Basic_NN.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training Error = 0.0258\n",
      "Test Error = 0.0154\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas\n",
    "\n",
    "# Function that creates the X matrix as defined for fitting our model\n",
    "def create_X(x,deg):\n",
    "    X = np.ones((len(x),deg+1))\n",
    "    for i in range(1,deg+1):\n",
    "        X[:,i] = x**i\n",
    "    return X\n",
    "\n",
    "# Function for predicting the response\n",
    "def predict_y(x,beta):\n",
    "    return np.dot(create_X(x,len(beta)-1),beta)\n",
    "\n",
    "# Function for fitting the model\n",
    "def fit_beta(df,deg):\n",
    "    return np.linalg.lstsq(create_X(df.x,deg),df.y,rcond=None)[0]\n",
    "\n",
    "# Function for computing the MSE\n",
    "def mse(y,yPred):\n",
    "    return np.mean((y-yPred)**2)\n",
    "\n",
    "# Loading training, validation and test data\n",
    "dfTrain = pandas.read_csv('Data_Train.csv')\n",
    "dfVal = pandas.read_csv('Data_Val.csv')\n",
    "dfTest = pandas.read_csv('Data_Test.csv')\n",
    "\n",
    "############ TRAINING A MODEL\n",
    "\n",
    "# Fitting model\n",
    "deg = 1\n",
    "X = create_X(dfTrain.x,deg)\n",
    "beta = fit_beta(dfTrain,deg)\n",
    "\n",
    "# Computing training error\n",
    "yPredTrain = predict_y(dfTrain.x,beta)\n",
    "err = mse(dfTrain.y,yPredTrain)\n",
    "print('Training Error = {:2.3}'.format(err))\n",
    "\n",
    "# Computing test error\n",
    "yPredTest = predict_y(dfTest.x,beta)\n",
    "err = mse(dfTest.y,yPredTest)\n",
    "print('Test Error = {:2.3}'.format(err))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "############ PLOTTING FITTED MODEL\n",
    "x = np.linspace(0,1,100)\n",
    "y = predict_y(x,beta)\n",
    "\n",
    "plt.plot(x,y,'b-',dfTrain.x,dfTrain.y,'r.')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "Training Error = 0.199\n",
      "Validation Error = 0.247\n",
      "1\n",
      "Training Error = 0.0258\n",
      "Validation Error = 0.0249\n",
      "2\n",
      "Training Error = 0.0188\n",
      "Validation Error = 0.0186\n",
      "3\n",
      "Training Error = 0.00967\n",
      "Validation Error = 0.00843\n",
      "4\n",
      "Training Error = 0.00929\n",
      "Validation Error = 0.00934\n",
      "5\n",
      "Training Error = 0.00902\n",
      "Validation Error = 0.0109\n",
      "6\n",
      "Training Error = 0.00874\n",
      "Validation Error = 0.0108\n",
      "7\n",
      "Training Error = 0.00873\n",
      "Validation Error = 0.0109\n",
      "8\n",
      "Training Error = 0.00873\n",
      "Validation Error = 0.0111\n",
      "9\n",
      "Training Error = 0.00823\n",
      "Validation Error = 0.0152\n",
      "10\n",
      "Training Error = 0.00673\n",
      "Validation Error = 0.0392\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "############ HYPER-PARAMETER TUNING\n",
    "\n",
    "# Initializing range of degree values to be tested and errors\n",
    "#degRange = list(range(1,11))\n",
    "degRange = range(0,11)\n",
    "errTrain = np.zeros(len(degRange))\n",
    "errVal = np.zeros(len(degRange))\n",
    "\n",
    "# Computing error as a function of degree\n",
    "# ...\n",
    "for i in degRange:\n",
    "    print(i)\n",
    "    X = create_X(dfTrain.x,i)\n",
    "    beta = fit_beta(dfTrain,i)\n",
    "    yPredTra = predict_y(dfTrain.x,beta)\n",
    "    errTrain[i] = mse(dfTrain.y,yPredTra)\n",
    "    print('Training Error = {:2.3}'.format(errTrain[i]))\n",
    "    yPredVal = predict_y(dfVal.x,beta)\n",
    "    errVal[i] = mse(dfVal.y,yPredVal)\n",
    "    print('Validation Error = {:2.3}'.format(errVal[i]))\n",
    "\n",
    "# Plotting training and validation errors\n",
    "#plt.plot(degRange,errTrain,'b-',degRange,errVal,'r-')\n",
    "plt.plot(degRange,errTrain,'b-',degRange,errVal,'r-')\n",
    "plt.legend(('Training Error','Validation Error'))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(20, 2)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dfTrain.shape\n",
    "\n",
    "dfVal.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training Error = 0.00862\n",
      "Test Error = 0.0108\n"
     ]
    }
   ],
   "source": [
    "############ TRAINING SELECTED MODEL\n",
    "\n",
    "# Concatenating data training and validation data frames\n",
    "frames = [dfTrain, dfVal]\n",
    "df = pandas.concat(frames) # ...\n",
    "\n",
    "# Fit model using the optimal degree found in the previous cell\n",
    "degOpt = 6 # ...\n",
    "# ...\n",
    "X = create_X(df.x,degOpt)\n",
    "betaOpt = fit_beta(df,degOpt)\n",
    "\n",
    "# Compute and print training and test errors\n",
    "# ...\n",
    "# Computing training error\n",
    "yPredTrainOpt = predict_y(df.x,betaOpt)\n",
    "errTrainOpt = mse(df.y,yPredTrainOpt)\n",
    "print('Training Error = {:2.3}'.format(errTrainOpt))\n",
    "\n",
    "# Computing test error\n",
    "yPredTestOpt = predict_y(dfTest.x,betaOpt)\n",
    "errTestOpt = mse(dfTest.y,yPredTestOpt)\n",
    "print('Test Error = {:2.3}'.format(errTestOpt))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "############ PLOTTING FITTED MODEL\n",
    "# Plot the fitted model as in the second cell\n",
    "# ...\n",
    "x = np.linspace(0,1,100)\n",
    "y = predict_y(x,betaOpt)\n",
    "\n",
    "plt.plot(x,y,'b-',df.x,df.y,'r.')\n",
    "plt.show()"
   ]
  },
  {
   "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
}