DeepLearning_Introduction_woSP.ipynb

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    "## <font color='blue'>Deep Learning</font>\n",
    "<br>\n",
    "## Sanjiv R. Das\n",
    "<br>\n",
    "### Professor of Finance and Data Science\n",
    "### Santa Clara University\n",
    "<br>\n",
    "## <font color='green'>London, June 2018</font>\n",
    "<br>\n",
    "\n",
    "REFERENCE BOOK: http://srdas.github.io/DLBook\n",
    "\n",
    "WORKSHOP (June 26, 2 hours)\n",
    "\n",
    "TITLE: Introduction to Deep Learning\n",
    "\n",
    "ABSTRACT: This workshop will cover the essentials of deep learning from a mathematical and programming perspective.\n",
    "- What is deep learning?\n",
    "- Types of deep learning\n",
    "- Mathematics of Deep Learning: universal approximation using neural nets, Backpropagation, and techniques for fitting deep learning nets.\n",
    "- Programming deep learning: tensorflow, mxnet, h2o in R and Python with applications."
   ]
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     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "import pandas as pd\n",
    "from IPython.external import mathjax"
   ]
  },
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   "source": [
    "![](images/ML.png)\n",
    "\n",
    "https://medium.com/machine-learning-for-humans/why-machine-learning-matters-6164faf1df12\n"
   ]
  },
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   "source": [
    "![](images/DL_PatternRecognition.png)"
   ]
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   "source": [
    "## Examples of Different Types of Neurons\n",
    "\n",
    "#### Net input \n",
    "\n",
    "$$\n",
    "a_j^{(r)} = \\sum_{i=1}^{n^{(r-1)}} W_{ij} Z_i^{(r-1)} + b_j^{(r)}\n",
    "$$\n",
    "\n"
   ]
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   "source": [
    "#### Sigmoid\n",
    "\n",
    "$$\n",
    "Z_j^{(r)} = \\frac{1}{1+\\exp(a_j^{(r)})} \\in (0,1)\n",
    "$$\n",
    "\n"
   ]
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   "source": [
    "#### ReLU (restricted linear unit)\n",
    "\n",
    "$$\n",
    "Z_j^{(r)} = \\max[0, a_j^{(r)}] \\in (0,1)\n",
    "$$\n",
    "\n"
   ]
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   "source": [
    "#### TanH (hyperbolic tangent)\n",
    "\n",
    "$$\n",
    "Z_j^{(r)} = \\tanh[a_j^{(r)}] \\in (-1,+1)\n",
    "$$"
   ]
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   "source": [
    "![](images/NN_diagram.png)"
   ]
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   "source": [
    "![](images/NN_subset.png)"
   ]
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   "source": [
    "![](images/Activation_functions.png)"
   ]
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   "source": [
    "![](images/Softmax.png)"
   ]
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     "text": [
      "[0.034 0.057 0.072 0.18  0.205 0.012 0.276 0.004 0.096 0.063]\n",
      "final tag = 6\n"
     ]
    }
   ],
   "source": [
    "#The Softmax function\n",
    "#Assume 10 output nodes with randomly generated values\n",
    "z = randn(32)  #inputs from last hidden layer of 32 nodes to the output layer\n",
    "w = rand(32*10).reshape((10,32))  #weights for the output layer\n",
    "b = rand(10)   #bias terms at output later\n",
    "a = w.dot(z) + b  #Net input at output layer\n",
    "e = exp(a)\n",
    "softmax_output = e/sum(e)\n",
    "print(softmax_output.round(3))\n",
    "print('final tag =',where(softmax_output==softmax_output.max())[0][0])"
   ]
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   "source": [
    "![](images/Loss_function.png)"
   ]
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   "source": [
    "## More on Cross Entropy\n",
    "\n",
    "https://rdipietro.github.io/friendly-intro-to-cross-entropy-loss/\n",
    "\n",
    "Notation from the previous slides: \n",
    "\n",
    "- $y_i$: actual probability of the correct class $i$, i.e., $1$ or $0$. \n",
    "- $a_i$: predicted probability of the correct class. \n",
    "- $n$: number of observations in the data. \n",
    "\n"
   ]
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   "source": [
    "#### Entropy \n",
    "\n",
    "$$\n",
    "E = - \\frac{1}{n} \\sum_i [y_i \\ln y_i]\n",
    "$$"
   ]
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     "text": [
      "1.58481870497303\n",
      "1.4854752972273344\n",
      "0.9219280948873623\n"
     ]
    }
   ],
   "source": [
    "y = [0.33, 0.33, 0.34]\n",
    "bits = log2(y)\n",
    "entropy = -sum(y*bits)\n",
    "print(entropy)\n",
    "\n",
    "y = [0.2, 0.3, 0.5]\n",
    "entropy = -sum(y*log2(y))\n",
    "print(entropy)\n",
    "\n",
    "y = [0.1, 0.1, 0.8]\n",
    "entropy = -sum(y*log2(y))\n",
    "print(entropy)\n"
   ]
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    "Cross-entropy:\n",
    "\n",
    "$$\n",
    "C = - \\frac{1}{n} \\sum_i [y_i \\ln a_i]\n",
    "$$\n",
    "\n",
    "where $a_i = {\\hat y_i}$.\n",
    "\n",
    "Note that $C > E$ always. "
   ]
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     "text": [
      "0.3219280948873623\n",
      "1.7369655941662063\n"
     ]
    }
   ],
   "source": [
    "#Correct prediction\n",
    "y = [0, 0, 1]\n",
    "yhat = [0.1, 0.1, 0.8]\n",
    "crossentropy = -sum(y*log2(yhat))\n",
    "print(crossentropy)\n",
    "\n",
    "#Wrong prediction\n",
    "yhat = [0.1, 0.6, 0.3]\n",
    "crossentropy = -sum(y*log2(yhat))\n",
    "print(crossentropy)"
   ]
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   "source": [
    "### Kullback-Leibler Divergence\n",
    "\n",
    "$$\n",
    "KL = \\sum_i y_i \\cdot \\log \\left(\\frac{y_i}{\\hat{y_i}} \\right)\n",
    "$$\n",
    "\n",
    "Measures the extra bits required if the wrong selection is made. "
   ]
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     "text": [
      "-0.32192809488736235\n",
      "-1.7369655941662063\n"
     ]
    }
   ],
   "source": [
    "#Correct prediction\n",
    "y = [0, 0, 1.0]\n",
    "yhat = [0.1, 0.1, 0.8]\n",
    "KL = -sum(y[2]*log2(y[2]/yhat[2]))\n",
    "print(KL)\n",
    "\n",
    "#Wrong prediction\n",
    "yhat = [0.1, 0.6, 0.3]\n",
    "KL = -sum(y[2]*log2(y[2]/yhat[2]))\n",
    "print(KL)"
   ]
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   "source": [
    "![](images/Gradient_descent.png)"
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   "source": [
    "## Batch Stochastic Gradient\n",
    "\n",
    "![](images/batch_stochastic_gradient.png)"
   ]
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   "source": [
    "1.\tInitialize all the weight and bias parameters $(w_{ij}^{(r)},b_i^{(r)})$  (this is a critical step).\n",
    "\n",
    "2.\tFor $q = 0,...,{M\\over B}-1$ repeat the following steps (2a) - (2f):\n",
    "\n",
    "a. For the training inputs $X_i(m), qB\\le m\\le (q+1)B$, compute the model predictions $y(m)$ given by\n",
    "\n",
    "$$\n",
    "a_i^{(r)}(m) = \\sum_{j=1}^{P^{r-1}} w_{ij}^{(r)}z_j^{(r-1)}(m)+b_i^{(r)} \\quad \\mbox{and} \\quad z_i^{(r)}(m) = f(a_i^{(r)}(m)), \\quad 2 \\leq r \\leq R, 1 \\leq i \\leq P^r  \n",
    "$$\n",
    "\n",
    "and for $r=1$,\n",
    "\n",
    "$$\n",
    "a_i^{(1)}(m) = \\sum_{j=1}^{P^1} w_{ij}^{(1)}x_j(m)+b_i^{(1)} \\quad \\mbox{and} \\quad z_i^{(1)}(m) = f(a_i^{(1)}(m)), \\quad  1 \\leq i \\leq N    \n",
    "$$\n",
    "\n",
    "The logits and classification probabilities are computed using\n",
    "\n",
    "$$\n",
    "a_i^{(R+1)}(m) = \\sum_{j=1}^K w_{ij}^{(R+1)}z_j^{(R)}(m)+b_i^{(R+1)} \\quad \\mbox{and} \\quad y_i(m) = \\frac{\\exp(a_i^{(R+1)}(m))}{\\sum_{k=1}^K \\exp(a_k^{(R+1)}(m))}, \\quad  1 \\leq i \\leq K   \n",
    "$$\n",
    "\n",
    "This step constitutes the _forward pass_ of the algorithm."
