trees.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "evaluation_example.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyPxhA4icPBmlmDPmXn8n7Ua",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/foxtrotmike/CS909/blob/master/trees.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dvgzgm4PzVGS",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from numpy.random import randn #importing randn\n",
        "import numpy as np #importing numpy\n",
        "import matplotlib.pyplot as plt #importing plotting module\n",
        "import itertools\n",
        "import warnings\n",
        "\n",
        "def plotit(X,Y=None,clf=None,  conts = None, ccolors = ('b','k','r'), colors = ('c','y'), markers = ('s','o'), hold = False, transform = None,extent = None,**kwargs):\n",
        "    \"\"\"\n",
        "    A function for showing data scatter plot and classification boundary\n",
        "    of a classifier for 2D data\n",
        "        X: nxd  matrix of data points\n",
        "        Y: (optional) n vector of class labels\n",
        "        clf: (optional) classification/discriminant function handle\n",
        "        conts: (optional) contours (if None, contours are drawn for each class boundary)\n",
        "        ccolors: (optional) colors for contours   \n",
        "        colors: (optional) colors for each class (sorted wrt class id)\n",
        "            can be 'scaled' or 'random' or a list/tuple of color ids\n",
        "        markers: (optional) markers for each class (sorted wrt class id)\n",
        "        hold: Whether to hold the plot or not for overlay (default: False).\n",
        "        transform: (optional) a function handle for transforming data before passing to clf\n",
        "        kwargs: any keyword arguments to be passed to clf (if any)        \n",
        "    \"\"\"\n",
        "    if clf is not None and X.shape[1]!=2:\n",
        "        warnings.warn(\"Data Dimensionality is not 2. Unable to plot.\")\n",
        "        return\n",
        "    if markers is None:\n",
        "        markers = ('.',)\n",
        "    eps=1e-6\n",
        "    d0,d1 = (0,1)\n",
        "    if extent is None:\n",
        "        minx, maxx = np.min(X[:,d0])-eps, np.max(X[:,d0])+eps\n",
        "        miny, maxy = np.min(X[:,d1])-eps, np.max(X[:,d1])+eps\n",
        "        extent = [minx,maxx,miny,maxy]\n",
        "    else:\n",
        "        [minx,maxx,miny,maxy] = extent\n",
        "    if Y is not None:\n",
        "        classes = sorted(set(Y))\n",
        "        if conts is None:\n",
        "            conts = list(classes)        \n",
        "        vmin,vmax = classes[0]-eps,classes[-1]+eps\n",
        "    else:\n",
        "        vmin,vmax=-2-eps,2+eps\n",
        "        if conts is None:            \n",
        "            conts = sorted([-1+eps,0,1-eps])\n",
        "        \n",
        "    if clf is not None:\n",
        "        npts = 150\n",
        "        x = np.linspace(minx,maxx,npts)\n",
        "        y = np.linspace(miny,maxy,npts)\n",
        "        t = np.array(list(itertools.product(x,y)))\n",
        "        if transform is not None:\n",
        "            t = transform(t)\n",
        "        z = clf(t,**kwargs)\n",
        "        \n",
        "        z = np.reshape(z,(npts,npts)).T        \n",
        "        \n",
        "        \n",
        "        plt.contour(x,y,z,conts,linewidths = [2],colors=ccolors,extent=extent, label='f(x)=0')\n",
        "        #plt.imshow(np.flipud(z), extent = extent, cmap=plt.cm.Purples, vmin = -2, vmax = +2); plt.colorbar()\n",
        "        plt.pcolormesh(x, y, z,cmap=plt.cm.Purples,vmin=vmin,vmax=vmax);plt.colorbar()\n",
        "        plt.axis(extent)\n",
        "    \n",
        "    if Y is not None:        \n",
        "        for i,y in enumerate(classes):\n",
        "            if colors is None or colors=='scaled':\n",
        "                cc = np.array([[i,i,i]])/float(len(classes))\n",
        "            elif colors =='random':\n",
        "                cc = np.array([[np.random.rand(),np.random.rand(),np.random.rand()]])\n",
        "            else:\n",
        "                cc = colors[i%len(colors)]\n",
        "            mm = markers[i%len(markers)]\n",
        "            plt.scatter(X[Y==y,d0],X[Y==y,d1], marker = mm,c = cc, s = 30)     \n",
