VI_BMM.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "source": [
        "#### binomial mixture model with variational inference ####\n",
        "\n",
        "# imports\n",
        "from scipy.special import comb\n",
        "import matplotlib.pyplot as plt\n",
        "import pandas as pd\n",
        "import seaborn as sns\n",
        "import torch\n",
        "torch.manual_seed(4)\n",
        "\n",
        "x_train= pd.read_csv(f'/content/gdrive/My Drive/X_data.csv', header=None)\n",
        "x_train = torch.tensor(x_train.to_numpy())"
      ],
      "metadata": {
        "id": "-2ZJzFyOrbpd"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "##### variational inference implementation ######\n",
        "def VI_bmm(x_,K=3,iter=500,runs=1):\n",
        "  n, d = x_.shape\n",
        "  best_VI=-1e16\n",
        "  best_LLs=[]\n",
        "\n",
        "  #initializing priors\n",
        "  alpha0 = 0.1\n",
        "  a0 = 0.5\n",
        "  b0 = 0.5\n",
        "\n",
        "  for j in range(runs):\n",
        "    # initializing variational parameters\n",
        "    a_s = torch.FloatTensor(1,K).uniform_(10, 100)\n",
        "    b_s = torch.FloatTensor(1,K).uniform_(10, 100)\n",
        "    alphas = torch.FloatTensor(1,K).uniform_(0,1)\n",
        "\n",
        "    # initializing log expectations for parameters\n",
        "    lnpi =torch.digamma(alphas) - torch.digamma(torch.sum(alphas))\n",
        "    ln_pos_theta = torch.digamma(a_s) -torch.digamma(a_s + b_s)\n",
        "    ln_neg_theta = torch.digamma(b_s) -torch.digamma(a_s + b_s)\n",
        "    constant=torch.log(torch.tensor(comb(20, x_)))\n",
        "\n",
        "    LLs =[]\n",
        "    for i in range(iter):\n",
        "      # update q(ci)\n",
        "      phi =torch.exp(lnpi + x_*ln_pos_theta + (20 -x_)*ln_neg_theta + constant)\n",
        "      phi = phi/ torch.sum(phi, axis=1)[:,None]\n",
        "\n",
        "      # update q(pi) q(theta) parameters\n",
        "      nj= torch.sum(phi, axis=0)\n",
        "      alphas =alpha0 + nj\n",
        "      a_s=a0 + torch.sum(phi*x_, axis=0)\n",
        "      b_s=b0 + torch.sum(phi*(20-x_), axis=0)\n",
        "\n",
        "      # update log expectations for parameters\n",
        "      lnpi =torch.digamma(alphas) - torch.digamma(torch.sum(alphas))\n",
        "      ln_pos_theta = torch.digamma(a_s) -torch.digamma(a_s + b_s)\n",
