Chapter_5_Homework.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 5_7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# This file is associated with the book\n",
    "# \"Machine Learning Refined\", Cambridge University Press, 2016.\n",
    "# by Jeremy Watt, Reza Borhani, and Aggelos Katsaggelos.\n",
    "\n",
    "import numpy as np\n",
    "import numpy.matlib\n",
    "import matplotlib.pyplot as plt\n",
    "from __future__ import division\n",
    "import pylab"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First a simple data loading function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# load data\n",
    "def load_data():\n",
    "    data = np.array(np.genfromtxt('noisy_sin_samples.csv', delimiter=','))\n",
    "    x = np.reshape(data[:,0],(np.size(data[:,0]),1))\n",
    "    y = np.reshape(data[:,1],(np.size(data[:,1]),1))\n",
    "    return x,y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we need a function to transform input features into Fourier features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#YOUR CODE GOES HERE takes poly features of the input \n",
    "\n",
    "def poly_features(x,D):\n",
    "    F = []\n",
    "\n",
    "    for i in x:\n",
    "        f_col = []\n",
    "        for j in range(1 , D + 1):\n",
    "            f_col.append(i ** j)\n",
    "        F.append(f_col)\n",
    "    F = np.array(F)\n",
    "    F.shape = (len(x),D)\n",
    "    F = F.T\n",
    "    \n",
    "    return F\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we need a variety of plotting functions - to plot our datapoints, polynomial models, and errors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# plot the polynomial  \n",
    "def plot_model(w,D):\n",
    "    # plot determined surface in 3d space\n",
    "    s = np.arange(0,1,.01)\n",
    "    f = poly_features(s,D)\n",
    "    z = np.dot(f.T,w)\n",
    "\n",
    "    # plot contour in original space\n",
    "    plt.plot(s,z, color = 'r', linewidth = 2)\n",
    "    plt.ylim([-1.5,1.5])\n",
    "    plt.xlim([0,1])\n",
    "\n",
    "# plot mse's over all D tested \n",
    "def plot_mse(mses,deg):\n",
    "    plt.plot(np.arange(1,np.size(mses)+1),mses,'ro--')\n",
    "    plt.title('MSE on entire dataset in D', fontsize=18)\n",
    "    plt.xlabel('degree D', fontsize=18)\n",
    "    plt.ylabel('MSE       ', fontsize=18)\n",
    "\n",
    "# plot data \n",
    "def plot_data(x,y,deg):\n",
    "    for i in np.arange(1,7):\n",
    "        plt.subplot(2,3,i)\n",
    "        plt.scatter(x,y,s = 30, color = 'k')\n",
    "\n",
    "        # graph info labels\n",
    "        s = 'D = ' + str(deg[i-1])\n",
    "        plt.title(s, fontsize=15)\n",
    "        plt.axis('off')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, a function to loop through the degrees we wish to test and trains a model for each, plotting the resulting fit to the dataset and error."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# run over all the degrees, fit each models, and calculate errors\n",
    "def try_all_degs(x,y,deg_range):\n",
    "    # plot datapoints - one panel for each deg in deg_range\n",
    "    fig = plt.figure(figsize = (8,4))\n",
    "    plot_data(x,y,deg_range)\n",
    "\n",
    "    # generate nonlinear features\n",
    "    mses = []\n",
    "\n",
    "    for D in np.arange(0,np.size(deg_range)):\n",
    "        # generate poly feature transformation\n",
    "        F = poly_features(x,deg_range[D])\n",
    "        # get weights for current model\n",
    "        temp = np.linalg.pinv(np.dot(F,F.T))\n",
    "        w = np.dot(np.dot(temp,F),y)\n",
    "        MSE = np.linalg.norm(np.dot(F.T,w)-y)/np.size(y)\n",
    "        mses.append(MSE)\n",
    "\n",
    "        # plot fit to data\n",
    "        plt.subplot(2,3,D+1)\n",
    "        plot_model(w,deg_range[D])\n",
    "\n",
    "    # make plot of mse's\n",
    "    fig = plt.figure(figsize = (5,5))\n",
    "    plot_mse(mses,deg_range)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that everything is defined, lets run all."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Library/Python/2.7/site-packages/matplotlib/cbook/deprecation.py:107: MatplotlibDeprecationWarning: Adding an axes using the same arguments as a previous axes currently reuses the earlier instance.  In a future version, a new instance will always be created and returned.  Meanwhile, this warning can be suppressed, and the future behavior ensured, by passing a unique label to each axes instance.\n",