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    "b. Evaluate the gradients $\\delta_k^{(R+1)}(m)$ for the logit layer nodes using\n",
    "\n",
    "$$\n",
    "\\delta_k^{(R+1)}(m) = y_k(m) - t_k(m),\\ \\ 1\\le k\\le K\n",
    "$$\n",
    "\n",
    "This step and the following one constitute the start of the backward pass of the algorithm, in which we compute the gradients $\\delta_k^{(r)}, 1 \\leq k \\leq K, 1\\le r\\le R$ for all the hidden nodes.\n",
    "\n",
    "c. Back-propagate the $\\delta$s using the following equation to obtain the $\\delta_j^{(r)}(m), 1 \\leq r \\leq R, 1 \\leq j \\leq P^r$  for each hidden node in the network.\n",
    "\n",
    "$$\n",
    "\\delta_j^{(r)}(m) = f'(a_j^{(r)}(m)) \\sum_k w_{kj}^{(r+1)} \\delta_k^{(r+1)}(m), \\quad 1 \\leq r \\leq R\n",
    "$$\n"
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   "source": [
    "d. Compute the gradients of the Cross Entropy Function $\\mathcal L(m)$ for the $m$-th training vector $(X{(m)}, T{(m)})$ with respect to all the weight and bias parameters using the following equation.\n",
    "\n",
    "$$\n",
    "\\frac{\\partial\\mathcal L(m)}{\\partial w_{ij}^{(r+1)}} = \\delta_i^{(r+1)}(m) z_j^{(r)}(m) \\quad \\mbox{and} \\quad \\frac{\\partial \\mathcal L(m)}{\\partial b_i^{(r+1)}} = \\delta_i^{(r+1)}(m), \\quad 0 \\leq r \\leq R\n",
    "$$\n",
    "\n",
    "e. Change the model weights according to the formula\n",
    "\n",
    "$$\n",
    "w_{ij}^{(r)} \\leftarrow w_{ij}^{(r)} - \\frac{\\eta}{B}\\sum_{m=qB}^{(q+1)B} \\frac{\\partial\\mathcal L(m)}{\\partial w_{ij}^{(r)}},  \n",
    "$$\n",
    "\n",
    "$$\n",
    "b_i^{(r)} \\leftarrow b_i^{(r)} - \\frac{\\eta}{B}\\sum_{m=qB}^{(q+1)B} \\frac{\\partial{\\mathcal L}(m)}{\\partial b_i^{(r)}},\n",
    "$$\n",
    "\n",
    "f. Increment $q\\leftarrow (q+1)\\mod B$ and go back to step $(a)$."
   ]
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   "source": [
    "Compute the Loss Function $L$ over the Validation Dataset given by\n",
    "\n",
    "$$\n",
    "L = -{1\\over V}\\sum_{m=1}^V\\sum_{k=1}^K t_k{(m)} \\log y_k{(m)}\n",
    "$$\n",
    "\n",
    "If $L$ has dropped below some threshold, then stop. Otherwise go back to Step 2."
   ]
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   "source": [
    "## Gradient Descent Example\n",
    "\n",
    "![](images/Gradient_Descent_Scheme.png)"
   ]
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fbd2550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f(x):\n",
    "    return 3*x**2 -5*x + 10\n",
    "\n",
    "x = linspace(-4,4,100)\n",
    "plot(x,f(x))\n",
    "grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-1.8501500000001698 29.519915067502733\n",
      "-1.0452550000002532 18.503949045077853\n",
      "-0.4818285000003115 13.105618610239208\n",
      "-0.08742995000019249 10.460081738472072\n",
      "0.18864903499989083 9.163520200219716\n",
      "0.3819043244999847 8.528031116715445\n",
      "0.5171830271499616 8.216519714966186\n",
      "0.6118781190049631 8.06379390252634\n",
      "0.6781646833034642 7.988898596522943\n",
      "0.7245652783124417 7.95215813604575\n",
      "0.7570456948186948 7.934126078037087\n",
      "0.7797819863730542 7.925269906950447\n",
      "0.7956973904611502 7.920916059254301\n",
      "0.8068381733227685 7.918772647178622\n",
      "0.8146367213259147 7.917715356568335\n",
      "0.8200957049281836 7.917192371084045\n",
      "0.8239169934497053 7.916932669037079\n",
      "0.8265918954147882 7.9168030076222955\n",
      "0.8284643267903373 7.916737788340814\n",
      "0.8297750287532573 7.916704651261121\n"
     ]
    }
   ],
   "source": [
    "dx = 0.001\n",
    "eta = 0.05  #learning rate\n",
    "x = -3\n",
    "for j in range(20):\n",
    "    df_dx = (f(x+dx)-f(x))/dx\n",
    "    x = x - eta*df_dx\n",
    "    print(x,f(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Vanishing Gradients\n",
    "\n",
    "- In large problems, gradients simply vanish too soon before training has reached an acceptable level of accuracy. \n",
    "\n",
    "- There are several issues with gradient descent that need handling, and to solve this, there are several fixes that may be applied. \n",
    "\n",
    "- Learning rate $\\eta$ may be too large or too small.\n",
    "\n",
    "![](images/LearningRate_Matters.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Gradients in Multiple Dimensions\n",
    "\n",
    "![](images/GD_MultipleDimensions.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Saddle Points\n",
    "\n",
    "<img src=\"images/GD_saddle.png\" height=\"100\" width=\"300\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Effect of the Learning Rate\n",
    "\n",
    "The idea is to start with a high learning rate and then adaptively reduce it as we get closer to the minimum of the loss function. \n",
    "\n",
    "![](images/LearningRateAnnealing.png)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Annealing\n",
    "\n",
    "Reduce the learning rate as a step function when the reduction in the loss function begins to plateau.\n",
    "\n",
    "![](images/LearningRateAnnealing2.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Learning Rate Algorithms\n",
    "\n",
    "- Improve the speed of convergence (for example the Momentum, Nesterov Momentum, and Adam algorithms).\n",
    "\n",
    "- Adapt the effective Learning Rate as the training progresses (for example the ADAGRAD, RMSPROP and Adam algorithms).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Momentum\n",
    "\n",
    "Fixes the problem where the gradient is multidimensional and has a fast gradient on some axes and a slow one on the others. \n",
    "\n",
    "At the end of the $n^{th}$ iteration of the Backprop algorithm, define a sequence $v(n)$ by\n",
    "\n",
    "$$\n",
    "v(n) = \\rho\\; v(n-1) - \\eta \\; g(n), \\quad \\quad v(0)=0\n",
    "$$\n",
    "\n",
    "where $\\rho$ is new hyper-parameter called the \"momentum\" parameter, and $g(n)$ is the gradient evaluated at parameters value $w(n)$, defined by\n",
    "\n",
    "$$\n",
    "g(n) = \\frac{\\partial {\\mathcal L(n)}}{\\partial w}\n",
    "$$\n",
    "\n",
    "for Stochastic Gradient Descent and \n",
    "\n",
    "$$\n",
    "g(n) = {1\\over B}\\sum_{m=nB}^{(n+1)B}\\frac{\\partial {\\mathcal L(m)}}{\\partial w}\n",
    "$$\n",
    "\n",
    "for Batch Stochastic Gradient Descent (note that in this case $n$ is an index into the batch number). \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The change in parameter values on each iteration is now defined as\n",
    "\n",
    "\\begin{equation}\n",
    "w(n+1) = w(n) + v(n)  \n",
    "\\end{equation}\n",
    "\n",
    "It can be shown from these equations that $v(n)$ can be written as\n",
    "\n",
    "\\begin{equation}\n",
    "v(n) = - \\eta\\sum_{i=0}^{n-1} \\rho^{n-i} g(i)   \n",
    "\\end{equation}\n",
    "\n",
    "so that\n",
    "\n",
    "\\begin{equation}\n",
    "w(n+1) = w(n) - \\eta\\sum_{i=0}^{n-1} \\rho^{n-i} g(i)   \n",
    "\\end{equation}\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Behavior of Momentum Parameter\n",
    "\n",
    "When the momentum parameter $\\rho = 0$, then this equation reduces to the usual Stochastic Gradient Descent iteration. On the other hand, when $\\rho > 0$, then we get some interesting behaviors:\n",
    "\n",
    "- If the gradients $g(i)$ are such that they change sign frequently (as in the steep side of the loss surface), then the stepsize $\\sum_{i=0}^n \\rho^{n-i}g(i)$ will be small. Thus the change in these parameters with the number of iterations will limited.\n",
    "\n",
    "- If the gradients $g(i)$ are such that they maintain their sign (as in the shallow portion of the loss surface), then the stepsize $\\sum_{i=0}^n \\rho^{n-i}g(i)$ will be large. This means that if the gradients maintain their sign then the corresponding parameters will take bigger and bigger steps as the algorithm progresses, even though the individual gradients may be small."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Properties of the Momentum algorithm\n",
    "\n",
