vapnik.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "barebones.ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyNlMuVboqnBRtanr/bbd6Ol",
      "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/vapnik.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\"\"\"\n",
        "Author: Fayyaz Minhas\n",
        "Simple demonstration of learning with statistical predicates by Vapnik\n",
        "\"\"\"\n"
      ],
      "metadata": {
        "id": "cERNHvoLYvEV"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "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",
        "#nothing to see here - just a plotting function\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 or len(conts)<2:\n",
        "            #conts = list(classes)\n",
        "            vmin,vmax = classes[0]-eps,classes[-1]+eps\n",
        "        else:            \n",
        "            vmin,vmax= np.min(conts)-eps,np.max(conts)+eps\n",
        "        \n",
        "    else:\n",
        "        vmin,vmax=-2-eps,2+eps\n",
        "        if conts is None or len(conts)<2:            \n",
        "            conts = sorted([-1+eps,0,1-eps])\n",
        "        else:\n",
        "            vmin,vmax= np.min(conts)-eps,np.max(conts)+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",
        "            \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",
        "            \n",
        "            mm = markers[i%len(markers)]\n",
        "            plt.scatter(X[Y==y,d0],X[Y==y,d1], marker = mm,c = cc, s = 50)     \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"
      ],
      "metadata": {
        "id": "rJDByivYBQIz"
      },
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TG-En3BVlBGG",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 653
        },
        "outputId": "d963e36e-2184-4991-90cd-91c4d720a1e4"
      },
      "source": [
        "\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import torch\n",
        "import torch.nn.modules as nn\n",
        "import torch.optim as optim\n",
        "from sklearn.datasets import make_moons, make_circles;  \n",
        "#Let's generate some data\n",
        "seed = 0\n",
        "np.random.seed(seed=seed)\n",
        "torch.manual_seed(seed)\n",
        "\n",
        "X,y = make_circles(n_samples=800,  shuffle=True, noise=0.05, random_state=seed, factor = 0.5); Xp = X[y==1]; Xn = X[y!=1]\n",
        "Xp = 1.0+np.random.randn(200,2); Xn = -1-np.random.randn(10,2);\n",
        "inputs = np.vstack((Xp,Xn))\t\n",
        "#labels\n",
        "targets = np.hstack((np.ones(len(Xp)),-0*np.ones(len(Xn))))\n",
        "ttargets = targets+0 #copy of true labels\n",
        " \n",
        "from sklearn.metrics.pairwise import rbf_kernel\n",
        "#K = (np.dot(inputs,inputs.T)+1)**2\n",
        "K = rbf_kernel(inputs,gamma=0.5)\n",
        "K = torch.from_numpy(K).float() #kernel\n",
        "P = (1*np.ones(K.shape)+1*inputs@inputs.T)/2.0#\n",
        "P = torch.from_numpy(P).float() #kernel\n",
        "M = 0*torch.eye(K.shape[0])+1*K+1*P #Learning with statistical invariants\n",
        "#M = torch.eye(K.shape[0]) #No statistical invariants\n",
        "device = torch.device('cpu')\n",
        "#device = torch.device('cuda') # Uncomment this to run on GPU\n",
        "x = torch.from_numpy(inputs).float()\n",
        "y = torch.from_numpy(targets).float()\n",
        "N, D_in,D_out = x.shape[0], x.shape[1], 1\n",
        "\n",
        "class Feedforward(torch.nn.Module):\n",
        "        def __init__(self, input_size, hidden_size):\n",
        "            super(Feedforward, self).__init__()\n",
        "            self.input_size = input_size\n",
        "            self.hidden_size  = hidden_size\n",
        "            self.fc1 = torch.nn.Linear(self.input_size, self.hidden_size)\n",
        "            self.relu = torch.nn.ReLU()\n",
        "            self.fc2 = torch.nn.Linear(self.hidden_size, self.hidden_size)\n",
        "            self.sigmoid = torch.nn.Sigmoid()\n",
        "            self.fc3 = torch.nn.Linear(self.hidden_size, 1)\n",
