVF7/Mv\n4lQOjDFpfCU/qC6ecBGHGjwSNYkNmrJt5fToAc89B717B10zUd5I1BRrB8qNzz6DI4+EyZNh4MCg\na+M9dbAk8v7wB5g2DV56KeiaSDI1eCTqHn4YHn8cXn0VTCjf6dGhvBEpLtOnw4gRsHAh7LFH0LXx\nlha5kMgbOhTmz9eEShHx39ChUF/vfMkjIiLNBg2Cfv3gxhuDrklx0R0sCY3x42HOHHjqqaBrIon0\njbKUgpdegtGj4R//gFatgq5N6VLeiBSf+no44giYOhWOPTbo2nhHd7CkJFx6Kbz+OixaFHRNRKTU\nnHoqdO7sLE8sIiLNOnWCu++Giy+GrVuDrk1x0B0sCZVx42DxYpg0KeiaSBN9oyyl4u234Ywz4P33\nozfXICyUNyLFyVrni6j+/WHMmKBr4w0tciElY+NGOPhgmDvX+a8ETw0eKSXnnguHH675BkFR3ogU\nrxUr4HvfgzffhEMPDbo2+VMHS0rKDTfAmjXOyl4SPDV4pJT861/QqxfEYrDPPkHXpvQob0SK2/jx\n8Le/wV//Gv5VV9XBkpLy2WfQo4ezqmD37kHXRtTgkVIzciR8+SX88Y9B16T0KG9EitvWrXDUUXDr\nrfDjHwddm/yogyUl57rrYP16NXCKgRo8Umo+/xwOOwxmz4aKiqBrU1qUNyLFb9YsuOgiZ1Gydu2C\nrk3uAutgGWPaA1OA7sBy4CfW2o0pjlsObAR2AFuttb0znFMBJFl9+qlzF+sf/4Bu3YKuTWnzs8Hj\ndeYobyRX48c7Gw9PnRp0TUqL8kYkHIYMceZh3Xxz0DXJXZAdrN8Cn1lr7zDGjAbaW2uvTXHcMuB7\n1tr1Ls6pABJXrrkGvvoKfve7oGtS2nxu8HiaOcobyVVDg7PYxZ//DAMHBl2b0qG8EQmHlSvh6KNh\n3rzwLkoWZAdrCXCCtXatMWYfYLa19rAUx/0L6GWt/czFORVA4sq6dc4wnffeg65dg65N6fK5weNp\n5ihvJB9TpsAddzjLt5dpV0lfKG9EwuO22+Ctt8J7pz/IjYY7W2vXAlhr1wCd0xxngRnGmLeNMcPy\nLFMEcDb9HDrUaeBIyVDmSNH4yU+gdWt44omgayIForwRycNVVznzsF55Jeia+K9VtgOMMTOALol/\nwgmTX6c4PN1XM/2ttZ8YYzrhhNBia+0b6cocO3bsNz/X1NRQU1OTrZpSQuINcerW1VHVuYpRo8qp\nqIBrr4V99w26ZqVh9uzZzJ49u2Dn9ztzlDeSTWLmlLct/+bvxsDddzt7Y511Fuy+e4CVjCjljZSa\ndHkTRm3bwrhxMGoUvPNO8d/p9zJv8h0iuBioSbh9/qq19vAsz7kJiFtrx6d5XLfQJa14Q5zqCdXE\n6mNUdqqkdmgtN15bzo4dcO+9QdeuNPk8ZMfTzFHeSDapMie50TN4MPTsCddfH1AlS4jyRqLMTd6E\njbXQty+MGAE//WnQtWmZIIcIvghc2PjzBcALyQcYY9oZY/Zs/HkP4IdAXZ7lSomqW1dHrD7Gth3b\nWFS/iFh9jNGjYdIkWLUq6NqJD5Q54qtUmZPst791VhVcsyaACkohKW/EV27yJmyMgbvugjFjYMuW\noGvjn3w7WL8FTjLGLAVOBG4HMMbsa4x5qfGYLsAbxpgFwN+Bqdbal/MsV0pUVecqKjtV0rqsNRWd\nKqjsVMk++8Allzi3oZPFG+LMWTmHeEPc/8pKIShzxFepMifZwQfDBRfATTcpcyJGeSO+cpM3icKS\nN9XVcMwxcP/9QdfEP9poWEIn3hD/5vZ5063z+npnRcH586F79+bjonarvRhp40+JulSZk2z9ejik\nKk6HUdUsiytzCkV5I1HnJm+ajgtTG2fpUjj+eFiyBDp0CLo27gQ5RFDEd+Vty+m7f9+dgqRTJxg+\nHG69tfm4KN5qFxH/pcqcZO3bw/kj6/hgvTJHRHLnJm8gfG2cQw+Fs89OPdooitTBksgYORKefRaW\nLXN+b+mtdhGRfNzw8yrabKykFcocESmsMLZxbrgBJkyATz4JuiaFpyGCEiljx8KKFc4HGNzfapfc\naciOSLO/vBDnmjtjzP9rJd/ZU5njNeWNSLMwtnGuugq2bw/Hys/55I06WBIpGzbAIYfA66/D4RkX\n0xWvqMEj0sxaOPlkGDQIrrwy6NpEj/JGJNzWroWKCli4ELp2Dbo2mamDJZLgjjtg7lx45pmga1Ia\n1OAR2VksBjU14ZrMHRbKG5Hwu+Ya+Oor+N3vgq5JZupgiSTYvNm5i/Xss9C7d9C18U9Qu7+rwSOy\nq1/+0vlvsTcgcqW8aTnljYijaeXnBQvggAPcPSeIzFEHSyTJww/Dk0/CK684m9xFXZDLtarBI7Kr\nTz91hinPng2VxT/3vEWUN7lR3og0u+46Z3uLP/4x+7FBZY6WaRdJMnQofPwxzJgRdE38EbblWkWi\nrmNHGDMGfvUrZ15WlChvRCRfV18NTz0Fy5dnPzaMmaMOlkRSq1bOnljXXQc7dgRdm8IL43KtIlF3\n+eWwahW88ELQNfGW8kZE8tWhA/z853D33dmPDWPmaIigRJa1cOyxMGoUDBkSdG0KL6jlWjVkRyS9\nmTNh2DBYtAh23z3o2nhHedNyyhuRna1Z46wouHQpdOqU+dggMkdzsETSeOUV5xuSRYugbdugaxNN\navCIZHbWWXDUUXDjjUHXJPyUNyLRMnw4dO4MN98cdE12pQ6WSAanneYsmTxyZNA1iSY1eEQyW7EC\nevaE+fOhe/egaxNuyhuRaPnnP6FfP/jXv2DPPYOuzc7UwRLJYMkSqK6GxYudiefiLTV4RLK7+WZn\nY82nnw66JuGmvBGJniFDoG9fZ1GgYqIOlkgWI0Y4c7KiuidNkNTgEclu82ZnufaHHoIf/CDo2oSX\n8kYkeubPhx/9CD78ENq0Cbo2zbRMu0ijeEOcOSvnEG+I7/T3sWNhyhTnLpaIiFfSZU6y3XeH//ov\nZ2XBhgafKicikeI2b8KmZ09n38Anngi6Jt5RB0sio2kjugETB1A9oXqnAOrQwVmyfdSoACsoIpGS\nKXNSOf10OOwwuPNOnyooIpHR0rwJm2uvhTvuiM7WOupgSWRk24ju8sud+VgvvxxQBUUkUnLZ/PK+\n+5w7WcuW+VBBEYmMMG622xIDBzrDA2fODLom3lAHSyIj20Z0bds6DZtf/lJDdEQkf7lsftm9u3Mn\n/fLLnXmhIiJuhHGz3ZYwBq64wvkSKgq0yIVEipuN6M44w9mAeMwYnysXUZp0LqUsl80vt26FY45x\n5oYOHlzY+kWN8kZKWVAbfPtl82bnS6g334RDDgm6NlpFUMS1eEOcGQvrGHZ6Fe+8Vc5BBwVdo/BT\ng0cktXhDnLp1dVR1rtqlMVRbC+edB7EY7LVXQBX0ibXO8vRnnQVleY6bUd6IpJcpc8Li+uvhq6+c\nEUdBUwdLxIWmCaKx+hgdd1RyzIJapj8fzgAqJmrwiOwqMW8qO1VSO7R2lwbPJZc4Q5cfeCCgSvrk\nr391JrAvWOAMA8qH8kYkNTeZEwYrV8LRR8Py5VAecPW1TLuIC4kTRD8rcyaIvvhi0LUSkShyMyH9\nrrvg+eedu1lRds89zgai+XauRCS9qCyC0a0bnHgiPPpo0DXJjzpYUjKSJ4j+7sZKrrgCvvgi6JqJ\nSNS4mZD+7W87m59fcgls2RJAJX0Qi8HChXDOOUHXRCTaorQIxogRcP/94V6yXUMEpaQkTxC94AJn\n/sP99wdds/DSkB2R1NxOSD/7bGdC97hxPlbOJ8OGOd9I33ijN+dT3oikF5VFMKx1Nh++/Xb4t38L\nrh6agyWSo/Xr4YgjYPJkqKkJujbhpAaPSH7WrIEjj4S//c1ZXTAq6uuhRw9YuhQ6d/bmnMobkdLw\nyCPw3HMwdWpwddAcLJEctW8PDz4IF1+soYIiEox99oE77oChQ+Hrr4OujXcefBDOPNO7zpWIlI4h\nQ5zl2letCromuVEHS0reqafC8cc7q1xFSbwhzpyVc4g3xIOuiohkccEFcMABzt5YYZScNw0N8Pvf\nw3/8R8AVE5FQ2mMPp5M1ceKuj4WhfaMhgiJEb6ign8u1asiOiDfWrnWWJ37mGTjuuKBr416qvHlu\nSjmTJsGMGd6WpbwRKR3z5zv75334YfMeemFp3+gOlgjOUMGHHnK+Rf7ss6Brk7+oLNcqUkq6dIE/\n/AF+9rNwDVlOzpv31sa46y5naXYRkVz17Anf+Q7MnNn8t7C0b9TBEmk0aBAMHux0ssK8NChEa7lW\nkVJyxhkwYABcdVXQNXEvOW8Wv15Ju3ZwyilB10xEwu6SS+Dhh5t/D0v7RkMERRJs3eo0bs48E0aN\nCro2+fFruVYN2RHx1qZNcNRRcN99cNppQdfGnaa86fHtSnofXc5DD8H3v+99OcobkdKycSMceODO\nq5GGoX2jDpZIo3hDnLp1dez9dRXf71/OM89A//5B1yo3H38Ms2ZB167Qq5ez11ehqMEjkpumzKnq\nXLVLI+Gtt+DHP4Z586B794AqmIMHH4Snn/Z+7lUT5Y1IbjLlTbEbOhQqK+Hqq/0tV3OwRPLUNGly\nwMQBnDejmvsfinPuuc4+LrmerxAr3GQ67wcfOJt59uzpLNjx/PPO7/vt5wTTyJHOHToRCV5i5lRP\nqN7lM33ccc5d9CFDsi/dHkTepLJ5M/zmN