    "- The Momentum algorithm thus accelerates parameter convergence for parameters whose gradients consistently point in the same direction, and slows parameter change for parameters whose gradient changes sign frequently, thus resulting in faster convergence.\n",
    "- The variable $v(n)$ is analogous to velocity in a dynamical system, while the parameter $1-\\rho$ plays the role of the co-efficient of friction. \n",
    "- The value of $\\rho$ determines the degree of momentum, with the momentum becoming stronger as $\\rho$ approaches $1$. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Note that\n",
    "$$\n",
    "\\sum_{i=0}^{n} \\rho^{n-i}g(i) \\le {g_{max}\\over 1-\\rho}\n",
    "$$\n",
    "$\\rho$ is usually set to the neighborhood of $0.9$ and from the above equation it follows that\n",
    "$\\sum_{i=0}^n \\rho^{n-i}g(i)\\approx 10g$ assuming all the $g(i)$ are approximately equal to $g$.  Hence the effective gradient is ten times the value of the actual gradient. This results in an \"overshoot\" where the value of the parameter shoots past the minimum point to the other side of the bowl, and then reverses itself. This is a desirable behavior since it prevents the algorithm from getting stuck at a saddle point or a local minima, since the momentum carries it out from these areas."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Nesterov Momentum\n",
    "\n",
    "1.  Recall that the Momentum parameter update equations can be written as:\n",
    "$$\n",
    "v(n) = \\rho\\; v(n-1) - \\eta \\; g(w(n))\n",
    "$$\n",
    "$$\n",
    "w(n+1) = w(n) + v(n) \n",
    "$$\n",
    "2. These equations can be improved by evaluation of the gradient at parameter value $w(n+1)$ instead. \n",
    "3. Circular? in order to compute $w(n+1)$ we first need to compute $g(w(n))$. \n",
    "$$\n",
    "w(n+1)\\approx w(n) + \\rho v(n-1) \n",
    "$$\n",
    "4. Gives the velocity update equation for Nesterov Momentum\n",
    "$$\n",
    "v(n) = \\rho\\; v(n-1) - \\eta \\; g(w(n)+\\rho v(n-1))\n",
    "$$\n",
    "where $g(w(n)+\\rho v(n-1))$ denotes the gradient computed at parameter values $w(n) + \\rho v(n-1)$. \n",
    "5. Gradient Descent process speeds up considerably when compared to the plain Momentum method."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## The ADAGRAD Algorithm\n",
    "\n",
    "1. Parameter update rule:\n",
    "\\begin{equation}\n",
    "w(n+1) = w(n) - \\frac{\\eta}{\\sqrt{\\sum_{i=1}^n g(n)^2+\\epsilon}}\\; g(n) \n",
    "\\end{equation}\n",
    "\n",
    "2. Constant $\\epsilon$ has been added to better condition the denominator and is usually set to a small number such $10^{-7}$.\n",
    "\n",
    "3. Each parameter gets its own adaptive Learning Rate, such that large gradients have smaller learning rates and small gradients have larger learning rates ($\\eta$ is usually defaulted to $0.01$). As a result the progress along each dimension evens out over time, which helps the training process. \n",
    "\n",
    "4. The change in rates happens automatically as part of the parameter update equation.\n",
    "\n",
    "5. Downside: accumulation of gradients in the denominator leads to the continuous decrease in Learning Rates which can lead to a halt of training in large networks that require a greater number of iterations. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## The RMSPROP Algorithm\n",
    "\n",
    "1. Accumulates the sum of gradients using a sliding window:\n",
    "$$\n",
    "E[g^2]_n = \\rho E[g^2]_{n-1} + (1-\\rho) g(n)^2\n",
    "$$\n",
    "where $\\rho$ is a decay constant (usually set to $0.9$). This operation (called a Low Pass Filter) has a windowing effect, since it forgets gradients that are far back in time. \n",
    "2. The quantity $RMS[g]_n$ defined by\n",
    "$$\n",
    "RMS[g]_n = \\sqrt{E[g^2]_n + \\epsilon}\n",
    "$$\n",
    "\\begin{equation}\n",
    "w(n+1) = w(n) - \\frac{\\eta}{RMS[g]_n}\\; g(n)  \n",
    "\\end{equation}\n",
    "3. Note that\n",
    "$$\n",
    "E[g^2]_n = (1-\\rho)\\sum_{i=0}^n \\rho^{n-i} g(i)^2 \\le \\frac{g_{max}}{1-\\rho}\n",
    "$$\n",
    "which shows that the parameter $\\rho$ prevents the sum from blowing up, and a large value of $\\rho$ is equivalent to using a larger window of previous gradients in computing the sum. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## The ADAM Algorithm\n",
    "\n",
    "1. The Adaptive Moment Estimation (Adam) algorithm combines the best of algorithms such as Momentum that speed up the training process, with algorithms such as RMSPROP that adaptively vary the effective Learning Rate.\n",
    "\n",
    "$$\n",
    "\\Lambda(n) = \\beta\\Lambda(n-1) +(1-\\beta)g(n),\\ \\ \\ {\\hat\\Gamma}(n) = \\frac{\\Gamma(n)}{1-\\beta^n}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\Delta(n) = \\alpha\\Delta(n-1) + (1-\\alpha) g(n)^2,\\ \\ \\ {\\hat\\Delta}(n) = \\frac{\\Delta(n)}{1-\\alpha^n}\n",
    "$$\n",
    "\n",
    "$$\n",
    "w(n+1) = w(n) - \\eta\\frac{\\hat\\Lambda(n)}{\\sqrt{\\hat\\Delta(n) + \\epsilon}}\n",
    "$$\n",
    "\n",
    "2. $\\Delta(n)$ is identical to that of $E[g^2]_n$ in the RMSPROP, and it serves an identical purpose, i.e., rates for parameters with larger gradients are equalized with those for parameters with smaller gradients.\n",
    "\n",
    "3. The sequence $\\Lambda(n)$ is used to provide \"Momentum\" to the updates, and works in a fashion similar to the velocity sequence $v(n)$ in the Momentum algorithm.\n",
    "\n",
    "$$\n",
    "\\Lambda(n) = (1-\\rho)\\sum_{i=0}^n \\rho^{n-i} g(i) \\le \\frac{g_{max}}{1-\\rho}\n",
    "$$\n",
    "\n",
    "4. The parameters $\\alpha$ and $\\beta$ are usually defaulted to $10^{-8}$ and $0.999$ respectively."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "X2yeLvACV2J5",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "![](images/Chain_rule.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Df1hKlsFV2J7",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "![](images/Delta_values.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "yYel-DBjV2J7",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "![](images/Output_layer.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "DFaIaejRV2J8",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "![](images/Feedforward_Backprop.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "taA3tvKsV2J9",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "![](images/Recap.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "lS7OMpxhV2J-",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "![](images/Backprop_one_slide.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Back to Activation Functions (Vanishing Gradients)\n",
    "\n",
    "![](images/sigmoid_activation.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## tanh Activation\n",
    "\n",
    "![](images/tanh_activation.png)\n",
    "\n",
    "1. Unless the input is in the neghborhood of zero, the function enters its saturated regime. \n",
    "\n",
    "2. It is superior to the sigmoid in one respect, i.e., its output is zero centered. This  speeds up the training process. \n",
    "\n",
    "3. The $\\tanh$ function is rarely used in modern DLNs, the exception being a type DLN called LSTM."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## ReLU Activation\n",
    "\n",
    "![](images/relu_activation.png)\n",
    "\n",
    "$$\n",
    "z = \\max(0,a)\n",
    "$$\n",
    "\n",
    "1. No saturation problem. \n",
    "\n",
    "2. Gradients $\\frac{\\partial L}{\\partial w}$ propagate undiminished through the network, provided all the nodes are active."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Dead ReLU Problem\n",
    "\n",
    "![](images/dead_relu.png)\n",
    "\n",
    "1. The dotted line in this figure shows a case in which the weight parameters $w_i$ are such that the hyperplane $\\sum w_i z_i$ does not intersect the \"data cloud\" of possible input activations. This implies that there does not exist any possible input values that can lead to $\\sum w_i z_i > 0$. Hence the neuron's output activation will always be zero, and it will kill all gradients backpropagating down from higher layers.\n",
