SystemML - Linear Regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initial Configuration\n",
    "import findspark \n",
    "findspark.init()\n",
    "\n",
    "from pyspark.context import SparkContext\n",
    "from pyspark.sql.session import SparkSession\n",
    "sc = SparkContext('local') # we are hosting clusters locally.\n",
    "spark = SparkSession(sc) # create an interface to the spark session."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Archiver-Version: Plexus Archiver\n",
      "Artifact-Id: systemml\n",
      "Build-Jdk: 1.8.0_111\n",
      "Build-Time: 2018-01-11 16:39:06 CST\n",
      "Built-By: biuser\n",
      "Created-By: Apache Maven 3.0.5\n",
      "Group-Id: org.apache.systemml\n",
      "Main-Class: org.apache.sysml.api.DMLScript\n",
      "Manifest-Version: 1.0\n",
      "Minimum-Recommended-Spark-Version: 2.1.0\n",
      "Version: 1.1.0-SNAPSHOT\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from systemml import MLContext, dml\n",
    "\n",
    "# create a MLContext object\n",
    "ml = MLContext(sc)\n",
    "print(ml.info())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Apache SystemML has a large selection of algorithm implementations that can be used without modifications. For this example, an existing algorithm will be loaded and executed. First, setup diabetes datasets from scikit-learn."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(442, 10)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import datasets\n",
    "import numpy as np\n",
    "\n",
    "diabetes = datasets.load_diabetes()\n",
    "diabetes_X = diabetes.data[:, np.newaxis, 2]\n",
    "diabetes_X_train = diabetes_X[:-20]\n",
    "diabetes_X_test = diabetes_X[-20:]\n",
    "diabetes_y_train = diabetes.target[:-20].reshape(-1,1)\n",
    "diabetes_y_test = diabetes.target[-20:].reshape(-1,1)\n",
    "\n",
    "diabetes.data.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the next snippet, an existing implementation of Linear Regression Direct Solve is retrieved and run with diabetes input data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ANTLR Tool version 4.5.3 used for code generation does not match the current runtime version 4.7ANTLR Runtime version 4.5.3 used for parser compilation does not match the current runtime version 4.7ANTLR Tool version 4.5.3 used for code generation does not match the current runtime version 4.7ANTLR Runtime version 4.5.3 used for parser compilation does not match the current runtime version 4.7\n",
      "BEGIN LINEAR REGRESSION SCRIPT\n",
      "Reading X and Y...\n",
      "Calling the Direct Solver...\n",
      "Computing the statistics...\n",
      "AVG_TOT_Y,153.36255924170615\n",
      "STDEV_TOT_Y,77.21853383600028\n",
      "AVG_RES_Y,3.633533705616816E-14\n",
      "STDEV_RES_Y,63.038506337610244\n",
      "DISPERSION,3973.853281276927\n",
      "R2,0.3351312506863875\n",
      "ADJUSTED_R2,0.33354822985468835\n",
      "R2_NOBIAS,0.3351312506863875\n",
      "ADJUSTED_R2_NOBIAS,0.33354822985468835\n",
      "Writing the output matrix...\n",
      "END LINEAR REGRESSION SCRIPT\n",
      "SystemML Statistics:\n",
      "Total execution time:\t\t0.107 sec.\n",
      "Number of executed Spark inst:\t2.\n",
      "\n",
      "\n",
      "[152.91886229]\n"
     ]
    }
   ],
   "source": [
    "from systemml import MLContext, dml, dmlFromResource\n",
    "\n",
    "ml = MLContext(sc)\n",
    "\n",
    "dml_script = dmlFromResource(\"/scripts/algorithms/LinearRegDS.dml\")\n",
    "\n",
    "prog = dml_script.input(X=diabetes_X_train, y=diabetes_y_train).input('$icpt',1.0).output('beta_out')\n",
    "w = ml.execute(prog).get('beta_out')\n",
    "w = w.toNumPy()\n",
    "bias=w[1]\n",
    "print(bias)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results can be displayed graphically using matplotlib as shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c62910bdd8>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.scatter(diabetes_X_train, diabetes_y_train,  color='black')\n",