3DrrZ5WQ0TylC1vWnouv/Nm2DD405+cDYjDQh0sEXad\nNNmtZ4zzz3e+Qd68OfvzE4PByyBLLiPVeeNxGD0a+vVz6nrvvbBunbMS2RtvOCskTp7s3F4/5xx1\nskSKgZuJ2iNHOkNiRo/e+e9B5k0mDzwAvXs7/0SkeOS7MERT5qzetDqQvOnXD/QbKY4AABMISURB\nVHbbzWnThIU6WFLSmkKj+97dd5k0+ZvfQLducP75mRe9SA6GuR/PLcgKN8kBWbcuxuOPw+GHw5o1\nUFcHd94J1dXQqlXz81q3hmOOcTpcW7e6+0ZcRLyX2DFyM1HbGHj0Uedu9HPPNZ8jiLzJdt6NG53N\nkm+5xZPiRSRPLc2bTOdpypwTJp4QSN4YAxdeCI895klxvlAHS0pWYmgMemIQ08+bzutDX/9mT4Wy\nMmeDu08/db5JTnf7OjkYDMazFW7SBWSP9hXcckUld94Jf/mL0wjbZ5/M52rbFp56CrZtUydLxG/J\nHSOA2qG1O2VO8vFzVs6hVbs4U6bApZc6d6GDyBs3573lFmcl1oqKnIsXEY/kmjep7kglZs7yDcs5\n8NsHeraCX6YvuZOde67zRfGWLXkV6RstciEla87KOQyYOIBtO7bRuqw1rw99nb77993luPXroV9N\nnPjgatax68Z2TUG2qH4RFZ0qqB1aC5D3CjepNtMDmDg9xm1XVfLTs8u55RZo06Zl5/36a2c5+j59\nYMyYnKq2E006F8nObd5A6s/+XyaXc/vtMOP1OGe84F/euDnv2287qx0uXNi8ylehKG9Esss3bxI/\n78ltnOnnTeejTR/lvYJfcrluznviiXDZZc7mw37IJ29aZT9EJJqavqFtCo1038S0bw+3/bmOM1+M\nwW7Nt6+bwqq8bTm1Q2t3aYikCzO3kr+pfnd1jJf+2JfJk/vy6EQ46aTcztumjbPK1/bteVVPRFrA\nbd5A6uEyF1/cl6VL4YJzypk5tZZ/bips3jRlXLbzNjQ4K3yNH1/4zpWIuJNv3iR+7lO1cfbba7+8\n65hc7kebPsqaN+efD5Mm+dfByofuYElJc7uXQrwhTu8Hq1ny6SK6lFXw/rW17PWtwi5zmvit0cF7\nVfCtJ2rZv3M5jzwCnToVtOgW0TfKIu60JG+S74qXty1nxw6nYbH33jBhgjMvwcu6pSozm5tuggUL\n4IUXvK1POsobEXfyzRs/6tfScjdtcubGL1sGHToUvIraB0vED/GGOLVLY1x7cSUD+pRz331QVuBZ\njJu2xLljYow/3FzJzWPKuewyfxoxLaEGj4j30jWOvvyyeTN0L4b4uikznYULnSE7777r7LnnB+WN\niPf82rjXi3LPOQdOOAF+8YsCVw51sER8tXEjnH46dOzo7MvQvn1hylm9GkaMgPffhyefhKqq3M9V\nyA0G1eAR8dfq1c5qoVdcAVdeGUwdtm51lk7+xS/g4ot3fbxQmaO8ESlt06bBuHHw5pvNfyvGvNEq\ngiJppFtVZ++94ekX45R1n8MRveLMnOltOdu3O/vJHHWUs0Hw22+n7ly53ewv1f4ShdooUERyk+0z\nmfj4fvvBq686e9498IC35bh57qYtcS67DPbdFy66KPVxiZmzetNq5Y1IkcmUBV61EbzIm+Tn/vCH\n8MEHzjDBpuOKsY2jRS5EUsi0qk68Ic5JT1YTax+j2/BKfjaslp/8qJxx46Bdu9zLqehUyW3/r5ab\nf11O69bw2mvplzzOtupPouSJpPM+nsfIl0e6eq6IFJ7bVbwSHz/ggHJmzYKaGmcDzuHD8y/H7XM7\n2Uo6LKjlrVfLUw5ZTsyc2LoYJzx6Ass3LFfeiBSJbG2cXHPCbRn5PLd1a2ermcmT4cYbi7eNoztY\nIilk2vQu8bFVWxYxYVqM+no46CD4z/+E+vrcylm4ehGX3hBj+PDMnats9UuWvJ+NxRZko0ARyU22\nz3O6xw88EGbNgttuc+5mZRt91tLNg9M995Nti7j1oRjladosiZlz4LcPZPmG5cobkSLito2Tz2fW\nq7xJ9dzzz3c6WNYWbxsnrw6WMWawMabOGLPdGNMzw3EnG2OWGGPeN8aMzqdMET9k2mQz+bHjDq7k\n8cedTtGqVdCjh7Mp6LPPwsqVqRs9mzbB1Kkw6e4qyj6thO2t6d6ugvdeqeTCC7MvntGSTUCbllht\n2mCwT9c+nm1M6jdljkRRts9zpse/+10ne/70Jyd3Mm0g3tLNg5Ofe9AeTlYd0r6CgZXuMue1C19T\n3ogUmZa0cXL9zOabN5mee+yxznSKd98t3jZOXotcGGMOBXYADwJXW2vnpzimDHgfOBFYDbwNnGOt\nXZLmnJoEKkUh0+o2mR5bs8ZZQvnNN2HePDDfirPfUXW0+ryKr78o58utcT7eVkfvA6s4eWA5xw2M\n06ZrjKrOLVu9J59Vf7xcMcjPSedeZ47yRopFts9k1sfjzre6n38Ojz4ZZ80OZ8I3sNPk71w/+zNn\nwrkXxrnmzhjDz/Qvq5Ipb0S8kWsbJ9V5kjOm6XfIfRP0bHUYPRpatYJbb235c90KfBVBY8yrwMg0\n4dMXuMlae0rj79cC1lr72zTnUgBJZGzaEqfvQ9W8vz7GQXtW8vvjpjNi7iA+jEdn/lMQq3p5lTnK\nG4mSHTvgmhvi3BevZkeHGId3OgyAJZ8tyTlvrIX77oPbb4f//m9neeQgKW9EikfyXKnp501n0BOD\nfJn/9M47cN55sHRp4bavKfZVBLsCKxN+X9X4N5HIi9XX8cHGGNvZxoqvFrG8zTQ+jAc/NjjilDlS\nksrK4Kzhdezo4GRObO1iFn+6JOe8aWhwlmB/5BGYMyf4zlWRUt5IyUqeKzXtg2m+zX/63vec7SLe\ne69gReQl6yqCxpgZQJfEPwEWGGOtnVqISo0dO/abn2tqaqipqSlEMSIF1zSOuGmn8lMPOXWn38M0\nH6HJ7NmzmT17dsHO73fmKG8kSqo6V1HVxcmYvbYfyoZ6KOu4lB7fcZ83DQ0wcaJz1+rYY53hznvu\nWdh6p6O8ESleQbZxjIHBg+Gpp+DII705p5d549cQwbHW2pMbf9cQQSkpyWOBg9oxvVCKdMiOq8xR\n3kgUJWbM4sVw3T0x3p5WySknlnPhhXDiidCmzc7P2bbN2Vvm5ZfhrrvgiCNgzBjo3z+QS0hLeSNS\nXIJs48ydCxdcAIsXF2aYYLHMwbraWvu/KR7bDViKMwH0E2AecK61dnGacymAREIkwAZP3pmjvJFS\n8fnnMGWKc2dqwQLo2BH239/ZLPijj5x5DPvtB336wK9+Bb16BV3j1JQ3ItLEWujeHaZPh6oq788f\nWAfLGHMGcD/QEdgAvGutPcUYsy/wsLX23xuPOxm4F2fO15+ttbdnOKcCSCREfF7Vy9PMUd5IKdq2\nzVntdNUq+OQT6NoVKithjz2Crll2yhsRSXTVVbDXXpAw+tYzgd/B8pICSCRcgvhG2SvKG5FwUd6I\nSKI5c2DYMKir8/7cxb6KoIiIiIiIiKf69IENG5x5WMVEHSyRIhJviDNn5RziDfGgqyIiJUCZIyJ+\nKUTelJU1ryZYTNTBEikSTRv2DZg4gOoJ1WrwiEhBKXNExC+FzJszz4Tnn/fsdJ5QB0ukSCRv2KdN\niEWkkJQ5IuKXQubNccfBihXOwj3FQh0skSLRtGFf67LWod2EWETCQ5kjIn4pZN60agWnnAIvveTZ\nKfOmVQRFikgYNyHWql4i4RW2zFHeiIRXIfNmyhR47DGYNs27c2qZdhEJjBo8IuIX5Y2IpLJxI3Tr\n5uzt59WeflqmXUREREREStLee0Pv3jBjRtA1caiDJSIiIiIioXbaaTB1atC1cGiIoIjkRUN2RMQv\nyhsRSWfZMujXzxkmWObBLSQNERQRERERkZL13e9Cx44wb17QNVEHS0REREREIuD004tjmKA6WCIi\nIiIiEnrFMg9LHSwREREREQm9Pn1gzRpYsSLYeqiDJSIiIiIiobfbbvDzn8PKlcHWQ6sIikhetKqX\niPhFeSMiftEqgiIiIiIiIkVAHSwRERERERGPqIMlIiIiIiLiEXWwREREREREPKIOloiIiIiIiEfU\nwRIREREREfGIOlgiIiIiIiIeUQdLRERERETEI+pgiYiIiIiIeEQdLBEREREREY+ogyUiIiIiIuIR\ndbBEREREREQ8og6WiIiIiIiIR9TBEhERERER8Yg6WCIiIiIiIh5RB0tERERERMQj6mCJiIiIiIh4\nRB0sERERERERj6iDJSIiIiIi4hF1sERERERERDyiDpaIiIiIiIhH1MESERERERHxiDpYIiIiIiIi\nHlEHS0RERERExCPqYImIiIiIiHhEHSwRERERERGPqIMlIiIiIiLiEXWwREREREREPJJXB8sYM9gY\nU2eM2W6M6ZnhuOXGmH8YYxYYY+blU6ZXZs+eHaly/CwrauX4WVbUyvFbWDNH7+XiL8fPsqJWjt9l\n+SWseQPRe49F8b0ctXL8LCsMeZPvHaz3gB8Dr2U5bgdQY609xlrbO88yPRHFN0HUrkn/74q/nACE\nMnP0Xi7+cvwsK2rl+F2Wj0KZNxC991gU38tRK8fPssKQN63yebK1dimAMcZkOdSg4Ygikidljoj4\nRXkjIrnyKxAsMMMY87YxZphPZYpI6VLmiIhflDcishNjrc18gDEzgC6Jf8IJkzHW2qmNx7wKjLTW\nzk9zjn2ttZ8YYzoBM4BfWmvfSHNs5gqJSNGx1mb7htc1PzNHeSMSPsobEfFLrnmTdYigtfakXE6c\ndI5PGv9bb4x5DugNpOxgeRmcIhI+fmaO8kaktClvRKQQvBwimDI4jDHtjDF7Nv68B/BDoM7DckWk\nNClzRMQvyhsRcS3fZdrPMMasBPoCLxlj/qfx7/saY15qPKwL8IYxZgHwd2CqtfblfMoVkdKkzBER\nvyhvRCRXWedgiYiIiIiIiDuBLCtqjPmzMWatMWZhhmPuM8Z8YIx51xhzdCHKMcacYIzZYIyZ3/jv\n1zmWs78xZpYxJmaMec8Yc0Wa4/K6JjfleHhNbY0xcxs3TowZY8YV6JqyluPVNTWeq6zxHC+meTzv\n9122cjy+nqwbXHr0WcpYjpfX5DXlTV7X5EvmKG/yy5tsZXn43vMlb9yUVayZ41feuCkrbJkTtbxx\nW1YYM8ePvGk8V3jbONZa3/8BxwNHAwvTPH4KMK3x5z7A3wtUzgnAix5czz7A0Y0/7wksBQ7z+ppc\nluPJNTWeq13jf3fDGfrQv0CvU7ZyvLymXwGTU53Pq+txUY6X17MMaJ/hca9eo2zleHZNXv9T3uR1\nTb5ljvIm97xxUZZXr5EveeOyrKLMHL/yxmVZocqcKOaNy7JClzl+5E3juULbxgnkDpZ1li9dn+GQ\nHwGPNR47F9jbGNMlw/G5lgNpJq62sJw11tp3G3/+AlgMdE06LO9rclkOeHBNjWV81fhjW5y7ncn/\nL716nbKVAx5ckzFmf2AQ8Kc0h3hyPS7KAY9eI7JvcOnJNbkop+mYoqO8yeuafMsc5U3On00/M8ev\nvHFTVtMxRcWvvHFZFoQoc6KYNy7LghBljto47hTrzuNdgZUJv39M6g+ZF/o13lacZoypyPdkxpgD\ncb5Rmpv0kKfXlKEc8OiaGm8BLwDWALOttYuSDvHkmlyUA95c0z3AKJw9TlLx6jXKVg54977LtsGl\nV9fkZiNNTz9LPlLe5FcWeHBdypu8XiO/MsevvHFTFoQzc/zMGwhp5kQlb1yWBeHKHLVxXFxT1n2w\nIu5/gQOstV8ZY04Bngd65Hoy4yzV+jRwZeO3LwWRpRzPrslauwM4xhizF/CyMeYEa+1r+dQ9x3Ly\nviZjzKnAWmvtu8aYGgr0zafLcrx83/W3CRtcGmMW2zSbeOcpWzmefpYiKpR546IsT65LeZMbnzPH\nr7xxU5YyJ7tQZk6U8sZlWaHJHLVx3F9Tsd7B+hjolvD7/o1/85S19oumW7fW2v8BWhtjvpPLuYwx\nrXACYZK19oUUh3hyTdnK8fKaEs65CZgG9Ep6yNPXKV05Hl1Tf+B0Y8wy4ElgoDHmsaRjvLierOV4\n+RrZhA0ugaYNLhN58hplK6cQ7zsfKW/yKMvr115502K+ZY5feeOmrBBnji95A+HMnKjmTaayQpY5\nauO4vKYgO1iG9D3sF4GfARhj+gIbrLVrvS7HJIzTNMb0Boy19vMcy3kEWGStvTfN415dU8ZyvLom\nY0xHY8zejT/vDpwEvJt0WN7X5KYcL67JWnu9tfYAa+13gXOAWdban3l9PW7K8fA1crPBpRevUdZy\nPP4sFYLyJvdrKnjmKG9yf438yhy/8sZtWUWeOX7lTcayQpo5kckbt2WFKXPUxnF/TYEMETTGPAHU\nAB2MMR8BNwFtAGutfchaO90YM8gY80/gS2BoIcoBBhtjfgFsBTYDQ3Ispz/w/4H3jDPO1gLXA929\nvCY35Xh1TcC+wKPGmKaJf5Osta8YYy718prclOPhNe2iANeTtRy8u54uwHPGGIvzWX7cWvtyAa4p\nazkeXpPnlDd5XZNfmaO88TBvksvCm2vyK29cleXRNXnOr7xxUxYhy5wI5o2rsjy6ppTUxvGmnFyu\nSRsNi4iIiIiIeKRY52CJiIiIiIiEjjpYIiIiIiIiHlEHS0RERERExCPqYImIiIiIiHhEHSwRERER\nERGPqIMlIiIiIiLiEXWwREREREREPPJ/Qv1WH25EUosAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117f1db70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Initialize predictors to be set of 15 powers of x\n",
    "predictors=['x']\n",
    "predictors.extend(['x_%d'%i for i in range(2,16)])\n",
    "\n",
    "#Set the different values of alpha to be tested\n",
    "alpha_ridge = [1e-15, 1e-10, 1e-8, 1e-4, 1e-3,1e-2, 1, 5, 10, 20]\n",
    "\n",
    "#Initialize the dataframe for storing coefficients.\n",
    "col = ['rss','intercept'] + ['coef_x_%d'%i for i in range(1,16)]\n",
    "ind = ['alpha_%.2g'%alpha_ridge[i] for i in range(0,10)]\n",
    "coef_matrix_ridge = pd.DataFrame(index=ind, columns=col)\n",
    "\n",
    "models_to_plot = {1e-15:231, 1e-10:232, 1e-4:233, 1e-3:234, 1e-2:235, 5:236}\n",
    "for i in range(10):\n",
    "    coef_matrix_ridge.iloc[i,] = ridge_regression(data, predictors, alpha_ridge[i], models_to_plot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>rss</th>\n",
       "      <th>intercept</th>\n",
       "      <th>coef_x_1</th>\n",
       "      <th>coef_x_2</th>\n",
       "      <th>coef_x_3</th>\n",
       "      <th>coef_x_4</th>\n",
       "      <th>coef_x_5</th>\n",
       "      <th>coef_x_6</th>\n",
       "      <th>coef_x_7</th>\n",
       "      <th>coef_x_8</th>\n",
       "      <th>coef_x_9</th>\n",
       "      <th>coef_x_10</th>\n",
       "      <th>coef_x_11</th>\n",
       "      <th>coef_x_12</th>\n",
       "      <th>coef_x_13</th>\n",
       "      <th>coef_x_14</th>\n",
       "      <th>coef_x_15</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>alpha_1e-15</th>\n",
       "      <td>0.87</td>\n",
       "      <td>95</td>\n",
       "      <td>-3e+02</td>\n",
       "      <td>3.8e+02</td>\n",
       "      <td>-2.4e+02</td>\n",
       "      <td>66</td>\n",
       "      <td>0.96</td>\n",
       "      <td>-4.8</td>\n",
       "      <td>0.64</td>\n",
       "      <td>0.15</td>\n",
       "      <td>-0.026</td>\n",
       "      <td>-0.0054</td>\n",
       "      <td>0.00086</td>\n",
       "      <td>0.00022</td>\n",
       "      <td>-5.5e-05</td>\n",
       "      <td>3.9e-06</td>\n",
       "      <td>-6.9e-08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_1e-10</th>\n",
       "      <td>0.92</td>\n",
       "      <td>11</td>\n",
       "      <td>-29</td>\n",
       "      <td>31</td>\n",
       "      <td>-15</td>\n",
       "      <td>2.9</td>\n",
       "      <td>0.17</td>\n",
       "      <td>-0.091</td>\n",
       "      <td>-0.011</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.00064</td>\n",
       "      <td>2.4e-05</td>\n",
       "      <td>-2e-05</td>\n",
       "      <td>-4.2e-06</td>\n",
       "      <td>2.2e-07</td>\n",