      "  warnings.warn(message, mplDeprecation, stacklevel=1)\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAe0AAAEKCAYAAAA/9Q3BAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nU3dXAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x288 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAVwAAAFZCAYAAADU25efAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# load data and defined degree range\n",
    "x, y = load_data()\n",
    "deg_range = [1,3,5,7,15,20]           # degree polys to try\n",
    "\n",
    "# run all over degree range\n",
    "try_all_degs(x,y,deg_range)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 5_11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import csv\n",
    "\n",
    "def read_data(filename):\n",
    "    '''\n",
    "    Read data from csvfile\n",
    "    Parameters:\n",
    "    ----------------------------------------------------\n",
    "    filename: path to data file\n",
    "    Returns:\n",
    "    ----------------------------------------------------\n",
    "    X: ndarray of shape (1, P)\n",
    "    y: ndarray of shape (P, 1)\n",
    "\n",
    "    Hints:\n",
    "    ----------------------------------------------------\n",
    "    Make sure the shapes of X, y conform to above. You may\n",
    "    find \"np.genfromtxt(, delimiter=','), np.newaxis\" useful\n",
    "    '''\n",
    "    ####################################################\n",
    "    ###                  Your Code                   ###\n",
    "    ####################################################\n",
    "    reader = csv.reader(open(filename, \"r\"), delimiter = \",\")\n",
    "    d = list(reader)\n",
    "    data = np.array(d).astype(\"float\")\n",
    "    X = data[:,0];\n",
    "    y = data[:,1];\n",
    "    X.shape = (1, len(X))\n",
    "    y.shape = (len(y), 1)\n",
    "    ####################################################\n",
    "    ###                    End                       ###\n",
    "    ####################################################\n",
    "    assert X.shape == (1, data[:, 0].size), \"Shape of X incorrect\"\n",
    "    assert y.shape == (data[:,-1].size, 1), \"Shape of y incorrect\"\n",
    "    return X, y\n",
    "\n",
    "def fourier_basis(X, D):\n",
    "    '''\n",
    "    Return Fourier basis for X (with ONE bias dimension)\n",
    "    Parameters:\n",
    "    ----------------------------------------------------\n",
    "    X: data ndarray of shape (1, P)\n",
    "    D: degree of Fourier basis features\n",
    "    Returns:\n",
    "    ----------------------------------------------------\n",
    "    F: ndarray of shape (2D+1, P)\n",
    "\n",
    "    Hints:\n",
    "    ----------------------------------------------------\n",
    "    Make sure the shapes of F conform to above. You may\n",
    "    find \"np.arange, np.reshape, np.concatenate(, axis=0),\n",
    "    np.ones, np.cos, np.sin\"  useful\n",
    "    '''\t\n",
    "    ####################################################\n",
    "    ###                  Your Code                   ###\n",
    "    ####################################################\n",
    "    f = np.ones((1, X.size))\n",
    "    m = np.arange(1, D + 1).reshape(D, 1)\n",
    "    w = 2 * np.pi * np.dot(m, X) \n",
    "    F_1 = np.cos(w)\n",
    "    F_2 = np.sin(w)\n",
    "\n",
    "    F = np.concatenate((f, F_1, F_2), axis = 0)\n",
    "    ####################################################\n",
    "    ###                    End                       ###\n",
    "    ####################################################\n",
    "    assert F.shape == (2*D+1, X.size), \"Shape of F incorrect\"\n",
    "    return F\n",
    "\n",
    "def poly_basis(X, D):\n",
    "    '''\n",
    "    Return polynomial basis for X (with ONE bias dimension)\n",
    "    Parameters:\n",
    "    ----------------------------------------------------\n",
    "    X: data ndarray of shape (1, P)\n",
    "    D: degree of Fourier basis features\n",
    "    Returns:\n",
    "    ----------------------------------------------------\n",
    "    F: ndarray of shape (D+1, P)\n",
    "\n",
    "    Hints:\n",
    "    ----------------------------------------------------\n",
    "    Make sure the shapes of F conform to above. You may\n",
    "    find \"np.arange, np.reshape, np.power\"  useful\n",
    "    '''\t\n",
    "    ####################################################\n",
    "    ###                  Your Code                   ###\n",
    "    ####################################################\n",
    "    f = np.ones((1, X.size))\n",
    "    m = np.arange(1, D + 1).reshape(D, 1)\n",
    "    y = np.power(X, m)\n",