        "        def forward(self, x):\n",
        "            x = self.fc1(x)\n",
        "            x = self.sigmoid(x)\n",
        "            x = self.fc2(x)\n",
        "            x = self.relu(x)\n",
        "            x = self.fc3(x)\n",
        "            x = self.relu(x)\n",
        "            return x\n",
        "model = Feedforward(D_in, 100)\n",
        "\n",
        "optimizer = optim.Adam(model.parameters(), lr=1e-3)\n",
        "\n",
        "L = [] #history of losses\n",
        "for epoch in range(5000):\n",
        "      \"\"\"\n",
        "      # REPRESENTATION\n",
        "      \"\"\"\n",
        "      y_pred = model(x).flatten()#x@wb+bb\n",
        "      \"\"\"\n",
        "      # EVALUATION\n",
        "      \"\"\"\n",
        "      obj = (y-y_pred)@M@(y-y_pred)\n",
        "      \"\"\"\n",
        "      #OPTIMIZATION\n",
        "      \"\"\"    \n",
        "      obj.backward()\n",
        "      # Using built-in optimizer\n",
        "      optimizer.step()\n",
        "      optimizer.zero_grad()\n",
        "      L.append(obj.detach().numpy()) #save for history and plotting\n",
        "\n",
        "#plt.close(\"all\")\n",
        "plt.figure()\n",
        "plt.plot(L);plt.yscale('log')\n",
        "\n",
        "plt.grid(); plt.xlabel('Epochs'); plt.ylabel('value');plt.legend(['Loss','Objective'])\n",
        "\n",
        "def clf(inputs): \n",
        "  return model(torch.from_numpy(inputs).float()).detach().numpy()#inputs@wbn+bbn\n",
        "\n",
        "plt.figure()\n",
        "plotit(inputs,targets,clf=clf,conts=[0.5])\n"
      ],
      "execution_count": 87,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-1-5604fef99228>:63: UserWarning: The following kwargs were not used by contour: 'label'\n",
            "  plt.contour(x,y,z,conts,linewidths = [2],colors=ccolors,extent=extent, label='f(x)=0')\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[-2.7327221869191334,\n",
              " 3.383145774863942,\n",
              " -2.719590307416195,\n",
              " 3.2567244972982095]"
            ]
          },
          "metadata": {},
          "execution_count": 87
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#y_pred = x@wb+bb#wb@K\n",
        "#berr = torch.mean(y_pred[uidx])-cratio\n",
        "z = clf(inputs)\n",
        "#print(\"Accuracy\",np.mean(z*ttargets>0))\n",
        "from sklearn.metrics import roc_auc_score\n",
        "print(\"AUROC\",roc_auc_score(ttargets, z))\n",
        "#print(\"AUROC\",roc_auc_score(ttargets, wbn))"
      ],
      "metadata": {
        "id": "ERafpLRRK0Dm",
        "outputId": "c12ca74b-605a-4b6a-a78f-24d088795c16",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "AUROC 0.797453125\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "inputs.T@z,inputs.T@ttargets"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fMNXav9EES6i",
        "outputId": "ac55691f-fcba-4688-a0fb-c35a76e50241"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([[100.06629391],\n",
              "        [ 82.403701  ]]), array([111.02932579,  92.04020602]))"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "model"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vNGTkMrFFHkC",
        "outputId": "697bbb5d-67c7-4e1b-b9c1-2025c0502349"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Feedforward(\n",
              "  (fc1): Linear(in_features=2, out_features=100, bias=True)\n",
              "  (relu): ReLU()\n",
              "  (fc2): Linear(in_features=100, out_features=100, bias=True)\n",
              "  (sigmoid): Sigmoid()\n",
              "  (fc3): Linear(in_features=100, out_features=1, bias=True)\n",
              ")"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "y_pred.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MPV5JSUhKXYc",
        "outputId": "43de3be4-51e5-46f0-9349-0e82c7f275ce"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([200])"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "p5LW2UEsKZ56"
      },
      "execution_count": 7,
      "outputs": []
    }
  ]
}