    "\n",
    "2. Vary initialization to correct this. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Leaky ReLU\n",
    "\n",
    "![](images/leaky_relu.png)\n",
    "\n",
    "$$\n",
    "z = \\max(ca,a),\\ \\ 0\\le c<1\n",
    "$$\n",
    "\n",
    "- Fixes the dead ReLU problem. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## PreLU \n",
    "\n",
    "![](images/prelu.png)\n",
    "\n",
    "$$\n",
    "z_i = \\max(\\beta_i a_i,a_i), \\quad 1 \\le i \\le S\n",
    "$$\n",
    "\n",
    "1. Instead of deciding on the value of $c$ through experimentation, why not determine it using Backpropagation as well. This is the idea behind the Pre-ReLU or PReLU function.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Note that each neuron $i$ now has its own parameter $\\beta_i, 1\\le i\\le S$, where $S$ is the number of nodes in the network. These parameters are iteratively estimated using Backprop.\n",
    "\n",
    "$$\n",
    "\\frac{\\partial\\mathcal L}{\\partial\\beta_i} = \\frac{\\partial\\mathcal L}{\\partial z_i}\\frac{\\partial z_i}{\\partial\\beta_i},\\ \\ 1\\le i\\le S\n",
    "$$\n",
    "\n",
    "Substituting the value for $\\frac{\\partial z_i}{\\partial\\beta_i}$ we obtain\n",
    "$$\n",
    "\\frac{\\partial\\mathcal L}{\\partial\\beta_i} = a_i\\frac{\\partial\\mathcal L}{\\partial z_i}\\ \\ if\\ a_i \\le 0\\ \\ \\mbox{and} \\ \\ 0 \\ \\ \\mbox{otherwise}\n",
    "$$\n",
    "\n",
    "which is then used to update $\\beta_i$ using $\\beta_i\\rightarrow\\beta_i - \\eta\\frac{\\partial\\mathcal L}{\\partial\\beta_i}$.\n",
    "\n",
    "Once training is complete, the PreLU based DLN network ends up with a different value of $\\beta_i$ at each neuron, which increases the flexibility of the network at the cost of an increase in the number of parameters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Maxout\n",
    "\n",
    "![](images/maxout.png)\n",
    "\n",
    "Generalizes Leaky ReLU. \n",
    "\n",
    "$$\n",
    "z'_i = \\max(c\\big[\\sum_j w_{ij}z_j +b_i\\big],\\sum_j w_{ij}z_j +b_i),\n",
    "$$\n",
    "\n",
    "We may allow the two hyperplanes to be independent with their own set of parameters, as shown in the Figure above."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Initializing Weights\n",
    "\n",
    "In practice, the DLN weight parameters are initialized with random values drawn from Gaussian or Uniform distributions and the following rules are used: \n",
    "\n",
    "- Guassian Initialization: If the weight is between layers with $n_{in}$ input neurons and $n_{out}$ output neurons, then they are initialized using a Gaussian random distribution with mean zero and standard deviation $\\sqrt{2\\over n_{in}+n_{out}}$. \n",
    "\n",
    "- Uniform Initialization: In the same configuration as above, the weights should be initialized using an Uniform distribution between $-r$ and $r$, where $r = \\sqrt{6\\over n_{in}+n_{out}}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "When using the ReLU or its variants, these rules have to be modified slightly:\n",
    "\n",
    "- Guassian Initialization: If the weight is between layers with $n_{in}$ input neurons and $n_{out}$ output neurons, then they are initialized using a Gaussian random distribution with mean zero and standard deviation $\\sqrt{4\\over n_{in}+n_{out}}$. \n",
    "\n",
    "- Uniform Initialization: In the same configuration as above, the weights should be initialized using an Uniform distribution between $-r$ and $r$, where $r = \\sqrt{12\\over n_{in}+n_{out}}$.\n",
    "\n",
    "The reasoning behind scaling down the initialization values as the number of incident weights increases is to prevent saturation of the node activations during the forward pass of the Backprop algorithm, as well as large values of the gradients during backward pass. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Data Preprocessing\n",
    "\n",
    "![](images/data_preprocessing.png)\n",
    "\n",
    "**Centering**: This is also sometimes called Mean Subtraction, and is the most common form of preprocessing. Given an input dataset consisting of $M$ vectors $X(m) = (x_1(m),...,x_N(m)), m = 1,...,M$, it consists of subtracting the mean across each individual input component $x_i, 1\\leq i\\leq N$ such that\n",
    "$$\n",
    "x_i(m) \\leftarrow x_i(m) - \\frac{\\sum_{s=1}^{M}x_i(s)}{M},\\ \\ 1\\leq i\\leq N, 1\\le m\\le M\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**Scaling**: After the data has been centered, it can be scaled in one of two ways:\n",
    "\n",
    "+ By dividing by the standard deviation, once again along each dimension, so that the overall transform is\n",
    "        \n",
    "$$\n",
    "x_i(m) \\leftarrow \\frac{x_i(m) - - \\frac{\\sum_{s=1}^{M}x_i(s)}{M}}{\\sigma_i},\\ \\ 1\\leq i\\leq N, 1\\le m\\le M\n",
    "$$\n",
    "\n",
    "+ By Normalizing each dimension so that the min and max along each axis are -1 and +1 repectively.\n",
    "   \n",
    "- In general Scaling helps optimization because it balances out the rate at which the weights connected to the input nodes learn."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Zero Centering Helps\n",
    "\n",
    "![](images/zero_centering_helps.png)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Recall that for a K-ary Linear Classifier, the parameter update equation is given by:\n",
    "\n",
    "$$\n",
    "w_{kj} \\leftarrow w_{kj} - \\eta x_j(y_k-t_k),\\ \\ 1\\le k\\le K,\\ \\ 1\\le j\\le N\n",
    "$$\n",
    "\n",
    "If the training sample is such that $t_q = 1$ and $t_k = 0, j\\ne q$, then the update becomes:\n",
    "\n",
    "$$\n",
    "w_{qj} \\leftarrow w_{qj} - \\eta x_j(y_q-1)\n",
    "$$\n",
    "\n",
    "and\n",
    "\n",
    "$$ \n",
    "w_{kj} \\leftarrow w_{kj} - \\eta x_j(y_k),\\ \\ k\\ne q\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Lets assume that the input data is not centered so that $x_j\\ge 0, j=1,...,N$. Since $0\\le y_k\\le 1$ it follows that \n",
    "\n",
    "$$\n",
    "\\Delta w_{kj} = -\\eta x_jy_k <0, k\\ne q\n",
    "$$ \n",
    "\n",
    "and \n",
    "\n",
    "$$\n",
    "\\Delta w_{qj} = -\\eta x_j(y_q - 1) > 0\n",
    "$$ \n",
    "\n",
    "i.e. the update results in all the weights moving in the same direction, except for one. This is shown graphically in the Figure above, in which the system is trying move in the direction of the blue arrow which is the quickest path to the minimum. However if the input data is not centered, then it is forced to move in a zig-zag fashion as shown in the red-curve.The zig-zag motion is caused due to the fact that all the parameters move in the same direction at each step due to the lact of zero-centering in the input data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Batch Normalization\n",
    "\n",
    "Normalization applied to the hidden layers. \n",
    "\n",
    "![](images/batch_normalization.png)\n",
    "\n",
    "* It enables higher learning rates: In a non-normalized network, a large learning rate can lead to oscillations and cause the loss function increase rather than decrease. \n",
    "\n",
    "* It enables better Gradient Propagation through the network, thus enabling DLNs with more hidden layers.\n",
    "\n",
    "* It helps to reduce strong dependencies on the parameter initialization values.\n",
    "\n",
    "* It helps to regularize the model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "collapsed": true,
    "id": "szakpJ4cV2J_",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Under and Over-fitting\n",
    "\n",
    "![](images/underoverfitting.png)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "collapsed": true,
    "id": "k7JQUIdAV2KD",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Regularization\n",
    "\n",
    "* Early Stopping\n",
    "\n",
    "* L1 Regularization\n",
    "\n",
    "* L2 Regularization\n",
    "\n",
    "* Dropout Regularization\n",
    "\n",
    "* Training Data Augmentation\n",
    "\n",
    "* Batch Normalization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Early Stopping\n",
    "\n",