    "    # for d in range(1,D+1):\n",
    "    # \tF = np.concatenate((F,np.power(X,d)), axis = 0)\n",
    "    # F.shape = (D + 1, X.size)\n",
    "    F = np.concatenate((f, y), axis = 0)\n",
    "    ####################################################\n",
    "    ###                    End                       ###\n",
    "    ####################################################\n",
    "    assert F.shape == (D+1, X.size), \"Shape of F incorrect\"\n",
    "    return F\n",
    "\n",
    "def least_square_sol(F, y):\n",
    "    '''\n",
    "    Refer to eq. 5.19 in the text\n",
    "    Parameters:\n",
    "    ----------------------------------------------------\n",
    "    F: ndarray of shape (2D+1 or D+1 depends on what basis, P)\n",
    "    y: ndarray of shape (P, 1)\n",
    "    Returns:\n",
    "    ----------------------------------------------------\n",
    "    w: learned weighter vector of shape (2D+1, 1)\n",
    "\n",
    "    Hints:\n",
    "    ----------------------------------------------------\n",
    "    You may find \"np.linalg.pinv, np.dot\"  useful\n",
    "    '''\t\n",
    "    ####################################################\n",
    "    ###                  Your Code                   ###\n",
    "    ####################################################\n",
    "    w = np.dot(np.linalg.pinv(np.dot(F, F.T)), np.dot(F,y))\n",
    "\n",
    "    ####################################################\n",
    "    ###                    End                       ###\n",
    "    ####################################################\n",
    "    assert w.shape == (F.shape[0], 1), \"Shape of w incorrect\"\n",
    "    return w\n",
    "\n",
    "def mean_square_error(w, F, y):\n",
    "    '''\n",
    "    Refer to eq. 5.19 in the text\n",
    "    Parameters:\n",
    "    ----------------------------------------------------\n",
    "    w: learned weighter vector of shape (2D+1, 1)\n",
    "    F: ndarray of shape (2D+1, P)\n",
    "    y: ndarray of shape (P, 1)\n",
    "    Returns:\n",
    "    ----------------------------------------------------\n",
    "    mse: a scaler, mean square error of your learned model\n",
    "\n",
    "    Hints:\n",
    "    ----------------------------------------------------\n",
    "    You may find \"np.dot, np.mean\"  useful\n",
    "    '''\t\n",
    "    ####################################################\n",
    "    ###                  Your Code                   ###\n",
    "    ####################################################\n",
    "    mse = np.mean(np.dot((np.dot(F.T, w) - y).T, (np.dot(F.T, w) - y)))\n",
    "\n",
    "    # temp = np.power(np.dot(F.T,w) - y, 2)\n",
    "    # mse = np.mean(temp)\n",
    "\n",
    "    ####################################################\n",
    "    ###                    End                       ###\n",
    "    ####################################################\n",
    "    return mse\n",
    "\n",
    "def random_split(P, K):\n",
    "    '''\n",
    "    Return a list of K arrays, each of which are indices \n",
    "    of data point\n",
    "\n",
    "    Parameters:\n",
    "    ----------------------------------------------------\n",
    "    P: number of data points\n",
    "    K: number of folds\n",
    "    Returns:\n",
    "    ----------------------------------------------------\n",
    "    folds: a list of K arrays, each of which are position \n",
    "    indices of data point\n",
    "\n",
    "    Hints:\n",
    "    ----------------------------------------------------\n",
    "    You may find \"np.split, np.random.permutation, np.arange\" \n",
    "    useful\t\n",
    "    '''\n",
    "    ####################################################\n",
    "    ###                  Your Code                   ###\n",
    "    ####################################################\n",
    "    folds = np.arange(P)\n",
    "    folds = np.random.permutation(folds)\n",
    "    folds = np.split(folds, K)\n",
    "\n",
    "    ####################################################\n",
    "    ###                    End                       ###\n",
    "    ####################################################\n",
    "    assert len(folds) == K, 'Number of folds incorrect'\n",
    "    return folds\n",
    "\n",
    "def train_val_split(X, y, folds, fold_id):\n",
    "    '''\n",
    "    Split the data into training and validation sets\n",
    "    Parameters:\n",
    "    ----------------------------------------------------\n",
    "    X: ndarray of shape (1, P)\n",
    "    y: ndarray of shape (P, 1)\n",
