vapnik2.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "barebones.ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyNS6WSr6ax7h5ADb/q2BnF+",
      "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/vapnik2.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",
        "outputId": "74ce487b-64a5-4432-be32-e13202260c88",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "'\\nAuthor: Fayyaz Minhas\\nSimple demonstration of learning with statistical predicates by Vapnik\\n'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "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": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TG-En3BVlBGG",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 599
        },
        "outputId": "6616b62c-ec90-4711-cff6-1d5dba66f153"
      },
      "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 = -0.5-np.random.randn(30,2);\n",
        "inputs = np.vstack((Xp,Xn))\t\n",
        "from sklearn.preprocessing import StandardScaler\n",
        "inputs = StandardScaler().fit_transform(inputs)\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=1.0)\n",
        "K = torch.from_numpy(K).float() #kernel\n",
        "psi2 = []\n",
        "for k in range(inputs.shape[0]):\n",
        "  r = inputs[k:k+1,:]\n",
        "  psi2.append((r.T@r).flatten())\n",
        "psi2 = np.array(psi2)\n",
        "P2 = psi2@psi2.T #makes the psi(x)=x@x.T\n",
        "\n",
        "P = (1*np.ones(K.shape)+1*inputs@inputs.T+P2)/3.0#psi(x)=1,psi(x)=x,psi(x)=x@x.T\n",
        "P = torch.from_numpy(P).float() #kernel\n",
        "M = 1*torch.eye(K.shape[0])+0*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, layer_size):\n",
        "            super(Feedforward, self).__init__()\n",
        "            self.layer_size = layer_size            \n",
        "            self.fc1 = torch.nn.Linear(self.layer_size[0], self.layer_size[1])\n",
        "            self.relu = torch.nn.ReLU()\n",
        "            self.fc2 = torch.nn.Linear(self.layer_size[1], self.layer_size[2])\n",
        "            self.sigmoid = torch.nn.Sigmoid()\n",
        "            self.tanh = torch.nn.Tanh()\n",
        "            self.fc3 = torch.nn.Linear(self.layer_size[2], self.layer_size[-1])\n",
        "        def forward(self, x):\n",
        "            x = self.fc1(x)\n",
        "            x = self.tanh(x)\n",
        "            x = self.fc2(x)\n",
        "            x = self.tanh(x)\n",
        "            x = self.fc3(x)\n",
        "            \n",
        "            return x\n",
        "model = Feedforward([D_in,500,200,D_out])\n",
        "\n",
        "optimizer = optim.Adam(model.parameters(), lr=1e-4)\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": 60,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-9-5604fef99228>: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": [
              "[-2.700724809315917, 2.402643142730158, -3.0587196692755185, 2.223110674491954]"
            ]
          },
          "metadata": {},
          "execution_count": 60
        }
      ]
    },
    {
      "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": "7baf05da-5d57-4ade-bce1-2a434927d8fe",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "AUROC 0.9925\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "inputs.T@z,inputs.T@ttargets"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fMNXav9EES6i",
        "outputId": "e54f381a-0d65-4925-ec4e-0321c151b6d2"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([[17.63204968],\n",
              "        [19.53351413]]), array([17.63227685, 19.53598008]))"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "model"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vNGTkMrFFHkC",
        "outputId": "fca45a62-5b7c-42ed-fecf-e79be01fdb1c"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Feedforward(\n",
              "  (fc1): Linear(in_features=2, out_features=500, bias=True)\n",
              "  (relu): ReLU()\n",
              "  (fc2): Linear(in_features=500, out_features=100, bias=True)\n",
              "  (sigmoid): Sigmoid()\n",
              "  (tanh): Tanh()\n",
              "  (fc3): Linear(in_features=100, out_features=1, bias=True)\n",
              ")"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "y_pred.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MPV5JSUhKXYc",
        "outputId": "751f9e66-1421-4023-a3d3-b375e3cd641b"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([210])"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "(inputs@inputs.T).shape"
      ],
      "metadata": {
        "id": "p5LW2UEsKZ56",
        "outputId": "752d6649-eb72-4b53-8ce5-e2febeadd393",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(210, 210)"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "IcEuhE00kTh4"
      },
      "execution_count": 49,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "psi2.shape"
      ],
      "metadata": {
        "id": "9uuWvG1yl5Qp",
        "outputId": "63fccefb-1c5d-4097-f92d-508bbe7f375f",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 50,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(210, 4)"
            ]
          },
          "metadata": {},
          "execution_count": 50
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "psi2@psi2.T"
      ],
      "metadata": {
        "id": "soaHGbPQmloJ",
        "outputId": "53f7814f-07e1-459c-c143-315250aa3b68",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1.12249779e+01, 8.12275618e+00, 8.62681120e+00, ...,\n",
              "        4.75318453e+01, 1.98001944e+01, 4.87947750e+01],\n",
              "       [8.12275618e+00, 3.34733969e+01, 3.45356815e-02, ...,\n",
              "        7.47836960e+01, 3.89896888e+01, 1.10659866e+02],\n",
              "       [8.62681120e+00, 3.45356815e-02, 1.73567873e+01, ...,\n",
              "        1.70498847e+01, 4.87983252e+00, 8.84651913e+00],\n",
              "       ...,\n",
              "       [4.75318453e+01, 7.47836960e+01, 1.70498847e+01, ...,\n",
              "        2.71962622e+02, 1.25272920e+02, 3.29938204e+02],\n",
              "       [1.98001944e+01, 3.89896888e+01, 4.87983252e+00, ...,\n",
              "        1.25272920e+02, 5.94244333e+01, 1.59417546e+02],\n",
              "       [4.87947750e+01, 1.10659866e+02, 8.84651913e+00, ...,\n",
              "        3.29938204e+02, 1.59417546e+02, 4.32535048e+02]])"
            ]
          },
          "metadata": {},
          "execution_count": 52
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "JEtTCOBQnnHX"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}