    "![](images/early_stopping.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## L2 Regularization\n",
    "\n",
    "L2 Regularization is a commonly used technique in ML systems is also sometimes referred to as “Weight Decay”. It works by adding a quadratic term to the Cross Entropy Loss Function $\\mathcal L$, called the Regularization Term, which results in a new Loss Function $\\mathcal L_R$ given by:\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathcal L_R = {\\mathcal L} + \\frac{\\lambda}{2} \\sum_{r=1}^{R+1} \\sum_{j=1}^{P^{r-1}} \\sum_{i=1}^{P^r} (w_{ij}^{(r)})^2  \n",
    "\\end{equation}\n",
    "\n",
    "L2 Regularization also leads to more \"diffuse\" weight parameters, in other words, it encourages the network to use all its inputs a little rather than some of its inputs a lot. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## L1 Regularization\n",
    "\n",
    "L1 Regularization uses a Regularization Function which is the sum of the absolute value of all the weights in DLN, resulting in the following loss function ($\\mathcal L$ is the usual Cross Entropy loss):\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathcal L_R = \\mathcal L + {\\lambda} \\sum_{r=1}^{R+1} \\sum_{j=1}^{P^{r-1}} \\sum_{i=1}^{P^r} |w_{ij}^{(r)}|  (\\#eq:L1reg)\n",
    "\\end{equation}\n",
    "\n",
    "At a high level L1 Regularization is similar to L2 Regularization since it leads to smaller weights."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "1. Both L1 and L2 Regularizations lead to a reduction in the weights with each iteration. However the way the weights drop is different: \n",
    "\n",
    "2. In L2 Regularization the weight reduction is multiplicative and proportional to the value of the weight, so it is faster for large weights and de-accelerates as the weights get smaller. \n",
    "\n",
    "3. In L1 Regularization on the other hand, the weights are reduced by a fixed amount in every iteration, irrespective of the value of the weight. Hence for larger weights L2 Regularization is faster than L1, while for smaller weights the reverse is true. \n",
    "\n",
    "4. As a result L1 Regularization leads to DLNs in which the weight of most of the connections tends towards zero, with a few connections with larger weights left over. This type of DLN that results after the application of L1 Regularization is said to be “sparse”."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Dropout regularization\n",
    "\n",
    "![](images/dropout.png)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The basic idea behind Dropout is to run each iteration of the Backprop algorithm on randomly modified versions of the original DLN. The random modifications are carried out to the topology of the DLN using the following rules: \n",
    "\n",
    "-\tAssign probability values $p^{(r)}, 0 \\leq r \\leq R$, which is defined as the probability that a node is present in the model, and use these to generate $\\{0,1\\}$-valued Bernoulli random variables $e_j^{(r)}$:\n",
    "\n",
    "$$\n",
    "e_j^{(r)} \\sim Bernoulli(p^{(r)}), \\quad 0 \\leq r \\leq R,\\ \\  1 \\leq j \\leq P^r\n",
    "$$\n",
    "\n",
    "-\tModify the input vector as follows:\n",
    "\n",
    "\\begin{equation}\n",
    "\\hat x_j = e_j^{(0)} x_j, \\quad 1 \\leq j \\leq N   \n",
    "\\end{equation}\n",
    "\n",
    "- Modify the activations $z_j^{(r)}$ of the hidden layer r as follows:\n",
    "\n",
    "\\begin{equation}\n",
    "\\hat z_j^{(r)} = e_j^{(r)} z_j^{(r)}, \\quad 1 \\leq r \\leq R,\\ \\  1 \\leq j \\leq P^r   \n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "1. After the Backprop is complete, we have effectively trained a collection of up to $2^s$ thinned DLNs all of which share the same weights, where $s$ is the total number of hidden nodes in the DLN. \n",
    "\n",
    "2. In order to test the network, strictly speaking we should be averaging the results from all these thinned models, however a simple approximate averaging method works quite well. \n",
    "\n",
    "3. The main idea is to use the complete DLN as the test network."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Bagging (Ensemble Learning)\n",
    "\n",
    "![](images/bagging.png)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "wt-gcntLV2J-",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "![](images/TensorFlow_playground.png)\n",
    "\n",
    "http://playground.tensorflow.org/"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "9Dlk0NQqV2KG",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Pattern Recognition: Cancer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "nUzwo8kXV2KH",
    "outputId": "ec109240-6b58-4dcd-ca9b-14e7e2000fdb",
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "SFDAmTIdV2KN",
    "outputId": "4eb081d5-1a07-4bb3-a476-e34ab4a9a2e5",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Id</th>\n",
       "      <th>Cl.thickness</th>\n",
       "      <th>Cell.size</th>\n",
       "      <th>Cell.shape</th>\n",
       "      <th>Marg.adhesion</th>\n",
       "      <th>Epith.c.size</th>\n",
       "      <th>Bare.nuclei</th>\n",
       "      <th>Bl.cromatin</th>\n",
       "      <th>Normal.nucleoli</th>\n",
       "      <th>Mitoses</th>\n",
       "      <th>Class</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1000025</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>benign</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1002945</td>\n",
       "      <td>5</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>10</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>benign</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1015425</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>benign</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1016277</td>\n",
       "      <td>6</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "      <td>benign</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1017023</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>benign</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Id  Cl.thickness  Cell.size  Cell.shape  Marg.adhesion  Epith.c.size  \\\n",
       "0  1000025             5          1           1              1             2   \n",
       "1  1002945             5          4           4              5             7   \n",
       "2  1015425             3          1           1              1             2   \n",
       "3  1016277             6          8           8              1             3   \n",
       "4  1017023             4          1           1              3             2   \n",
       "\n",
       "   Bare.nuclei  Bl.cromatin  Normal.nucleoli  Mitoses   Class  \n",
       "0            1            3                1        1  benign  \n",
       "1           10            3                2        1  benign  \n",
       "2            2            3                1        1  benign  \n",
       "3            4            3                7        1  benign  \n",
       "4            1            3                1        1  benign  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Read in the data set\n",
    "data = pd.read_csv(\"data/BreastCancer.csv\")\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "0VC69V92V2KQ",
    "outputId": "01b961d2-f12a-49b8-92ed-0460b3abf5c3",
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   Cl.thickness  Cell.size  Cell.shape  Marg.adhesion  Epith.c.size  \\\n",
      "0             5          1           1              1             2   \n",
      "1             5          4           4              5             7   \n",
      "2             3          1           1              1             2   \n",
      "3             6          8           8              1             3   \n",
      "4             4          1           1              3             2   \n",
      "\n",
      "   Bare.nuclei  Bl.cromatin  Normal.nucleoli  Mitoses  \n",
      "0            1            3                1        1  \n",
      "1           10            3                2        1  \n",
      "2            2            3                1        1  \n",