       "      <td>2.3e-07</td>\n",
       "      <td>-2.3e-08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_1e-08</th>\n",
       "      <td>0.95</td>\n",
       "      <td>1.3</td>\n",
       "      <td>-1.5</td>\n",
       "      <td>1.7</td>\n",
       "      <td>-0.68</td>\n",
       "      <td>0.039</td>\n",
       "      <td>0.016</td>\n",
       "      <td>0.00016</td>\n",
       "      <td>-0.00036</td>\n",
       "      <td>-5.4e-05</td>\n",
       "      <td>-2.9e-07</td>\n",
       "      <td>1.1e-06</td>\n",
       "      <td>1.9e-07</td>\n",
       "      <td>2e-08</td>\n",
       "      <td>3.9e-09</td>\n",
       "      <td>8.2e-10</td>\n",
       "      <td>-4.6e-10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_0.0001</th>\n",
       "      <td>0.96</td>\n",
       "      <td>0.56</td>\n",
       "      <td>0.55</td>\n",
       "      <td>-0.13</td>\n",
       "      <td>-0.026</td>\n",
       "      <td>-0.0028</td>\n",
       "      <td>-0.00011</td>\n",
       "      <td>4.1e-05</td>\n",
       "      <td>1.5e-05</td>\n",
       "      <td>3.7e-06</td>\n",
       "      <td>7.4e-07</td>\n",
       "      <td>1.3e-07</td>\n",
       "      <td>1.9e-08</td>\n",
       "      <td>1.9e-09</td>\n",
       "      <td>-1.3e-10</td>\n",
       "      <td>-1.5e-10</td>\n",
       "      <td>-6.2e-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_0.001</th>\n",
       "      <td>1</td>\n",
       "      <td>0.82</td>\n",
       "      <td>0.31</td>\n",
       "      <td>-0.087</td>\n",
       "      <td>-0.02</td>\n",
       "      <td>-0.0028</td>\n",
       "      <td>-0.00022</td>\n",
       "      <td>1.8e-05</td>\n",
       "      <td>1.2e-05</td>\n",
       "      <td>3.4e-06</td>\n",
       "      <td>7.3e-07</td>\n",
       "      <td>1.3e-07</td>\n",
       "      <td>1.9e-08</td>\n",
       "      <td>1.7e-09</td>\n",
       "      <td>-1.5e-10</td>\n",
       "      <td>-1.4e-10</td>\n",
       "      <td>-5.2e-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_0.01</th>\n",
       "      <td>1.4</td>\n",
       "      <td>1.3</td>\n",
       "      <td>-0.088</td>\n",
       "      <td>-0.052</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>-0.0014</td>\n",
       "      <td>-0.00013</td>\n",
       "      <td>7.2e-07</td>\n",
       "      <td>4.1e-06</td>\n",
       "      <td>1.3e-06</td>\n",
       "      <td>3e-07</td>\n",
       "      <td>5.6e-08</td>\n",
       "      <td>9e-09</td>\n",
       "      <td>1.1e-09</td>\n",
       "      <td>4.3e-11</td>\n",
       "      <td>-3.1e-11</td>\n",
       "      <td>-1.5e-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_1</th>\n",
       "      <td>5.6</td>\n",
       "      <td>0.97</td>\n",
       "      <td>-0.14</td>\n",
       "      <td>-0.019</td>\n",
       "      <td>-0.003</td>\n",
       "      <td>-0.00047</td>\n",
       "      <td>-7e-05</td>\n",
       "      <td>-9.9e-06</td>\n",
       "      <td>-1.3e-06</td>\n",
       "      <td>-1.4e-07</td>\n",
       "      <td>-9.3e-09</td>\n",
       "      <td>1.3e-09</td>\n",
       "      <td>7.8e-10</td>\n",
       "      <td>2.4e-10</td>\n",
       "      <td>6.2e-11</td>\n",
       "      <td>1.4e-11</td>\n",
       "      <td>3.2e-12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_5</th>\n",
       "      <td>14</td>\n",
       "      <td>0.55</td>\n",
       "      <td>-0.059</td>\n",
       "      <td>-0.0085</td>\n",
       "      <td>-0.0014</td>\n",
       "      <td>-0.00024</td>\n",
       "      <td>-4.1e-05</td>\n",
       "      <td>-6.9e-06</td>\n",
       "      <td>-1.1e-06</td>\n",
       "      <td>-1.9e-07</td>\n",
       "      <td>-3.1e-08</td>\n",
       "      <td>-5.1e-09</td>\n",
       "      <td>-8.2e-10</td>\n",
       "      <td>-1.3e-10</td>\n",
       "      <td>-2e-11</td>\n",
       "      <td>-3e-12</td>\n",
       "      <td>-4.2e-13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_10</th>\n",
       "      <td>18</td>\n",
       "      <td>0.4</td>\n",
       "      <td>-0.037</td>\n",
       "      <td>-0.0055</td>\n",
       "      <td>-0.00095</td>\n",
       "      <td>-0.00017</td>\n",
       "      <td>-3e-05</td>\n",
       "      <td>-5.2e-06</td>\n",
       "      <td>-9.2e-07</td>\n",
       "      <td>-1.6e-07</td>\n",
       "      <td>-2.9e-08</td>\n",
       "      <td>-5.1e-09</td>\n",
       "      <td>-9.1e-10</td>\n",
       "      <td>-1.6e-10</td>\n",
       "      <td>-2.9e-11</td>\n",
       "      <td>-5.1e-12</td>\n",
       "      <td>-9.1e-13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_20</th>\n",
       "      <td>23</td>\n",
       "      <td>0.28</td>\n",
       "      <td>-0.022</td>\n",
       "      <td>-0.0034</td>\n",
       "      <td>-0.0006</td>\n",
       "      <td>-0.00011</td>\n",
       "      <td>-2e-05</td>\n",
       "      <td>-3.6e-06</td>\n",
       "      <td>-6.6e-07</td>\n",
       "      <td>-1.2e-07</td>\n",
       "      <td>-2.2e-08</td>\n",
       "      <td>-4e-09</td>\n",
       "      <td>-7.5e-10</td>\n",
       "      <td>-1.4e-10</td>\n",
       "      <td>-2.5e-11</td>\n",
       "      <td>-4.7e-12</td>\n",
       "      <td>-8.7e-13</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              rss intercept coef_x_1 coef_x_2 coef_x_3 coef_x_4 coef_x_5  \\\n",
       "alpha_1e-15  0.87        95   -3e+02  3.8e+02 -2.4e+02       66     0.96   \n",
       "alpha_1e-10  0.92        11      -29       31      -15      2.9     0.17   \n",
       "alpha_1e-08  0.95       1.3     -1.5      1.7    -0.68    0.039    0.016   \n",
       "alpha_0.0001 0.96      0.56     0.55    -0.13   -0.026  -0.0028 -0.00011   \n",
       "alpha_0.001     1      0.82     0.31   -0.087    -0.02  -0.0028 -0.00022   \n",
       "alpha_0.01    1.4       1.3   -0.088   -0.052    -0.01  -0.0014 -0.00013   \n",
       "alpha_1       5.6      0.97    -0.14   -0.019   -0.003 -0.00047   -7e-05   \n",
       "alpha_5        14      0.55   -0.059  -0.0085  -0.0014 -0.00024 -4.1e-05   \n",
       "alpha_10       18       0.4   -0.037  -0.0055 -0.00095 -0.00017   -3e-05   \n",
       "alpha_20       23      0.28   -0.022  -0.0034  -0.0006 -0.00011   -2e-05   \n",
       "\n",
       "             coef_x_6 coef_x_7 coef_x_8 coef_x_9 coef_x_10 coef_x_11  \\\n",
       "alpha_1e-15      -4.8     0.64     0.15   -0.026   -0.0054   0.00086   \n",
       "alpha_1e-10    -0.091   -0.011    0.002  0.00064   2.4e-05    -2e-05   \n",
       "alpha_1e-08   0.00016 -0.00036 -5.4e-05 -2.9e-07   1.1e-06   1.9e-07   \n",
       "alpha_0.0001  4.1e-05  1.5e-05  3.7e-06  7.4e-07   1.3e-07   1.9e-08   \n",
       "alpha_0.001   1.8e-05  1.2e-05  3.4e-06  7.3e-07   1.3e-07   1.9e-08   \n",
       "alpha_0.01    7.2e-07  4.1e-06  1.3e-06    3e-07   5.6e-08     9e-09   \n",
       "alpha_1      -9.9e-06 -1.3e-06 -1.4e-07 -9.3e-09   1.3e-09   7.8e-10   \n",
       "alpha_5      -6.9e-06 -1.1e-06 -1.9e-07 -3.1e-08  -5.1e-09  -8.2e-10   \n",
       "alpha_10     -5.2e-06 -9.2e-07 -1.6e-07 -2.9e-08  -5.1e-09  -9.1e-10   \n",
       "alpha_20     -3.6e-06 -6.6e-07 -1.2e-07 -2.2e-08    -4e-09  -7.5e-10   \n",
       "\n",
       "             coef_x_12 coef_x_13 coef_x_14 coef_x_15  \n",
       "alpha_1e-15    0.00022  -5.5e-05   3.9e-06  -6.9e-08  \n",
       "alpha_1e-10   -4.2e-06   2.2e-07   2.3e-07  -2.3e-08  \n",
       "alpha_1e-08      2e-08   3.9e-09   8.2e-10  -4.6e-10  \n",
       "alpha_0.0001   1.9e-09  -1.3e-10  -1.5e-10  -6.2e-11  \n",
       "alpha_0.001    1.7e-09  -1.5e-10  -1.4e-10  -5.2e-11  \n",
       "alpha_0.01     1.1e-09   4.3e-11  -3.1e-11  -1.5e-11  \n",
       "alpha_1        2.4e-10   6.2e-11   1.4e-11   3.2e-12  \n",
       "alpha_5       -1.3e-10    -2e-11    -3e-12  -4.2e-13  \n",
       "alpha_10      -1.6e-10  -2.9e-11  -5.1e-12  -9.1e-13  \n",
       "alpha_20      -1.4e-10  -2.5e-11  -4.7e-12  -8.7e-13  "
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Set the display format to be scientific for ease of analysis\n",
    "pd.options.display.float_format = '{:,.2g}'.format\n",
    "coef_matrix_ridge"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## LASSO regression\n",
    "\n",
    "This is similar to ridge regression with the exception that the absolute value of the parameters is used to penalize the objective function.\n",
    "\n",
    "*Min Objective = Residual sum of squares + $\\alpha$ $\\cdot$ Sum of absolute value of parameters*\n",
    "\n",
    "Each non-zero coefficient/parameter adds to the penalty, thus if a feature has little influence on the prediction/outcome, zero will be selected as the coefficient. In this manner, LASSO can be used to select a subset of features that perform well in linear model predictions.\n",
    "\n",
    "Unlike ridge regression, when features are collinear/multicollinear, the value of the coefficients do not accurately reflect the importance of each feature."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import Lasso\n",
    "def lasso_regression(data, predictors, alpha, models_to_plot={}):\n",
    "    #Fit the model\n",
    "    lassoreg = Lasso(alpha=alpha,normalize=True, max_iter=1e5)\n",
    "    lassoreg.fit(data[predictors],data['y'])\n",
    "    y_pred = lassoreg.predict(data[predictors])\n",
    "    \n",
    "    #Check if a plot is to be made for the entered alpha\n",
    "    if alpha in models_to_plot:\n",
    "        plt.subplot(models_to_plot[alpha])\n",
    "        plt.tight_layout()\n",
    "        plt.plot(data['x'],y_pred)\n",
    "        plt.plot(data['x'],data['y'],'.')\n",