        "         \n",
        "    else:\n",
        "        plt.scatter(X[:,d0],X[:,d1],marker = markers[0], c = 'k', s = 5)\n",
        "    plt.xlabel('$x_1$')\n",
        "    plt.ylabel('$x_2$')   \n",
        "    if not hold:\n",
        "        plt.grid()        \n",
        "        plt.show()\n",
        "    return extent\n",
        "\n",
        "def getExamples(n=100,d=2):\n",
        "    \"\"\"\n",
        "    Generates n d-dimensional normally distributed examples of each class        \n",
        "    The mean of the positive class is [1] and for the negative class it is [-1]\n",
        "    \"\"\"\n",
        "    Xp = randn(n,d)#+1   #generate n examples of the positie class\n",
        "    Xp=Xp+1\n",
        "    Xn1 = randn(int(n/2),d)#-1   #generate n examples of the negative class\n",
        "    Xn1=Xn1-1\n",
        "    Xn2 = randn(int(n/2),d)#-1   #generate n examples of the negative class\n",
        "    Xn2=Xn2+2\n",
        "    Xn = np.vstack((Xn1,Xn2))  #Stack the examples together to a single matrix\n",
        "    X = np.vstack((Xp,Xn))  #Stack the examples together to a single matrix\n",
        "    Y = np.array([+1]*n+[-1]*n) #Associate Labels\n",
        "    return (X,Y) "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AQasnnxPYyPe",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from sklearn.model_selection import train_test_split\n",
        "\n",
        "X,y = getExamples(n=100)\n",
        "Xtr, Xv, ytr, yv = train_test_split(X, y, test_size=0.2, shuffle = True, stratify = None)#, random_state=42)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_nBpCZfD1EpT",
        "colab_type": "code",
        "outputId": "87bfa9db-e97c-4989-82df-83aaf0ef2d59",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 459
        }
      },
      "source": [
        "from sklearn import tree \n",
        "clf = tree.DecisionTreeClassifier(max_depth = 1)\n",
        "clf.fit(Xtr,ytr)\n",
        "zv = clf.predict_proba(Xv)[:,1] # decision trees do not produce decision_function\n",
        "print('Probilities',zv)\n",
        "# calculate the number of true poisitives and false positives at a threshold of t\n",
        "from sklearn.metrics import roc_auc_score\n",
        "print('AUC-ROC',roc_auc_score(yv,zv))\n",
        "plt.figure() \n",
        "plotit(X = X, Y = y, clf = clf.predict, conts =[-1,0,1], colors = 'random')"
      ],
      "execution_count": 69,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Probilities [0.58273381 0.58273381 0.58273381 0.58273381 0.58273381 0.58273381\n",
            " 0.58273381 0.58273381 0.58273381 0.58273381 0.58273381 0.58273381\n",
            " 0.58273381 0.58273381 0.         0.58273381 0.58273381 0.58273381\n",
            " 0.58273381 0.58273381 0.58273381 0.58273381 0.58273381 0.58273381\n",
            " 0.58273381 0.58273381 0.58273381 0.58273381 0.         0.58273381\n",
            " 0.         0.58273381 0.58273381 0.58273381 0.58273381 0.\n",
            " 0.58273381 0.58273381 0.58273381 0.58273381]\n",
            "AUC-ROC 0.4949874686716792\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:58: UserWarning: The following kwargs were not used by contour: 'label'\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
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YD1DP1YfX++STezcv5deW8UkZMS01xSG6f9Nuun+zrcAmrzo15lwgWNGboE7VErb3ZnXM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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[-3.272931827544153, 4.552488642801589, -3.3447281466753354, 4.218688881251389]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 69
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uYAxyLOL2k82",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 459
        },
        "outputId": "0a716d60-f154-4edc-ac54-6809b2bfca12"
      },
      "source": [
        "from sklearn.ensemble import RandomForestClassifier\n",
        "clf = RandomForestClassifier(n_estimators=10, max_depth=5)\n",
        "clf.fit(Xtr,ytr)\n",
        "zv = clf.predict_proba(Xv)[:,1] # decision trees do not produce decision_function\n",
        "print('Probilities',zv)\n",
        "# calculate the number of true poisitives and false positives at a threshold of t\n",
        "from sklearn.metrics import roc_auc_score\n",