      "3            4            3                7        1  \n",
      "4            1            3                1        1  \n",
      "0    benign\n",
      "1    benign\n",
      "2    benign\n",
      "3    benign\n",
      "4    benign\n",
      "Name: Class, dtype: object\n"
     ]
    }
   ],
   "source": [
    "x = data.loc[:,'Cl.thickness':'Mitoses']\n",
    "print(x.head())\n",
    "y = data.loc[:,'Class']\n",
    "print(y.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "TmWrZ0IXV2KS",
    "outputId": "896ab9d5-7d33-4d6e-fa07-45261bdc251f",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.],\n",
       "       [0.],\n",
       "       [0.],\n",
       "       [0.],\n",
       "       [0.],\n",
       "       [1.],\n",
       "       [0.],\n",
       "       [0.],\n",
       "       [0.],\n",
       "       [0.]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Convert the class variable into binary numeric\n",
    "ynum = zeros((len(x),1))\n",
    "for j in arange(len(y)):\n",
    "    if y[j]==\"malignant\":\n",
    "        ynum[j]=1\n",
    "ynum[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "JBii4baCV2KW",
    "outputId": "e7395100-4913-4c40-b6a1-b6e21946b5f8",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/srdas/anaconda3/lib/python3.6/site-packages/h5py/__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n",
      "  from ._conv import register_converters as _register_converters\n",
      "Using TensorFlow backend.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 0.]\n",
      " [1. 0.]\n",
      " [1. 0.]\n",
      " [1. 0.]\n",
      " [1. 0.]\n",
      " [0. 1.]\n",
      " [1. 0.]\n",
      " [1. 0.]\n",
      " [1. 0.]\n",
      " [1. 0.]]\n",
      "(683, 9)\n",
      "(683, 2)\n",
      "(683, 1)\n"
     ]
    }
   ],
   "source": [
    "## Make label data have 1-shape, 1=malignant\n",
    "from keras import utils\n",
    "y.labels = utils.to_categorical(ynum, num_classes=2)\n",
    "#x = x.as_matrix()\n",
    "print(y.labels[:10])\n",
    "print(shape(x))\n",
    "print(shape(y.labels))\n",
    "print(shape(ynum))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "uqrp-OBEV2Ka",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "## Define the neural net and compile it\n",
    "from keras.models import Sequential\n",
    "from keras.layers import Dense, Activation\n",
    "\n",
    "model = Sequential()\n",
    "model.add(Dense(32, activation='relu', input_dim=9))\n",
    "model.add(Dense(32, activation='relu'))\n",
    "model.add(Dense(32, activation='relu'))\n",
    "model.add(Dense(1, activation='sigmoid'))\n",
    "model.compile(optimizer='rmsprop',\n",
    "              loss='binary_crossentropy',\n",
    "              metrics=['accuracy'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "wCBy6RkdV2Kc",
    "outputId": "b1d35cf1-4bba-40ba-ca55-c6cb3211870d",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/25\n",
      " - 0s - loss: 0.6186 - acc: 0.5476\n",
      "Epoch 2/25\n",
      " - 0s - loss: 0.4578 - acc: 0.8946\n",
      "Epoch 3/25\n",
      " - 0s - loss: 0.3477 - acc: 0.9151\n",
      "Epoch 4/25\n",
      " - 0s - loss: 0.2756 - acc: 0.9458\n",
      "Epoch 5/25\n",
      " - 0s - loss: 0.2359 - acc: 0.9444\n",
      "Epoch 6/25\n",
      " - 0s - loss: 0.2116 - acc: 0.9414\n",
      "Epoch 7/25\n",
      " - 0s - loss: 0.1978 - acc: 0.9502\n",
      "Epoch 8/25\n",
      " - 0s - loss: 0.1680 - acc: 0.9561\n",
      "Epoch 9/25\n",
      " - 0s - loss: 0.1535 - acc: 0.9649\n",
      "Epoch 10/25\n",
      " - 0s - loss: 0.1389 - acc: 0.9649\n",
      "Epoch 11/25\n",
      " - 0s - loss: 0.1416 - acc: 0.9561\n",
      "Epoch 12/25\n",
      " - 0s - loss: 0.1184 - acc: 0.9649\n",
      "Epoch 13/25\n",
      " - 0s - loss: 0.1204 - acc: 0.9649\n",
      "Epoch 14/25\n",
      " - 0s - loss: 0.1076 - acc: 0.9678\n",
      "Epoch 15/25\n",
      " - 0s - loss: 0.0929 - acc: 0.9678\n",
      "Epoch 16/25\n",
      " - 0s - loss: 0.0966 - acc: 0.9707\n",
      "Epoch 17/25\n",
      " - 0s - loss: 0.0902 - acc: 0.9736\n",
      "Epoch 18/25\n",
      " - 0s - loss: 0.0809 - acc: 0.9722\n",
      "Epoch 19/25\n",
      " - 0s - loss: 0.0824 - acc: 0.9766\n",
      "Epoch 20/25\n",
      " - 0s - loss: 0.0741 - acc: 0.9766\n",
      "Epoch 21/25\n",
      " - 0s - loss: 0.0773 - acc: 0.9751\n",
      "Epoch 22/25\n",
      " - 0s - loss: 0.0657 - acc: 0.9839\n",
      "Epoch 23/25\n",
      " - 0s - loss: 0.0671 - acc: 0.9810\n",
      "Epoch 24/25\n",
      " - 0s - loss: 0.0647 - acc: 0.9780\n",
      "Epoch 25/25\n",
      " - 0s - loss: 0.0635 - acc: 0.9795\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x1134a5400>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Fit/train the model (x,y need to be matrices)\n",
    "model.fit(x, ynum, epochs=25, batch_size=32,verbose=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "QZDXxlqKV2Kg",
    "outputId": "c2f543bf-14c0-4db9-8f6e-af14242f1a49",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy =  0.9853587115666179\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[434,   0],\n",
       "       [ 10, 239]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Accuracy\n",
    "yhat = model.predict_classes(x, batch_size=32)\n",
    "acc = sum(yhat==ynum)\n",
    "print(\"Accuracy = \",acc/len(ynum))\n",
    "\n",
    "## Confusion matrix\n",
    "from sklearn.metrics import confusion_matrix\n",
    "confusion_matrix(yhat,ynum)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "KhwGxmE0V2Ki",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Another Canonical Example:  Digit Recognition (MNIST)\n",
    "\n",
    "- Extensible to many finance prediction problems. \n",
    "- Information set: 784 (28 x 28) pixels for category prediction. \n",
    "- Would you run a multinomial regression on these 784 columns. \n",
    "\n",
    "![](MNIST.png)\n",
    "\n",
    "https://www.cs.toronto.edu/~kriz/cifar.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "95m5gNX1V2Ki",
    "outputId": "eaf1583d-9b30-41b8-98db-6fb937a177de",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(60000, 785)\n",
      "(10000, 785)\n"
     ]
    }
   ],
   "source": [
    "## Read in the data set\n",
    "train = pd.read_csv(\"data/train.csv\", header=None)\n",
    "test = pd.read_csv(\"data/test.csv\", header=None)\n",
    "print(shape(train))\n",
    "print(shape(test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "uljZ25lAV2Km",
    "outputId": "25ddbe02-3031-42ac-a475-6e1168693d26",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(60000, 784)\n",
      "(60000, 1)\n",
      "(10000, 784)\n",
      "(10000, 1)\n",
      "(60000, 10)\n",
      "[[0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]\n",
      " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]]\n",
      "[[3]\n",
      " [0]\n",
      " [0]\n",
      " [2]]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/srdas/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:2: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  \n",
      "/Users/srdas/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:3: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n",
      "/Users/srdas/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:6: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  \n",
      "/Users/srdas/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:7: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  import sys\n"
     ]
    }
   ],
   "source": [
    "## Reformat the data\n",
    "X_train = train.as_matrix()[:,0:784]\n",
    "Y_train = train.as_matrix()[:,784:785]\n",
    "print(shape(X_train))\n",
    "print(shape(Y_train))\n",
    "X_test = test.as_matrix()[:,0:784]\n",
    "Y_test = test.as_matrix()[:,784:785]\n",
    "print(shape(X_test))\n",
    "print(shape(Y_test))\n",
    "y.labels = utils.to_categorical(Y_train, num_classes=10)\n",
    "print(shape(y.labels))\n",
    "print(y.labels[1:5,:])\n",
    "print(Y_train[1:5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "ajYuIw4VV2Kp",