    "        plt.title('Plot for alpha: %.3g'%alpha)\n",
    "    \n",
    "    #Return the result in pre-defined format\n",
    "    rss = sum((y_pred-data['y'])**2)\n",
    "    ret = [rss]\n",
    "    ret.extend([lassoreg.intercept_])\n",
    "    ret.extend(lassoreg.coef_)\n",
    "    return ret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.5/site-packages/sklearn/linear_model/coordinate_descent.py:466: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": 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CRZqgvMkurc2cd95xm17MmAE9eqSwQJFGaA1WjqupgYEDoU8fuO46v6uRXKMH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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117433908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Initialize predictors to all 15 powers of x\n",
    "predictors=['x']\n",
    "predictors.extend(['x_%d'%i for i in range(2,16)])\n",
    "\n",
    "#Define the alpha values to test\n",
    "alpha_lasso = [1e-15, 1e-10, 1e-8, 1e-5,1e-4, 1e-3,1e-2, 1, 5, 10]\n",
    "\n",
    "#Initialize the dataframe to store coefficients\n",
    "col = ['rss','intercept'] + ['coef_x_%d'%i for i in range(1,16)]\n",
    "ind = ['alpha_%.2g'%alpha_lasso[i] for i in range(0,10)]\n",
    "coef_matrix_lasso = pd.DataFrame(index=ind, columns=col)\n",
    "\n",
    "#Define the models to plot\n",
    "models_to_plot = {1e-10:231, 1e-5:232,1e-4:233, 1e-3:234, 1e-2:235, 1:236}\n",
    "\n",
    "#Iterate over the 10 alpha values:\n",
    "for i in range(10):\n",
    "    coef_matrix_lasso.iloc[i,] = lasso_regression(data, predictors, alpha_lasso[i], models_to_plot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>rss</th>\n",
       "      <th>intercept</th>\n",
       "      <th>coef_x_1</th>\n",
       "      <th>coef_x_2</th>\n",
       "      <th>coef_x_3</th>\n",
       "      <th>coef_x_4</th>\n",
       "      <th>coef_x_5</th>\n",
       "      <th>coef_x_6</th>\n",
       "      <th>coef_x_7</th>\n",
       "      <th>coef_x_8</th>\n",
       "      <th>coef_x_9</th>\n",
       "      <th>coef_x_10</th>\n",
       "      <th>coef_x_11</th>\n",
       "      <th>coef_x_12</th>\n",
       "      <th>coef_x_13</th>\n",
       "      <th>coef_x_14</th>\n",
       "      <th>coef_x_15</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>alpha_1e-15</th>\n",
       "      <td>0.96</td>\n",
       "      <td>0.22</td>\n",
       "      <td>1.1</td>\n",
       "      <td>-0.37</td>\n",
       "      <td>0.00089</td>\n",
       "      <td>0.0016</td>\n",
       "      <td>-0.00012</td>\n",
       "      <td>-6.4e-05</td>\n",
       "      <td>-6.3e-06</td>\n",
       "      <td>1.4e-06</td>\n",
       "      <td>7.8e-07</td>\n",
       "      <td>2.1e-07</td>\n",
       "      <td>4e-08</td>\n",
       "      <td>5.4e-09</td>\n",
       "      <td>1.8e-10</td>\n",
       "      <td>-2e-10</td>\n",
       "      <td>-9.2e-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_1e-10</th>\n",
       "      <td>0.96</td>\n",
       "      <td>0.22</td>\n",
       "      <td>1.1</td>\n",
       "      <td>-0.37</td>\n",
       "      <td>0.00088</td>\n",
       "      <td>0.0016</td>\n",
       "      <td>-0.00012</td>\n",
       "      <td>-6.4e-05</td>\n",
       "      <td>-6.3e-06</td>\n",
       "      <td>1.4e-06</td>\n",
       "      <td>7.8e-07</td>\n",
       "      <td>2.1e-07</td>\n",
       "      <td>4e-08</td>\n",
       "      <td>5.4e-09</td>\n",
       "      <td>1.8e-10</td>\n",
       "      <td>-2e-10</td>\n",
       "      <td>-9.2e-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_1e-08</th>\n",
       "      <td>0.96</td>\n",
       "      <td>0.22</td>\n",
       "      <td>1.1</td>\n",
       "      <td>-0.37</td>\n",
       "      <td>0.00077</td>\n",
       "      <td>0.0016</td>\n",
       "      <td>-0.00011</td>\n",
       "      <td>-6.4e-05</td>\n",
       "      <td>-6.3e-06</td>\n",
       "      <td>1.4e-06</td>\n",
       "      <td>7.8e-07</td>\n",
       "      <td>2.1e-07</td>\n",
       "      <td>4e-08</td>\n",
       "      <td>5.3e-09</td>\n",
       "      <td>2e-10</td>\n",
       "      <td>-1.9e-10</td>\n",
       "      <td>-9.3e-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_1e-05</th>\n",
       "      <td>0.96</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.6</td>\n",
       "      <td>-0.13</td>\n",
       "      <td>-0.038</td>\n",
       "      <td>-0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>7.7e-06</td>\n",
       "      <td>1e-06</td>\n",
       "      <td>7.7e-08</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-7e-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_0.0001</th>\n",
       "      <td>1</td>\n",
       "      <td>0.9</td>\n",