        "      ln_neg_theta = torch.digamma(b_s) -torch.digamma(a_s + b_s)\n",
        "\n",
        "      # variational objective function: evidence lower bound (ELBO)\n",
        "      VI =-(torch.sum((alphas-1)*lnpi,axis=0) + torch.lgamma(torch.sum(alphas,axis=0)) - torch.sum(torch.lgamma(alphas)) )    -\\\n",
        "        torch.sum(((a_s-1)* ln_pos_theta) + ((b_s-1)* ln_neg_theta) -torch.lgamma(a_s) -torch.lgamma(b_s) +torch.lgamma(a_s +b_s) )+\\\n",
        "        torch.sum((alpha0-1)*lnpi) + ((a0-1)* torch.sum(ln_pos_theta)) + (b0-1)*torch.sum(ln_neg_theta)+\\\n",
        "        torch.sum(phi*lnpi) + torch.sum(phi* (x_*ln_pos_theta + (20 -x_)*ln_neg_theta +constant)) -torch.sum(phi*torch.log(phi))\n",
        "      LLs+=[VI]\n",
        "    # saving best run\n",
        "    if best_VI<VI:\n",
        "       best_VI=VI\n",
        "       best_LLs=LLs\n",
        "       best_phi=phi\n",
        "  return best_LLs, best_phi"
      ],
      "metadata": {
        "id": "0gLUxjK6uMX6"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# binomial mixture model with variational inference\n",
        "LL3,phi1=VI_bmm(x_train, 3,iter=500,runs=10)\n",
        "LL9,phi2=VI_bmm(x_train, 9,iter=500,runs=10)\n",
        "LL15,phi3=VI_bmm(x_train, 15,iter=500,runs=10)"
      ],
      "metadata": {
        "id": "YKCoxQWHtRzj"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# plot evidence lower bound (ELBO)\n",
        "fig =plt.figure()\n",
        "plt.plot(range(2,501),LL3[1:],color=\"red\",label='3')\n",
        "plt.plot(range(2,501),LL9[1:],color=\"blue\",label='9')\n",
        "plt.plot(range(2,501),LL15[1:],color=\"goldenrod\",label='15')\n",
        "plt.title(\"VI for Binomial Mixture Model\")\n",
        "plt.ylabel(\"Log Likelihood\")\n",
        "plt.xlabel(\"Iteration\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "BurkviLZuiMa",
        "outputId": "652bc538-58c0-4063-c642-01f5aa5f7608"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# examine cluster assignments for x=1...x=20\n",
        "# K = 3\n",
        "qs =[]\n",
        "for x in range (0,21):\n",
        "  qs+=[phi1[np.where(x_train == x)[0]][-1].numpy()]\n",
        "result=pd.DataFrame(np.round(np.array(qs).T, 3).tolist())\n",
        "sns.heatmap(result)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 452
        },
        "id": "haO6lQWDwCd6",