    "outputId": "2ca6f553-5453-4053-d04c-a618553d8c06",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(Y_train); grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "FLmodhhuV2Ks",
    "outputId": "dbb810a4-7667-4c0a-f555-0345c43e1b4b",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "## Define the neural net and compile it\n",
    "from keras.models import Sequential\n",
    "from keras.layers import Dense, Activation, Dropout\n",
    "from keras.optimizers import SGD\n",
    "\n",
    "data_dim = shape(X_train)[1]\n",
    "\n",
    "model = Sequential([\n",
    "    Dense(100, input_shape=(784,)),\n",
    "    Activation('sigmoid'),\n",
    "    Dense(100),\n",
    "    Activation('sigmoid'),\n",
    "    Dense(100),\n",
    "    Activation('sigmoid'),\n",
    "    Dense(100),\n",
    "    Activation('sigmoid'),\n",
    "    Dense(10),\n",
    "    Activation('softmax'),\n",
    "])\n",
    "\n",
    "#model = Sequential()\n",
    "#model.add(Dense(100, activation='sigmoid', input_dim=data_dim))\n",
    "#model.add(Dropout(0.25))\n",
    "#model.add(Dense(100, activation='sigmoid'))\n",
    "#model.add(Dropout(0.25))\n",
    "#model.add(Dense(100, activation='sigmoid'))\n",
    "#model.add(Dropout(0.25))\n",
    "#model.add(Dense(100, activation='sigmoid'))\n",
    "#model.add(Dropout(0.25))\n",
    "#model.add(Dense(10, activation='softmax'))\n",
    "model.compile(optimizer='rmsprop',\n",
    "              loss='categorical_crossentropy',\n",
    "              metrics=['accuracy'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "hZyMJ25qV2Ku",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/10\n",
      " - 7s - loss: 0.7339 - acc: 0.7693\n",
      "Epoch 2/10\n",
      " - 7s - loss: 0.3392 - acc: 0.9016\n",
      "Epoch 3/10\n",
      " - 8s - loss: 0.2837 - acc: 0.9159\n",
      "Epoch 4/10\n",
      " - 9s - loss: 0.2514 - acc: 0.9253\n",
      "Epoch 5/10\n",
      " - 10s - loss: 0.2290 - acc: 0.9307\n",
      "Epoch 6/10\n",
      " - 9s - loss: 0.2204 - acc: 0.9336\n",
      "Epoch 7/10\n",
      " - 10s - loss: 0.2124 - acc: 0.9357\n",
      "Epoch 8/10\n",
      " - 9s - loss: 0.2053 - acc: 0.9384\n",
      "Epoch 9/10\n",
      " - 9s - loss: 0.1949 - acc: 0.9414\n",
      "Epoch 10/10\n",
      " - 9s - loss: 0.1930 - acc: 0.9415\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x1151adcf8>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Fit/train the model (x,y need to be matrices)\n",
    "model.fit(X_train, y.labels, epochs=10, batch_size=32,verbose=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "2LKRob6aV2Kx",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " \n",
      "[[5804    0   64   27    9   67   57   13   30   21]\n",
      " [   4 6577   21   19   17    8    8   36   77   26]\n",
      " [  11   42 5593   97   24   11   13   58   39   11]\n",
      " [   9   18   37 5539    0   82    0   32   79   43]\n",
      " [  11    6   54    3 5520   12   34   23   19  140]\n",
      " [  18   30   12  234    9 5063   56   14   96   49]\n",
      " [  26    6   72   15   44   68 5722    1   34    1]\n",
      " [   0   12   33   44   10   12    0 5995    7   99]\n",
      " [  34   48   62  119   22   74   28   14 5389   53]\n",
      " [   6    3   10   34  187   24    0   79   81 5506]]\n",
      "Accuracy =  0.9451333333333334\n"
     ]
    }
   ],
   "source": [
    "## In Sample\n",
    "yhat = model.predict_classes(X_train, batch_size=32)\n",
    "\n",
    "## Confusion matrix\n",
    "from sklearn.metrics import confusion_matrix\n",
    "cm = confusion_matrix(yhat,Y_train)\n",
    "print(\" \")\n",
    "print(cm)\n",
    "\n",
    "##\n",
    "acc = sum(diag(cm))/len(Y_train)\n",
    "print(\"Accuracy = \",acc)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "_pq--84CV2Ky",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " \n",
      "[[ 963    0   16    2    1   12   13    2    9    6]\n",
      " [   0 1114    2    0    3    3    1   14    8    5]\n",
      " [   1    5  959   15    5    2    5   14    4    0]\n",
      " [   1    2    9  922    0   15    0    9    9    8]\n",
      " [   0    0    8    0  929    2    4    2    6   27]\n",
      " [   3    3    2   37    1  830   14    1   16    8]\n",
      " [   7    4   15    2   13    8  914    0    9    0]\n",
      " [   1    0    6    9    2    0    0  962    3   11]\n",
      " [   4    7   13   21    2   16    7    3  897   14]\n",
      " [   0    0    2    2   26    4    0   21   13  930]]\n",
      "Accuracy =  0.942\n"
     ]
    }
   ],
   "source": [
    "## Out of Sample\n",
    "yhat = model.predict_classes(X_test, batch_size=32)\n",
    "\n",
    "## Confusion matrix\n",
    "from sklearn.metrics import confusion_matrix\n",
    "cm = confusion_matrix(yhat,Y_test)\n",
    "print(\" \")\n",
    "print(cm)\n",
    "\n",
    "##\n",
    "acc = sum(diag(cm))/len(Y_test)\n",
    "print(\"Accuracy = \",acc)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "TQrufjbWV2K0",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Learning the Black-Scholes Equation\n",
    "\n",
    "See : Hutchinson, Lo, Poggio (1994)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "V3ucg3csV2K1",
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "from scipy.stats import norm\n",
    "def BSM(S,K,T,sig,rf,dv,cp):  #cp = {+1.0 (calls), -1.0 (puts)}\n",
    "    d1 = (math.log(S/K)+(rf-dv+0.5*sig**2)*T)/(sig*math.sqrt(T))\n",
    "    d2 = d1 - sig*math.sqrt(T)\n",
    "    return cp*S*math.exp(-dv*T)*norm.cdf(d1*cp) - cp*K*math.exp(-rf*T)*norm.cdf(d2*cp)\n",
    "\n",
    "df = pd.read_csv('/Users/srdas/GoogleDrive/Papers/DeepLearning/DLinFinance/BlackScholesNN/training.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "YGijAnC8V2K3",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Normalizing spot and call prices\n",
    "$C$ is homogeneous degree one, so\n",
    "$$ aC(S,K) = C(aS,aK) $$\n",
    "This means we can normalize spot and call prices and remove  a variable by dividing by $K$.\n",
    "$$ \\frac{C(S,K)}{K} = C(S/K,1) $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "Da1RXMHGV2K3",
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "df['Stock Price'] = df['Stock Price']/df['Strike Price']\n",
    "df['Call Price']  = df['Call Price'] /df['Strike Price']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "o5L7Gzz5V2K8",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Data, libraries, activation functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "k4ZLR7r9V2K8",
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "n = 300000\n",
    "n_train =  (int)(0.8 * n)\n",
    "train = df[0:n_train]\n",
    "X_train = train[['Stock Price', 'Maturity', 'Dividends', 'Volatility', 'Risk-free']].values\n",
    "y_train = train['Call Price'].values\n",
    "test = df[n_train+1:n]\n",
    "X_test = test[['Stock Price', 'Maturity', 'Dividends', 'Volatility', 'Risk-free']].values\n",
    "y_test = test['Call Price'].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "wM-vpsjUV2K_",
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "#Import libraries\n",
    "from keras.models import Sequential\n",
    "from keras.layers import Dense, Dropout, Activation, LeakyReLU\n",
    "from keras import backend\n",
    "\n",
    "def custom_activation(x):\n",
    "    return backend.exp(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "u7XJuLGPV2LB",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Set up, compile and fit the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "mZmzJ9taV2LC",
    "outputId": "30925310-9d87-4166-90a4-9bb0d04c5144",
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 216000 samples, validate on 24000 samples\n",
      "Epoch 1/10\n",
      " - 13s - loss: 0.0061 - val_loss: 6.8796e-04\n",
      "Epoch 2/10\n",
      " - 11s - loss: 0.0015 - val_loss: 2.9255e-04\n",
      "Epoch 3/10\n",
      " - 12s - loss: 0.0011 - val_loss: 8.2461e-04\n",
      "Epoch 4/10\n",
      " - 11s - loss: 9.2878e-04 - val_loss: 4.5576e-04\n",
      "Epoch 5/10\n",
      " - 12s - loss: 8.1162e-04 - val_loss: 4.2201e-04\n",
      "Epoch 6/10\n",
      " - 11s - loss: 7.3420e-04 - val_loss: 7.7427e-05\n",
      "Epoch 7/10\n",