       "      <td>0.17</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0.048</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>9.5e-06</td>\n",
       "      <td>5.1e-07</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-4.4e-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_0.001</th>\n",
       "      <td>1.7</td>\n",
       "      <td>1.3</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0.13</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.5e-08</td>\n",
       "      <td>7.5e-10</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_0.01</th>\n",
       "      <td>3.6</td>\n",
       "      <td>1.8</td>\n",
       "      <td>-0.55</td>\n",
       "      <td>-0.00056</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_1</th>\n",
       "      <td>37</td>\n",
       "      <td>0.038</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_5</th>\n",
       "      <td>37</td>\n",
       "      <td>0.038</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_10</th>\n",
       "      <td>37</td>\n",
       "      <td>0.038</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              rss intercept coef_x_1 coef_x_2 coef_x_3 coef_x_4 coef_x_5  \\\n",
       "alpha_1e-15  0.96      0.22      1.1    -0.37  0.00089   0.0016 -0.00012   \n",
       "alpha_1e-10  0.96      0.22      1.1    -0.37  0.00088   0.0016 -0.00012   \n",
       "alpha_1e-08  0.96      0.22      1.1    -0.37  0.00077   0.0016 -0.00011   \n",
       "alpha_1e-05  0.96       0.5      0.6    -0.13   -0.038       -0        0   \n",
       "alpha_0.0001    1       0.9     0.17       -0   -0.048       -0       -0   \n",
       "alpha_0.001   1.7       1.3       -0    -0.13       -0       -0       -0   \n",
       "alpha_0.01    3.6       1.8    -0.55 -0.00056       -0       -0       -0   \n",
       "alpha_1        37     0.038       -0       -0       -0       -0       -0   \n",
       "alpha_5        37     0.038       -0       -0       -0       -0       -0   \n",
       "alpha_10       37     0.038       -0       -0       -0       -0       -0   \n",
       "\n",
       "             coef_x_6 coef_x_7 coef_x_8 coef_x_9 coef_x_10 coef_x_11  \\\n",
       "alpha_1e-15  -6.4e-05 -6.3e-06  1.4e-06  7.8e-07   2.1e-07     4e-08   \n",
       "alpha_1e-10  -6.4e-05 -6.3e-06  1.4e-06  7.8e-07   2.1e-07     4e-08   \n",
       "alpha_1e-08  -6.4e-05 -6.3e-06  1.4e-06  7.8e-07   2.1e-07     4e-08   \n",
       "alpha_1e-05         0        0  7.7e-06    1e-06   7.7e-08         0   \n",
       "alpha_0.0001        0        0  9.5e-06  5.1e-07         0         0   \n",
       "alpha_0.001         0        0        0        0         0   1.5e-08   \n",
       "alpha_0.01         -0       -0       -0       -0         0         0   \n",
       "alpha_1            -0       -0       -0       -0        -0        -0   \n",
       "alpha_5            -0       -0       -0       -0        -0        -0   \n",
       "alpha_10           -0       -0       -0       -0        -0        -0   \n",
       "\n",
       "             coef_x_12 coef_x_13 coef_x_14 coef_x_15  \n",
       "alpha_1e-15    5.4e-09   1.8e-10    -2e-10  -9.2e-11  \n",
       "alpha_1e-10    5.4e-09   1.8e-10    -2e-10  -9.2e-11  \n",
       "alpha_1e-08    5.3e-09     2e-10  -1.9e-10  -9.3e-11  \n",
       "alpha_1e-05          0         0        -0    -7e-11  \n",
       "alpha_0.0001         0        -0        -0  -4.4e-11  \n",
       "alpha_0.001    7.5e-10         0         0         0  \n",
       "alpha_0.01           0         0         0         0  \n",
       "alpha_1             -0        -0        -0        -0  \n",
       "alpha_5             -0        -0        -0        -0  \n",
       "alpha_10            -0        -0        -0        -0  "
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coef_matrix_lasso"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, **even for a small value of alpha, a significant number of parameters are zero**. This is called sparsity.\n",
    "\n",
    "The difference between ridge and lasso lies in the fact that the derivative that is calculated during the gradient descent process is not defined everywhere due to the presence of the absolute value in the objective/cost function. Instead, a process known as **coordinate descent** is used. It begins by setting all parameters to zero, then updating the $j$*th* parameter with a value that minimizes the cost and repeats this process iteratively for all other features. The update rule considers the predicted outcome with all features excecpt the $j$*th*. If the residual is sufficiently small, then this feature is not important to the outcome so the parameter is left as zero.\n",
    "\n",