        "outputId": "fbfad729-4287-49c1-ce62-a35e367edf19"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Axes: >"
            ]
          },
          "metadata": {},
          "execution_count": 92
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# K = 9\n",
        "qs =[]\n",
        "for x in range (0,21):\n",
        "  qs+=[phi2[np.where(x_train == x)[0]][-1].numpy()]\n",
        "result=pd.DataFrame(np.round(np.array(qs).T, 3).tolist())\n",
        "sns.heatmap(result)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 452
        },
        "id": "Nm3AZNMRusYb",
        "outputId": "01764e88-1808-456f-e4e7-d74b4a319e5d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Axes: >"
            ]
          },
          "metadata": {},
          "execution_count": 93
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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evXopMTHR0nktzxlwuVy/HBgQoNDQUIWHh5e9Vr9+fR09etRqSAAAahbDZdvm8Xh07Ngxn808iV765Vt+Xl6eUlJSytoCAgKUkpKinJyccru5evVqdevWTampqYqMjNTVV1+t6dOnq7S01NLbtZQMxMfHa/v27WU/5+TkqEWLFmU/7927V9HR0ZY6AABATWPnMEF5k+YzMzPPOefhw4dVWlqqyMhIn/bIyEgVFhaW289du3bpzTffVGlpqd577z1NmTJFs2fP1p///GdL79fS0sLRo0f7ZBtXX321z+vvv/++brrpJksdAADgv1l6errS0tJ82uyaJ+f1etW0aVO9+OKLCgwMVFJSkvbt26ennnpKGRkZlY5jKRl44IELz/ifPn26lXAAANRIhtdlWyy3212pP/4REREKDAxUUVGRT3tRUZGioqLKPSY6OlrBwcEKDAwsa7vyyitVWFiokpIShYSEVKqPPJsAAACT6lhNEBISoqSkJGVnZ5e1eb1eZWdnq1u3buUe0717d+3YsUNe779PtG3bNkVHR1c6EZBIBgAAqDHS0tK0aNEivfzyy9qyZYtGjx6t4uJijRgxQpI0dOhQpaenl+0/evRo/etf/9K4ceO0bds2rVmzRtOnT1dqaqql8/JsAgAATAzDvmECKwYNGqRDhw5p6tSpKiwsVMeOHZWVlVU2qXDv3r0KCPj39/jmzZtr7dq1mjBhgjp06KDY2FiNGzdOkyZNsnRel2EYhq3vxE9nDu+q7i44U+kZ20J5jx6yL1bu+7bF+vqhLbbFmhxYbFus/CP2XfMnSk7ZEsdbMz4OgAqdLdlXpfF/TLZvMnyzzyt3q/7qxDABAAAOxzABAAAmdq4mqA1IBgAAMHHaiBnJAAAAJk6rDDBnAAAAh6MyAACAidMqAyQDAACYOG3OAMMEAAA4HJUBAABMGCaoJmEx11d3FxwpwGXfBd/AXce2WEnhrWyLlRlY+Yd1VOSdWdfaFivgmkdsi+UKrWtLHG/hTlviSNLZN/5mW6ylKxvYFmvxmd22xdp5/IBtsU6fLbEtFneSvHjVdTvi6sIwAQAADldjKgMAANQUVh49/N+AZAAAABMvwwQAAMBJqAwAAGDitAmEJAMAAJiwtBAAAIdz2upM5gwAAOBwVAYAADBhmAAAAIdjaSEAAHAUKgMAAJiwtBAAAIdjNQEAAHAUKgMAAJg4bQIhyQAAACZOmzPAMAEAAA5nS2XAMAy5XM7KogAA/72cNoHQlmTA7Xbrq6++0pVXXlmp/T0ejzwej08bCQUAoKZgzsAFpKWlldteWlqqGTNmqHHjxpKkOXPmXDBOZmampk2b5tPmCqgnV2ADK90BAKBKOG3OgKVkYO7cuUpMTNRll13m024YhrZs2aK6detW6tt9enr6OYlFw8YJVroCAABsYikZmD59ul588UXNnj1bN910U1l7cHCwli5dqnbt2lUqjtvtltvt9mljiAAAUFM4bZjA0mqChx9+WCtWrNDo0aP14IMP6syZM1XVLwAAqo1h41YbWF5a2KVLF+Xl5enQoUPq3LmzNm/ezLd6AABqMb9WE9SrV08vv/yyli9frpSUFJWWltrdLwAAqo3ThgkuamnhPffcox49eigvL09xcXF29QkAgGrFagKLmjVrpmbNmtnRFwAAUA14NgEAACbe6u7AJUYyAACAiSFnDRPwoCIAAByOygAAACbe2nKDAJuQDAAAYOJ12DAByQAAACbMGQAAAI5CZQAAABOWFgIA4HAMEwAAAEehMgAAgAnDBAAAOJzTkgGGCQAAcDiXYRg14j5LQSGx1d0FAEAtcbZkX5XGXxM52LZYtxW9blusqsIwAQAAJl5nLSZgmAAAAKejMgAAgAnPJgAAwOFqxGS6S4hkAAAAE5YWAgAAR6EyAACAidfFnAEAABzNaXMGGCYAAMDhqAwAAGDitAmEJAMAAJhwB0IAAOAoJAMAAJh45bJts2r+/PmKj49XaGiokpOTlZubW6njli9fLpfLpQEDBlg+J8kAAAAmho2bFStWrFBaWpoyMjKUn5+vxMRE9enTRwcPHrzgcd9//70efPBBXX/99RbP+AuSAQAAqpDH49GxY8d8No/HU+6+c+bM0ahRozRixAi1a9dOCxcuVJ06dbRkyZLzxi8tLdWQIUM0bdo0tWzZ0q8+kgwAAGDiddm3ZWZmKjw83GfLzMw855wlJSXKy8tTSkpKWVtAQIBSUlKUk5Nz3r4+/vjjatq0qe677z6/3y+rCQAAMLFzaWF6errS0tJ82txu9zn7HT58WKWlpYqMjPRpj4yM1HfffVdu7E8++USLFy9WQUHBRfWRZAAAABM770DodrvL/eN/sY4fP657771XixYtUkRExEXFIhkAAKAGiIiIUGBgoIqKinzai4qKFBUVdc7+O3fu1Pfff69+/fqVtXm9v9Q0goKCtHXrVrVq1apS576oZKC4uFhvvPGGduzYoejoaA0ePFiNGzeu8DiPx3PO5AnDMORy2IMhAAA1U3XcdCgkJERJSUnKzs4uWx7o9XqVnZ2tMWPGnLN/QkKCvvnmG5+2Rx99VMePH9ezzz6r5s2bV/rclpKBdu3a6ZNPPlGjRo30ww8/qGfPnvr555/Vpk0b7dy5U0888YQ+++wzXX755ReMk5mZqWnTpvm0uQLqyRXYwEp3AACoEtV1O+K0tDQNGzZMnTt3VteuXTV37lwVFxdrxIgRkqShQ4cqNjZWmZmZCg0N1dVXX+1z/GWXXSZJ57RXxNJqgu+++05nz56V9MuEiJiYGO3Zs0e5ubnas2ePOnTooMmTJ1cYJz09XUePHvXZXAH1LXUcAID/NoMGDdLTTz+tqVOnqmPHjiooKFBWVlbZpMK9e/fqwIEDtp/XZRhGpedJBAQEqLCwUE2bNlWrVq20cOFC/eY3vyl7/dNPP9U999yjvXv3Wu5IUEis5WMAAM50tmRflcb/S7Pf2xbrf358zbZYVcXynIFfx/VPnz6t6Ohon9diY2N16NAhe3oGAEA1MRw2hc1yMnDzzTcrKChIx44d09atW33GJfbs2VOpCYQAAKDmsJQMZGRk+Pxcr149n5/feecdv++LDABATVFdEwiri6U5A1WJOQMAgMqq6jkD85rbN2dgzA81f84AzyYAAMDhuAMhAAAmNaJkfgmRDAAAYFIddyCsTiQDAACYOG0CIXMGAABwOCoDAACYOK0yQDIAAICJ0yYQMkwAAIDDURkAAMCE1QQAADic0+YMMEwAAIDDURkAAMDEaRMISQYAADDxOiwdYJgAAACHozIAAICJ0yYQkgwAAGDirEECkgEAAM7htMoAcwYAAHA4KgMAAJhwB0IAAByOpYUAAMBRqAwAAGDirLoAyQAAAOdgNQEAAHAUKgMAAJg4bQIhyQAAACbOSgUYJgAAwPGoDAAAYOK0CYQkAwAAmDBnAAAAh3NWKsCcAQAAHI/KAAAAJswZAADA4QyHDRRYGibIz8/X7t27y35+9dVX1b17dzVv3lw9evTQ8uXLKxXH4/Ho2LFjPpthOOsfHgCAmsJSMjBixAjt3LlTkvTXv/5V//M//6POnTtr8uTJ6tKli0aNGqUlS5ZUGCczM1Ph4eE+m+E97t87AADAZl4bt9rAZVj4Sl6nTh1t2bJFcXFx6tSpk0aPHq1Ro0aVvb5s2TI9+eST+vbbby8Yx+PxyOPx+LQ1bJwgl8tlsfsAACc6W7KvSuP/MX6gbbFe+P4N22JVFUtzBurUqaPDhw8rLi5O+/btU9euXX1eT05O9hlGOB+32y232+3TRiIAAED1sDRMcMstt2jBggWSpF69eunNN9/0ef2NN95Q69at7esdAADVwLBxqw0sVQZmzpyp7t27q1evXurcubNmz56