      " - 12s - loss: 6.8677e-04 - val_loss: 2.7576e-04\n",
      "Epoch 8/10\n",
      " - 12s - loss: 6.5881e-04 - val_loss: 4.0098e-04\n",
      "Epoch 9/10\n",
      " - 12s - loss: 6.3421e-04 - val_loss: 1.6051e-04\n",
      "Epoch 10/10\n",
      " - 14s - loss: 6.1618e-04 - val_loss: 1.9364e-04\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x11471dcc0>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nodes = 120\n",
    "model = Sequential()\n",
    "\n",
    "model.add(Dense(nodes, input_dim=X_train.shape[1]))\n",
    "#model.add(\"relu\")\n",
    "model.add(Dropout(0.25))\n",
    "\n",
    "model.add(Dense(nodes, activation='elu'))\n",
    "model.add(Dropout(0.25))\n",
    "\n",
    "model.add(Dense(nodes, activation='relu'))\n",
    "model.add(Dropout(0.25))\n",
    "\n",
    "model.add(Dense(nodes, activation='elu'))\n",
    "model.add(Dropout(0.25))\n",
    "\n",
    "model.add(Dense(1))\n",
    "model.add(Activation(custom_activation))\n",
    "          \n",
    "model.compile(loss='mse',optimizer='rmsprop')\n",
    "\n",
    "model.fit(X_train, y_train, batch_size=64, epochs=10, validation_split=0.1, verbose=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "FMBxPQIRV2LE",
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def CheckAccuracy(y,y_hat):\n",
    "    stats = dict()\n",
    "    \n",
    "    stats['diff'] = y - y_hat\n",
    "    \n",
    "    stats['mse'] = mean(stats['diff']**2)\n",
    "    print(\"Mean Squared Error:      \", stats['mse'])\n",
    "    \n",
    "    stats['rmse'] = sqrt(stats['mse'])\n",
    "    print(\"Root Mean Squared Error: \", stats['rmse'])\n",
    "    \n",
    "    stats['mae'] = mean(abs(stats['diff']))\n",
    "    print(\"Mean Absolute Error:     \", stats['mae'])\n",
    "    \n",
    "    stats['mpe'] = sqrt(stats['mse'])/mean(y)\n",
    "    print(\"Mean Percent Error:      \", stats['mpe'])\n",
    "    \n",
    "    #plots\n",
    "    mpl.rcParams['agg.path.chunksize'] = 100000\n",
    "    figure(figsize=(14,10))\n",
    "    plt.scatter(y, y_hat,color='black',linewidth=0.3,alpha=0.4, s=0.5)\n",
    "    plt.xlabel('Actual Price',fontsize=20,fontname='Times New Roman')\n",
    "    plt.ylabel('Predicted Price',fontsize=20,fontname='Times New Roman') \n",
    "    plt.show()\n",
    "    \n",
    "    figure(figsize=(14,10))\n",
    "    plt.hist(stats['diff'], bins=50,edgecolor='black',color='white')\n",
    "    plt.xlabel('Diff')\n",
    "    plt.ylabel('Density')\n",
    "    plt.show()\n",
    "    \n",
    "    return stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "lR7QWR_TV2LH",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Predict and check accuracy (in-sample)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "uWTBULkOV2LH",
    "outputId": "879863f7-cc9d-4cd6-9d35-ad47a6576f62",
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean Squared Error:       0.00019331166020661818\n",
      "Root Mean Squared Error:  0.013903656361066257\n",
      "Mean Absolute Error:      0.01131060501646567\n",
      "Mean Percent Error:       0.0519749087373072\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "{'diff': array([0.00933984, 0.01065514, 0.01606907, ..., 0.00951744, 0.01472562,\n",
       "        0.01627947]),\n",
       " 'mse': 0.00019331166020661818,\n",
       " 'rmse': 0.013903656361066257,\n",
       " 'mae': 0.01131060501646567,\n",
       " 'mpe': 0.0519749087373072}"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train_hat = model.predict(X_train)\n",
    "#reduce dim (240000,1) -> (240000,) to match y_train's dim\n",
    "y_train_hat = squeeze(y_train_hat)\n",
    "CheckAccuracy(y_train, y_train_hat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "zThbPKpvV2LK",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Predict and check accuracy (validation-sample)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "tJuV4_AVV2LM",
    "outputId": "246e64f9-3331-4951-b331-bb2cd5ec1e8e",
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean Squared Error:       0.0001924910075256892\n",
      "Root Mean Squared Error:  0.013874112855447342\n",
      "Mean Absolute Error:      0.011297652288298902\n",
      "Mean Percent Error:       0.05193892352955392\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_test_hat = model.predict(X_test)\n",
    "y_test_hat = squeeze(y_test_hat)\n",
    "test_stats = CheckAccuracy(y_test, y_test_hat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "z68KZq3NV2LP",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Random Forest of decision trees\n",
    "\n",
    "A Random Forest uses several decision trees to make hypotheses about regions within subsamples of the data, then makes predictions based on the majority vote of these trees. This safeguards against overfitting/memorization of the training data.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "6Wi330jKV2LP",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Prepare Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "XDKL3SI5V2LP",
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "n = 300000\n",
    "n_train =  (int)(0.8 * n)\n",
    "train = df[0:n_train]\n",
    "X_train = train[['Stock Price', 'Maturity', 'Dividends', 'Volatility', 'Risk-free']].values\n",
    "y_train = train['Call Price'].values\n",
    "test = df[n_train+1:n]\n",
    "X_test = test[['Stock Price', 'Maturity', 'Dividends', 'Volatility', 'Risk-free']].values\n",
    "y_test = test['Call Price'].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "UC3v2UyQV2LS",
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def CheckAccuracy(y,y_hat):\n",
    "    stats = dict()\n",
    "    \n",
    "    stats['diff'] = y - y_hat\n",
    "    \n",
    "    stats['mse'] = mean(stats['diff']**2)\n",
    "    print(\"Mean Squared Error:      \", stats['mse'])\n",
    "    \n",
    "    stats['rmse'] = sqrt(stats['mse'])\n",
    "    print(\"Root Mean Squared Error: \", stats['rmse'])\n",
    "    \n",
    "    stats['mae'] = mean(abs(stats['diff']))\n",
    "    print(\"Mean Absolute Error:     \", stats['mae'])\n",
    "    \n",
    "    stats['mpe'] = sqrt(stats['mse'])/mean(y)\n",
    "    print(\"Mean Percent Error:      \", stats['mpe'])\n",
    "    \n",
    "    #plots\n",
    "    mpl.rcParams['agg.path.chunksize'] = 100000\n",
    "    #figure(figsize=(14,10))\n",
    "    plt.scatter(y, y_hat,color='black',linewidth=0.3,alpha=0.4, s=0.5)\n",
    "    plt.xlabel('Actual Price',fontsize=20,fontname='Times New Roman')\n",
    "    plt.ylabel('Predicted Price',fontsize=20,fontname='Times New Roman') \n",
    "    plt.show()\n",
    "    \n",
    "    #figure(figsize=(14,10))\n",
    "    plt.hist(stats['diff'], bins=50,edgecolor='black',color='white')\n",
    "    plt.xlabel('Diff')\n",
    "    plt.ylabel('Density')\n",
    "    plt.show()\n",
    "    \n",
    "    return stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "gBcFStK6V2LW",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Fit Random Forest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "4qi2ioHQV2LX",
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.ensemble import RandomForestRegressor\n",
    "\n",
    "forest = RandomForestRegressor()\n",
    "forest = forest.fit(X_train, y_train)\n",
    "y_test_hat = forest.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "EMiQ6y-aV2La",
    "outputId": "263a760b-b9ec-43dd-8089-9541e14ad05f",
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean Squared Error:       5.113459072207158e-05\n",
      "Root Mean Squared Error:  0.007150845455054359\n",
      "Mean Absolute Error:      0.005232728067483401\n",
      "Mean Percent Error:       0.02676979920311822\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "stats = CheckAccuracy(y_test, y_test_hat)"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "colab": {
   "collapsed_sections": [
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   ],
   "default_view": {},
   "name": "DeepLearning_Introduction.ipynb",
   "provenance": [],
   "version": "0.3.2",
   "views": {}
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}