    "    folds: a list of K arrays, each of which are indices \n",
    "    of data point\n",
    "    fold_id: the id of the fold you want to be validation set\n",
    "    Returns:\n",
    "    ----------------------------------------------------\n",
    "    X_train: training set of X\n",
    "    y_train: training label\n",
    "    X_val: validation set of X\n",
    "    y_val: validation label\n",
    "    '''\n",
    "    ####################################################\n",
    "    ###                  Your Code                   ###\n",
    "    ####################################################\n",
    "    X_val = X.iloc[folds[fold_id]]\n",
    "    X_val = X_val.values\n",
    "    X_val.shape = (1, X_val.size)\n",
    "    y_val = y[folds[fold_id]]\n",
    "    y_val = y_val.values\n",
    "    y_val.shape = (y_val.size, 1)\n",
    "\n",
    "    X_train = np.delete(X.values, folds[fold_id])\n",
    "    X_train.shape = (1, X_train.size)\n",
    "    y_train = np.delete(y.values, folds[fold_id])\n",
    "    y_train.shape = (y_train.size, 1)\n",
    "\n",
    "    ####################################################\n",
    "    ###                    End                       ###\n",
    "    ####################################################\n",
    "    assert y_val.size + y_train.size == y.size, 'Split incorrect'\n",
    "    return X_train, y_train, X_val, y_val\n",
    "\n",
    "def make_plot(D, MSE_train, MSE_val):\n",
    "    plt.figure()\n",
    "    train, = plt.plot(D, MSE_train, 'yv--')\n",
    "    val, = plt.plot(D, MSE_val, 'bv--')\n",
    "    plt.legend(handles=[train, val], labels=['training_error', 'validation error'], loc='center left', bbox_to_anchor=(1, 0.5))\n",
    "    plt.xlabel('Degree of Fourier basis')\n",
    "    plt.ylabel('Error in log scale')\n",
    "    plt.yscale('log')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def read_data(filename):\n",
    "    assert X.shape == (1, data[:, 0].size), \"Shape of X incorrect\"\n",
    "    assert y.shape == (data[:,-1].size, 1), \"Shape of y incorrect\"\n",
    "    return X, y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "data = pd.read_csv('wavy_data.csv', names=['x','y'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "num_fold, num_degree = 3, 8\n",
    "folds = random_split(P=data['y'].size, K=num_fold)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X_train, y_train, X_val, y_val = train_val_split(data['x'], data['y'], folds, fold_id=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The best degree of Fourier basis, in terms of validation error, is 7\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgAAAAEKCAYAAABkC+0BAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "MSE_train, MSE_val = [], []\n",
    "D = np.arange(1, num_degree+1)\n",
    "for d in D:\n",
    "    F_train = fourier_basis(X_train, D=d)\n",
    "    F_val = fourier_basis(X_val, D=d)\n",
    "    w = least_square_sol(F_train, y_train)\n",
    "    MSE_train.append(mean_square_error(w, F_train, y_train))\n",
    "    MSE_val.append(mean_square_error(w, F_val, y_val))\n",
    "#     make_plot(D, MSE_train, MSE_val)\n",
    "print 'The best degree of Fourier basis, in terms of validation error, is %d' % (MSE_val.index(min(MSE_val))+1)\n",
    "make_plot(D, MSE_train, MSE_val)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 5_12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The best degree of polynomial basis, in terms of validation error, is 2\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgUAAAEKCAYAAACCIiZFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = pd.read_csv('galileo_ramp_data.csv',names=['x','y'])\n",
    "X=data['x']\n",
    "y=data['y']\n",
    "num_fold, num_degree = 6, 6\n",
    "folds = random_split(P=y.size, K=num_fold)\n",
    "\n",
    "MSE_train, MSE_val = [0]*num_degree, [0]*num_degree\n",
    "D = np.arange(1, num_degree+1)\n",
    "for f in xrange(num_fold):\n",
    "    X_train, y_train, X_val, y_val = train_val_split(X, y, folds, fold_id=f)\n",
    "    for i, d in enumerate(D):\n",
    "        F_train = poly_basis(X_train, D=d)\n",
    "        F_val = poly_basis(X_val, D=d)\n",
    "        w = least_square_sol(F_train, y_train)\n",
    "        MSE_train[i] += mean_square_error(w, F_train, y_train)/num_fold\n",
    "        MSE_val[i] += mean_square_error(w, F_val, y_val)/num_fold\n",
    "\n",
    "print 'The best degree of polynomial basis, in terms of validation error, is %d' % (MSE_val.index(min(MSE_val))+1)\n",
    "\n",
    "make_plot(D, MSE_train, MSE_val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}