    "The following image describes the difference in the possible parameter values for the non-regularizated, ridge, LASSO regression. Here, $\\lambda$ represents a small tolerance value where the residual is small enough to declare that the given feature has little influence on the model.\n",
    "\n",
    "<img src=\"images/parameters.png\" width=\"300\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Other\n",
    "\n",
    "References:<br>\n",
    "http://scikit-learn.org/stable/modules/preprocessing.html#encoding-categorical-features<br>\n",
    "http://stats.stackexchange.com/questions/224051/one-hot-vs-dummy-encoding-in-scikit-learn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"enccat\"></a>\n",
    "---\n",
    "# Encoding categorical features\n",
    "\n",
    "## Overview\n",
    "\n",
    "Estimators expect continuous input and would interpret categories encoded as integers as being ordered, which is often not the case. Therefore we must create binary variables that describe the possible categorical values for each feature."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example\n",
    "\n",
    "Here we have 4 examples ($m=4$) and 3 categorical features ($n=3$) each with 2 possible categories ($k=2$). One hot encoder creates 6 total features, 2 for each of the 3 original features. ***Dummy variable trap*** states only $k-1$ features are needed for the original features that have $k$ categories, so in the end, we would expect only 3 total features ($n\\times(k-1) = 3\\times(2-1) = 3$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "     0    1    2    3    4    5\n",
       "0  1.0  0.0  1.0  0.0  0.0  1.0\n",
       "1  0.0  1.0  0.0  1.0  1.0  0.0\n",
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      ]
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     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# one hot encoding with all dummy variables present\n",
    "\n",
    "from sklearn.preprocessing import OneHotEncoder\n",
    "import pandas as pd\n",
    "enc = OneHotEncoder(sparse=False)\n",
    "df = pd.DataFrame(enc.fit_transform([[0, 0, 1], [1, 1, 0], [0, 1, 1], [1, 0, 1]]))\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "     0    2    4\n",
       "0  1.0  1.0  0.0\n",
       "1  0.0  0.0  1.0\n",
       "2  1.0  0.0  0.0\n",
       "3  0.0  1.0  0.0"
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     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "# one hot encoding with unneeded dummy variables dropped\n",
    "\n",
    "df.drop([1,3,5], axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "<a id=\"procon\"></a>\n",
    "[Return to top](#top)\n",
    "\n",
    "---\n",
    "# General Assembly\n",
    "\n",
    "References:<br>\n",
    "https://github.com/dbricare/DS-SF-27"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Pros and Cons of Machine Learning Algorithms"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Regression\n",
    "\n",
    "| Pros | Cons |\n",
    "| --- | --- |\n",
    "| Intuitive | Assumes linear association among variables |\n",
    "| Interpretable | Assumes normally distributed residuals |\n",
    "| Easy to compute predictions | Outliers have large influence on coefficent values |\n",
    "| No need to standardize data | &nbsp; |\n",
    "\n",
    "<br>\n",
    "\n",
    "## k-Nearest Neighbors\n",
    "\n",
    "| Pros | Cons |\n",
    "| --- | --- |\n",
    "| Intuitive | Not interpretable |\n",
    "| Easy to compute | Cannot be used with sparse data or more than 4 features |\n",
    "| Captures non-linearity | Data must be standardized |\n",
    "\n",
    "<br>\n",
    "\n",
    "## Logistic Regression\n",
    "\n",
    "| Pros | Cons |\n",
    "| --- | --- |\n",
    "| Computationally fast | Limited to binary classification or one-vs-rest approach for multiclass datasets |\n",
    "| Output is a (posterior) probability which is easy to interpret | &nbsp; |\n",
    "\n",
    "<br>\n",
    "\n",
    "## Simple Decision Trees\n",
    "\n",
    "| Pros | Cons |\n",
    "| --- | --- |\n",
    "| Intuitive | Low predictable power |\n",
    "| Interpretable | &nbsp; |\n",
    "| Easy to compute predictions | &nbsp; |\n",
    "| No need to standardize data | &nbsp; |\n",
    "\n",
    "<br>\n",
    "\n",
    "## Random Forests\n",
    "\n",
    "| Pros | Cons |\n",
    "| --- | --- |\n",
    "| Good predictive power | Not interpretable |\n",
    "| Easy to compute predictions | &nbsp; |\n",
    "| No need to standardize data | &nbsp; |\n",
    "\n",
    "## Gradient-boosting Trees\n",
    "\n",
    "| Pros | Cons |\n",
    "| --- | --- |\n",
    "| Good predictive power | Not interpretable |\n",
    "| Easy to compute predictions | Method is not parallelizable so slower than RF |\n",
    "| No need to standardize data | &nbsp; |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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