tDRs26Morr9TWrVv12WefadWqVVXVVwAALgmn3YHQUmUgJiZGX375pbp166asrCwZhqHc3Fx98MEHatasmf7v//5Pt956a1X1FQAAVAFLEwirUlBIbHV3AQBQS1T1BMJR8XfbFmvR9ytti1VVuOkQAAAmTrvpEMkAAAAmteX+AHbhQUUAADgclQEAAEwYJgAAwOEYJgAAAI5CZQAAABNvzVh1f8mQDAAAYOKsVIBhAgAAHI/KAAAAJk57NgHJAAAAJk5bWsgwAQAADkdlAAAAE6fdZ4BkAAAAE+YMAADgcMwZAAAAjkJlAAAAE+YMAADgcIbDbkfMMAEAADXI/PnzFR8fr9DQUCUnJys3N/e8+y5atEjXX3+9GjZsqIYNGyolJeWC+58PyQAAACZeGbZtVqxYsUJpaWnKyMhQfn6+EhMT1adPHx08eLDc/Tds2KDBgwdr/fr1ysnJUfPmzdW7d2/t27fP0nldRg2phQSFxFZ3FwAAtcTZEmt/7Kzq1+L/sy3Wm9v/f3k8Hp82t9stt9t9zr7Jycnq0qWL5s2bJ0nyer1q3ry5xo4dq4cffrjCc5WWlqphw4aaN2+ehg4dWuk+UhkAAKAKZWZmKjw83GfLzMw8Z7+SkhLl5eUpJSWlrC0gIEApKSnKycmp1LlOnjypM2fOqFGjRpb6yARCAABM7LzPQHp6utLS0nzayqsKHD58WKWlpYqMjPRpj4yM1HfffVepc02aNEkxMTE+CUVlkAwAAGBi5x0IzzckYLcZM2Zo+fLl2rBhg0JDQy0dSzIAAEANEBERocDAQBUVFfm0FxUVKSoq6oLHPv3005oxY4Y+/PBDdejQwfK5mTMAAICJYRi2bZUVEhKipKQkZWdnl7V5vV5lZ2erW7du5z1u1qxZeuKJJ5SVlaXOnTv79X6pDAAAYFJddyBMS0vTsGHD1LlzZ3Xt2lVz585VcXGxRowYIUkaOnSoYmNjyyYgzpw5U1OnTtWyZcsUHx+vwsJCSVK9evVUr169Sp+XZAAAAJPqelDRoEGDdOjQIU2dOlWFhYXq2LGjsrKyyiYV7t27VwEB/y7qL1iwQCUlJbrrrrt84mRkZOixxx6r9Hm5zwAAoNap6vsM9G7e17ZYH/yQZVusqkJlAAAAEztXE9QGJAMAAJjUkKL5JcNqAgAAHI7KAAAAJk4bJrBUGRg7dqw+/vjjiz6px+PRsWPHfDanlWQAADWXYeP/agNLycD8+fN1ww03qE2bNpo5c2bZekaryntog+E97lcsAABwcSzPGfjggw9066236umnn1aLFi3Uv39/vfvuu/J6K3+LhvT0dB09etRncwXUt9oVAACqhNcwbNtqA8vJQPv27TV37lzt379fr732mjwejwYMGKDmzZtr8uTJ2rFjR4Ux3G63GjRo4LO5XC6/3gAAAHYzbNxqA79XEwQHB2vgwIHKysrSrl27NGrUKP3tb39T27Zt7ewfAACoYrYsLWzRooUee+wx7d69W1lZNf9OSwAAXIhXhm1bbWBpaWFcXJwCAwPP+7rL5dJvfvObi+4UAADVqbb8EbeLpWRg9+7dVdUPAABqDKctd+cOhAAAOBx3IAQAwIRhAgAAHK623DnQLgwTAADgcFQGAAAwcdoEQpIBAABMnDZngGECAAAcjsoAAAAmDBMAAOBwDBMAAABHoTIAAICJ0+4zQDIAAICJlzkDAAA4m9MqA8wZAADA4agMAABgwjABAAAOxzABAABwFCoDAACYMEwAAIDDMUwAAAAchcoAAAAmDBMAAOBwDBMAAABHoTIAAICJYXiruwuXFMkAAAAmXocNE5AMAABgYjhsAiFzBgAAcDgqAwAAmDBMAACAwzFMAAAAHIXKAAAAJtyBEAAAh+MOhAAAwFEsJwPz5s3T0KFDtXz5cknSq6++qnbt2ikhIUGPPPKIzp49W2EMj8ejY8eO+WxOm6wBAKi5DMOwbasNLA0T/PnPf9asWbPUu3dvTZgwQXv27NFTTz2lCRMmKCAgQM8884yCg4M1bdq0C8bJzMw8Zx9XQD25AhtYfwcAANjMaUsLXYaFtKV169aaNWuW7rzzTn311VdKSkrSyy+/rCFDhkiSVq1apYceekjbt2+/YByPxyOPx+PT1rBxglwulx9vAQDgNGdL9lVp/CbhbW2LdejoVttiVRVLlYH9+/erc+fOkqTExEQFBASoY8eOZa936tRJ+/fvrzCO2+2W2+32aSMRAADUFLWlvG8XS3MGoqKi9M9//lOStH37dpWWlpb9LEnffvutmjZtam8PAQC4xLyGYdtWG1iqDAwZMkRDhw5V//79lZ2drYceekgPPvigfvrpJ7lcLj355JO66667qqqvAABcEk6rDFhKBqZNm6awsDDl5ORo1KhRevjhh5WYmKiHHnpIJ0+eVL9+/fTEE09UVV8BAEAVsDSBsCoFhcRWdxcAALVEVU8gDK/XyrZYR0/stC1WVeEOhAAAmNSQ78mXDHcgBADA4agMAABgUltWAdiFZAAAABMeVAQAAByFygAAACYMEwAA4HCsJgAAAI5CZQAAABOnTSAkGQAAwIRhAgAAHM4wDNs2q+bPn6/4+HiFhoYqOTlZubm5F9x/5cqVSkhIUGhoqNq3b6/33nvP8jlJBgAAqCFWrFihtLQ0ZWRkKD8/X4mJierTp48OHjxY7v6ffvqpBg8erPvuu09ffvmlBgwYoAEDBmjz5s2WzsuDigAAtU5VP6jIzr9Jxcd3yePx+LS53W653e5z9k1OTlaXLl00b948SZLX61Xz5s01duxYPfzww+fsP2jQIBUXF+vdd98ta7v22mvVsWNHLVy4sPKdNGqJ06dPGxkZGcbp06eJRawa2SdiEas29MkpsWqSjIwMQ5LPlpGRcc5+Ho/HCAwMNFatWuXTPnToUOP2228vN3bz5s2NZ555xqdt6tSpRocOHSz1sdYkA0ePHjUkGUePHiUWsWpkn4hFrNrQJ6fEqklOnz5tHD161GcrL+HZt2+fIcn49NNPfdonTpxodO3atdzYwcHBxrJly3za5s+fbzRt2tRSH1lNAABAFTrfkEBNwgRCAABqgIiICAUGBqqoqMinvaioSFFRUeUeExUVZWn/8yEZAACgBggJCVFSUpKys7PL2rxer7Kzs9WtW7dyj+nWrZvP/pK0bt268+5/PrVmmMDtdisjI8OWUguxan+smtgnYhGrNvTJKbFqq7S0NA0bNkydO3dW165dNXfuXBUXF2vEiBGSpKFDhyo2NlaZmZmSpHHjxqlXr16aPXu2brvtNi1fvlybNm3Siy++aOm8NWZpIQAAkObNm6ennnpKhYWF6tixo5577jklJydLkm644QbFx8dr6dKlZfuvXLlSjz76qL7//ntdccUVmjVrlm699VZL5yQZAADA4ZgzAACAw5EMAADgcCQDAAA4HMkAAAAOV2uSAauPdCzPRx99pH79+ikmJkYul0tvv/223/3JzMxUly5dVL9+fTVt2lQDBgzQ1q1b/Yq1YMECdejQQQ0aNFCDBg3UrVs3vf/++3737VczZsyQy+XS+PHjLR/72GOPyeVy+WwJCQl+92Xfvn36/e9/r8aNGyssLEzt27fXpk2bLMeJj48/p18ul0upqamWY5WWlmrKlCm6/PLLFRYWplatWumJJ57w+znmx48f1/jx4xUXF6ewsDBdd911+uKLLyo8rqLr0jAMTZ06VdHR0QoLC1NKSoq2b9/uV6y33npLvXv3VuPGjeVyuVRQUOBXv86cOaNJkyapffv2qlu3rmJiYjR06FDt37/fr3499thjSkhIUN26ddWwYUOlpKTo888/txznPz3wwANyuVyaO3euX30aPnz4OddZ3759/YolSVu2bNHtt9+u8PBw1a1bV126dNHevXstxyrv+ne5XHrqqacsxzpx4oTGjBmjZs2aKSwsTO3atTvvw20qilVUVKThw4crJiZGderUUd++fcu9Tivz2Xn69GmlpqaqcePGqlevnn7729+ec2Md2KtWJANWH+l4PsXFxUpMTNT8+fMvuk8bN25UamqqPvvsM61bt05nzpxR7969VVxcbDlWs2bNNGPGDOXl5WnTpk266aab1L9/f3377bd+9++LL77QX/7yF3Xo0MHvGFdddZUOHDhQtn3yySd+xfn555/VvXt3BQcH6/3339c///lPzZ49Ww0bNrQc64svvvDp07p16yRJd999t+VYM2fO1IIFCzRv3jxt2bJFM2fO1KxZs/T8889bjiVJ999/v9atW6dXX31V33zzjXr37q2UlBTt23fhp6tVdF3OmjVLzz33nBYuXKjPP/9cdevWVZ8+fXT69GnLsYqLi9WjRw/NnDmzwvdzoVgnT55Ufn6+pkyZovz8fL311lvaunWrbr/9dr/eY5s2bTRv3jx98803+uSTTxQfH6/evXvr0KFDluL8atWqVfrss88UExPj1/v7Vd++fX2ut9dff92vWDt37lSPHj2UkJCgDRs26Ouvv9aUKVMUGhpqOdZ/9ufAgQNasmSJXC6Xfvvb31qOlZaWpqysLL322mvasmWLxo8frzFjxmj16tWWYhmGoQEDBmjXrl36+9//ri+//FJxcXFKSUk55zOxMp+dEyZM0DvvvKOVK1dq48aN2r9/v+68885y3wNsYulJBtWka9euRmpqatnPpaWlRkxMjJGZmel3TEnnPBnqYhw8eNCQZGzcuNGWeA0bNjT++te/+nXs8ePHjSuuuMJYt26d0atXL2PcuHGWY2RkZBiJiYl+nd9s0qRJRo8ePWyJZTZu3DijVatWhtfrtXzsbbfdZowcOdKn7c477zSGDBliOdbJkyeNwMBA49133/Vp79SpkzF58uRKxzFfl16v14iKijKeeuqpsrYjR44YbrfbeP311y3F+k+7d+82JBlffvmlX/0qT25uriHJ2LNnz0XH+vWBNR9++KHlOD/++KMRGxtrbN682YiLizvniW6VjTVs2DCjf//+FR5bmViDBg0yfv/739sSy6x///7GTTfd5Fesq666ynj88cd92ipzzZpjbd261ZBkbN68uayttLTUaNKkibFo0aILxjJ/dh45csQIDg42Vq5cWbbPli1bDElGTk7OBWPBfzW+MlBSUqK8vDylpKSUtQUEBCglJUU5OTnV2DNfR48elSQ1atToouKUlpZq+fLlKi4utnw7yV+lpqbqtttu8/k388f27dsVExOjli1basiQIeWWNCtj9erV6ty5s+6++241bdpU11xzjRYtWnRRfZN+uTZee+01jRw5Ui6Xy/Lx1113nbKzs7Vt2zZJ0ldffaVPPvlEt9xyi+VYZ8+eVWlp6Tnf9MLCwvyuqEjS7t27VVhY6PP/ZXh4uJKTk2vU9S/98jvgcrl02WWXXVSckpISvfjiiwoPD1diYqKlY71er+69915NnDhRV1111UX1Q5I2bNigpk2bqm3btho9erR++uknyzG8Xq/WrFmjNm3aqE+fPmratKmSk5MvapjyV0VFRVqzZo3uu+8+v46/7rrrtHr1au3bt0+GYWj9+vXatm2bevfubSmOx+ORJJ/rPyAgQG63u8Lr3/zZmZeXpzNnzvhc8wkJCWrRokWNu+b/m9T4ZODw4cMqLS1VZGSkT3tkZKQKCwurqVe+vF6vxo8fr+7du+vqq6/2K8Y333yjevXqye1264EHHtCqVavUrl07y3GWL1+u/Pz8sltV+is5OVlLly5VVlaWFixYoN27d+v666/X8ePHLcfatWuXFixYoCuuuEJr167V6NGj9ac//Ukvv/zyRfXx7bff1pEjRzR8+HC/jn/44Yd1zz33KCEhQcHBwbrmmms0fvx4DRkyxHKs+vXrq1u3bnriiSe0f/9+lZaW6rXXXlNOTo4OHDjgV/8klV3jNfn6l34Z4500aZIGDx6sBg0a+BXj3XffVb169RQaGqpnnnlG69atU0REhKUYM2fOVFBQkP70pz/51Yf/1LdvX73yyivKzs7WzJkztXHjRt1yyy0qLS21FOfgwYM6ceKEZsyYob59++qDDz7QHXfcoTvvvFMbN268qD6+/PLLql+/vt8l9Oeff17t2rVTs2bNFBISor59+2r+/Pnq2bOnpTi//rFOT0/Xzz//rJKSEs2cOVM//vjjBa//8j47CwsLFRISck5SWdOu+f82tebZBDVZamqqNm/efFHfANu2bauCggIdPXpUb775poYNG6aNGzdaSgh++OEHjRs3TuvWrSt3LNKK//x23KFDByUnJysuLk5vvPGG5W8hXq9XnTt31vTp0yVJ11xzjTZv3qyFCxdq2LBhfvdx8eLFuuWWWy44Lnwhb7zxhv72t79p2bJluuqqq1RQUKDx48crJibGr369+uqrGjlypGJjYxUYGKhOnTpp8ODBysvL86t/tcWZM2c0cOBAGYahBQsW+B3nxhtvVEFBgQ4fPqxFixZp4MCB+vzzz9W0adNKHZ+Xl6dnn31W+fn5flWKzO65556y/27fvr06dOigVq1aacOGDbr55psrHcfr9UqS+vfvrwkTJkiSOnbsqE8//VQLFy5Ur169/O7jkiVLNGTIEL9/359//nl99tlnWr16teLi4vTRRx8pNTVVMTExliqLwcHBeuutt3TfffepUaNGCgwMVEpKim655ZYLTsi147MT9qjxlQF/Hul4KY0ZM0bvvvuu1q9fr2bNmvkdJyQkRK1bt1ZSUpIyMzOVmJioZ5991lKMvLw8HTx4UJ06dVJQUJCCgoK0ceNGPffccwoKCrL8jeY/XXbZZWrTpo127Nhh+djo6Ohzkporr7zS72EHSdqzZ48+/PBD3X///X7HmDhxYll1oH379rr33ns1YcIEv6sqrVq10saNG3XixAn98MMPys3N1ZkzZ9SyZUu/+/jrNV5Tr/9fE4E9e/Zo3bp1flcFJKlu3bpq3bq1rr32Wi1evFhBQUFavHhxpY//+OOPdfDgQbVo0aLs+t+zZ4/+93//V/Hx8X7361ctW7ZURESE5d+BiIgIBQUF2f478PHHH2vr1q1+/w6cOnVKjzzyiObMmaN+/fqpQ4cOGjNmjAYNGqSnn37acrykpCQVFBToyJEjOnDggLKysvTTTz+d9/o/32dnVFSUSkpKdOTIEZ/9a8o1/9+qxicD/jzS8VIwDENjxozRqlWr9I9//EOXX365rfG9Xm/ZOFxl3Xzzzfrmm29UUFBQtnXu3FlDhgxRQUGBAgMD/e7PiRMntHPnTkVHR1s+tnv37ucsHdq2bZvi4uL87s9LL72kpk2b6rbbbvM7xsmTJxUQ4PsrEBgYWPZNzl9169ZVdHS0fv75Z61du1b9+/f3O9bll1+uqKgon+v/2LFj+vzzz6v1+pf+nQhs375dH374oRo3bmxrfKu/A/fee6++/vprn+s/JiZGEydO1Nq1ay+6Pz/++KN++ukny78DISEh6tKli+2/A4sXL1ZSUpLleRW/OnPmjM6cOWP770B4eLiaNGmi7du3a9OmTedc/xV9diYlJSk4ONjnmt+6dav27t1b7df8f7NaMUxQ0SMdK+vEiRM+Wf3u3btVUFCgRo0aqUWLFpZipaamatmyZfr73/+u+vXrl41lhYeHKywszFKs9PR03XLLLWrRooWOHz+uZcuWacOGDZY/wOrXr3/OnIW6deuqcePGlucyPPjgg+rXr5/i4uK0f/9+ZWRkKDAwUIMHD7YUR/plmdB1112n6dOna+DAgcrNzdWLL75o+RGbv/J6vXrppZc0bNgwBQX5fwn369dPTz75pFq0aKGrrrpKX375pebMmaORI0f6FW/t2rUyDENt27bVjh07NHHiRCUkJFR4nVZ0XY4fP15//vOfdcUVV+jyyy/XlClTFBMTowEDBliO9a9//Ut79+4tux/Ar3+goqKizvnWdaFY0dHRuuuuu5Sfn693331XpaWlZb8DjRo1UkhISKVjNW7cWE8++aRuv/12RUdH6/Dhw5o/f7727dt3zpLRit6fOSEJDg5WVFSU2rZta+nfqlGjRpo2bZp++9vfKioqSjt37tRDDz2k1q1bq0+fPpb/3SdOnKhBgwapZ8+euvHGG5WVlaV33nlHGzZssBxL+iUhXLlypWbPnn3O8VZi9erVSxMnTlRYWJji4uK0ceNGvfLKK5ozZ47lWCtXrlSTJk3UokULffPNNxo3bpwGDBhwzmTEij47w8PDdd999yktLU2NGjVSgwYNNHbsWHXr1k3XXnvtBd8vLkJ1LmWw4vnnnzdatGhhhISEGF27djU+++wzyzHWr19vSDpnGzZsmOVY5cWRZLz00kuWY40cOdKIi4szQkJCjCZNmhg333yz8cEHH1iOUx5/lxYOGjTIiI6ONkJCQozY2Fhj0KBBxo4dO/zuxzvvvGNcffXVhtvtNhISEowXX3zR71hr1641JBlbt271O4ZhGMaxY8eMcePGGS1atDBCQ0ONli1bGpMnTzY8Ho9f8VasWGG0bNnSCAkJMaKioozU1FTjyJEjFR5X0XXp9XqNKVOmGJGRkYbb7TZuvvnm8773imK99NJL5b6ekZFhKdavSxPL29avX28p1qlTp4w77rjDiImJMUJCQozo6Gjj9ttvN3Jzcy2/P7MLLS28UKyTJ08avXv3Npo0aWIEBwcbcXFxxqhRo4zCwkK//t0NwzAWL15stG7d2ggNDTUSExONt99+2+9Yf/nLX4ywsLAKr6+KYh04cMAYPny4ERMTY4SGhhpt27Y1Zs+eXe5S3YpiPfvss0azZs2M4OBgo0WLFsajjz5a7u9SZT47T506Zfzxj380GjZsaNSpU8e44447jAMHDlzwveLi8AhjAAAcrsbPGQAAAFWLZAAAAIcjGQAAwOFIBgAAcDiSAQAAHI5kAAAAhyMZAADA4UgGAABwOJIBAAAcjmQAAACHIxkAAMDh/h/mns4JTb29QgAAAABJRU5ErkJggg==\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# K = 15\n",
        "qs =[]\n",
        "for x in range (0,21):\n",
        "  qs+=[phi3[np.where(x_train == x)[0]][-1].numpy()]\n",
        "result=pd.DataFrame(np.round(np.array(qs).T, 3).tolist())\n",
        "sns.heatmap(result)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 452
        },
        "id": "WyeQtmxo2LkM",
        "outputId": "8b0740ad-c086-48d8-cbb1-89372a4705d3"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Axes: >"
            ]
          },
          "metadata": {},
          "execution_count": 94
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}