        "print('AUC-ROC',roc_auc_score(yv,zv))\n",
        "plt.figure() \n",
        "plotit(X = X, Y = y, clf = clf.predict, conts =[-1,0,1], colors = 'random')"
      ],
      "execution_count": 70,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Probilities [0.18245614 0.76789714 0.76734936 0.62367046 0.2202451  0.85510172\n",
            " 0.78926325 0.71801983 0.80334936 0.80334936 0.20912993 0.06\n",
            " 0.06       0.09543741 0.12659574 0.12866667 0.80334936 0.348\n",
            " 0.29102564 0.60133333 0.76789714 0.54290584 0.80710172 0.39428571\n",
            " 0.76734936 0.78926325 0.38511905 0.73316986 0.         0.12416667\n",
            " 0.14147727 0.53136277 0.12866667 0.65628098 0.78926325 0.12659574\n",
            " 0.54875    0.81534936 0.83464714 0.22531328]\n",
            "AUC-ROC 0.7919799498746867\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:58: UserWarning: The following kwargs were not used by contour: 'label'\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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oojuJ6NHqavjXP2tZv/50XnnldKpr4LRTobw85+IOPMyOYUOpMarWz68+v401zalN2naO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\nAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[-3.272931827544153, 4.552488642801589, -3.3447281466753354, 4.218688881251389]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 70
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PYY32livzfQV",
        "colab_type": "code",
        "outputId": "4376c88f-2be9-440a-d72c-8aeb1c9b9098",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 69
        }
      },
      "source": [
        "!pip install xgboost"
      ],
      "execution_count": 71,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Requirement already satisfied: xgboost in /usr/local/lib/python3.6/dist-packages (0.90)\n",
            "Requirement already satisfied: numpy in /usr/local/lib/python3.6/dist-packages (from xgboost) (1.17.5)\n",
            "Requirement already satisfied: scipy in /usr/local/lib/python3.6/dist-packages (from xgboost) (1.4.1)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "W2e-D1SM1rLt",
        "colab_type": "code",
        "outputId": "f5b24917-3fe5-4db9-b772-f228fffe20ee",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 459
        }
      },
      "source": [
        "from xgboost import XGBClassifier\n",
        "clf = XGBClassifier(n_estimators=10, max_depth = 2, gamma = 0)\n",
        "clf.fit(Xtr,ytr)\n",
        "zv = clf.predict_proba(Xv)[:,1] # decision trees do not produce decision_function\n",
        "print('Probilities',zv)\n",
        "# calculate the number of true poisitives and false positives at a threshold of t\n",
        "from sklearn.metrics import roc_auc_score\n",
        "print('AUC-ROC',roc_auc_score(yv,zv))\n",
        "plt.figure() \n",
        "plotit(X = X, Y = y, clf = clf.predict, conts =[-1,0,1], colors = 'random')"
      ],
      "execution_count": 72,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Probilities [0.4048158  0.6183884  0.6183884  0.6183884  0.4048158  0.6183884\n",
            " 0.6183884  0.6183884  0.6183884  0.6183884  0.6183884  0.31445178\n",
            " 0.31445178 0.5086796  0.4632999  0.44396234 0.6183884  0.583029\n",
            " 0.30292028 0.583029   0.6183884  0.482113   0.6183884  0.4048158\n",
            " 0.6183884  0.6183884  0.4048158  0.6183884  0.21064427 0.4048158\n",
            " 0.35132116 0.6183884  0.44396234 0.6183884  0.6183884  0.4632999\n",
            " 0.4048158  0.6183884  0.6183884  0.4048158 ]\n",
            "AUC-ROC 0.819548872180451\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:58: UserWarning: The following kwargs were not used by contour: 'label'\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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lo2sK4DztZd9bOcrPL+HeaUuXj263T+pi3IQXaWnvCPyzHJY32cJtzNALRqup7ZZ1TOr+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\nAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[-3.272931827544153, 4.552488642801589, -3.3447281466753354, 4.218688881251389]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 72
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-RMNedUX2DeC",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QKUNRB-X2Gk6",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}