    "plt.scatter(diabetes_X_test, diabetes_y_test,  color='red')\n",
    "\n",
    "plt.plot(diabetes_X_test, (w[0]*diabetes_X_test)+bias, color='blue')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear Regression Direct Solve"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Least squares formulation\n",
    "w* = argminw ||Xw-y||2 = argminw (y - Xw)'(y - Xw) = argminw (w'(X'X)w - w'(X'y))/2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Setting the gradient\n",
    "dw = (X'X)w - (X'y) to 0, w = (X'X)-1(X' y) = solve(X'X, X'y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following cell creates and runs a script using Apache SystemML that generates a small Spark job for distributed data processing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SystemML Statistics:\n",
      "Total execution time:\t\t0.001 sec.\n",
      "Number of executed Spark inst:\t2.\n",
      "\r\n",
      "\n"
     ]
    }
   ],
   "source": [
    "script = \"\"\"\n",
    "    # add constant feature to X to model intercept\n",
    "    X = cbind(X, matrix(1, rows=nrow(X), cols=1))\n",
    "    A = t(X) %*% X\n",
    "    b = t(X) %*% y\n",
    "    w = solve(A, b)\n",
    "    bias = as.scalar(w[nrow(w),1])\n",
    "    w = w[1:nrow(w)-1,]\n",
    "\"\"\"\n",
    "\n",
    "prog = dml(script).input(X=diabetes_X_train, y=diabetes_y_train).output('w', 'bias')\n",
    "w, bias = ml.execute(prog).get('w','bias')\n",
    "w = w.toNumPy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c6291a2208>]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Display the results with matplotlib.\n",
    "plt.scatter(diabetes_X_train, diabetes_y_train,  color='black')\n",
    "plt.scatter(diabetes_X_test, diabetes_y_test,  color='red')\n",
    "\n",
    "plt.plot(diabetes_X_test, (w*diabetes_X_test)+bias, color='blue')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear Regression Batch Gradient Descent\n",
    "\n"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "Algorithm\n",
    "Step 1: Start with an initial point \n",
    "while(not converged) { \n",
    "  Step 2: Compute gradient dw. \n",
    "  Step 3: Compute stepsize alpha.     \n",
    "  Step 4: Update: wnew = wold + alpha*dw \n",
    "}\n",
    "\n",
    "Gradient formula\n",
    "dw = r = (X'X)w - (X'y)\n",
    "\n",
    "Step size formula\n",
    "Find number alpha to minimize f(w + alpha*r) \n",
    "alpha = -(r'r)/(r'X'Xr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create and execute an Apache SystemML script that uses Spark to distribute data processing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SystemML Statistics:\n",
      "Total execution time:\t\t0.131 sec.\n",
      "Number of executed Spark inst:\t2.\n",
      "\r\n",
      "\n"
     ]
    }
   ],
   "source": [
    "script = \"\"\"\n",
    "    # add constant feature to X to model intercepts\n",
    "    X = cbind(X, matrix(1, rows=nrow(X), cols=1))\n",
    "    max_iter = 100\n",
    "    w = matrix(0, rows=ncol(X), cols=1)\n",
    "    for(i in 1:max_iter){\n",
    "        XtX = t(X) %*% X\n",
    "        dw = XtX %*%w - t(X) %*% y\n",
    "        alpha = -(t(dw) %*% dw) / (t(dw) %*% XtX %*% dw)\n",
    "        w = w + dw*alpha\n",
    "    }\n",
    "    bias = as.scalar(w[nrow(w),1])\n",
    "    w = w[1:nrow(w)-1,]    \n",
    "\"\"\"\n",
    "\n",
    "prog = dml(script).input(X=diabetes_X_train, y=diabetes_y_train).output('w').output('bias')\n",
    "w, bias = ml.execute(prog).get('w', 'bias')\n",
    "w = w.toNumPy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visualize the results with matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c629213390>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(diabetes_X_train, diabetes_y_train,  color='black')\n",
    "plt.scatter(diabetes_X_test, diabetes_y_test,  color='red')\n",
    "\n",
    "plt.plot(diabetes_X_test, (w*diabetes_X_test)+bias, color='blue')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "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": 2
}