distances-overfit.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pickle as pkl\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import metrics\n",
    "# y = np.array([1, 1, 2, 2])\n",
    "# pred = np.array([0.1, 0.4, 0.35, 0.8])\n",
    "# fpr, tpr, thresholds = metrics.roc_curve(y, pred, pos_label=2)\n",
    "# metrics.auc(fpr, tpr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats # gaussian_kde"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open(\"x_defender.pickle\", \"rb\") as f:\n",
    "    x_defender = pkl.load(f)\n",
    "    \n",
    "with open(\"x_reserve.pickle\", \"rb\") as f:\n",
    "    x_reserve = pkl.load(f)\n",
    "    \n",
    "with open(\"y_defender_flipped.pickle\", \"rb\") as f:\n",
    "    y_defender = pkl.load(f)\n",
    "    \n",
    "with open(\"y_reserve_flipped.pickle\", \"rb\") as f:\n",
    "    y_reserve = pkl.load(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open(\"nn_dict.pickle\", 'rb') as f:\n",
    "  dump_dict = pkl.load(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['W1_early', 'W10_early', 'W2_early', 'W20_early', 'W1star', 'W10star', 'W2star', 'W20star', 'W1_last', 'W10_last', 'W2_last', 'W20_last', 'EPOCHS', 'norms', 'trng_loss', 'test_loss', 'best_ind'])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dump_dict.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W1_early is shape: (512, 128)\n",
      "W10_early is shape: (128,)\n",
      "W2_early is shape: (128, 10)\n",
      "W20_early is shape: (10,)\n",
      "W1star is shape: (512, 128)\n",
      "W10star is shape: (128,)\n",
      "W2star is shape: (128, 10)\n",
      "W20star is shape: (10,)\n",
      "W1_last is shape: (512, 128)\n",
      "W10_last is shape: (128,)\n",
      "W2_last is shape: (128, 10)\n",
      "W20_last is shape: (10,)\n",
      "norms is shape: (10010,)\n",
      "trng_loss is shape: (1001,)\n",
      "test_loss is shape: (1001,)\n"
     ]
    }
   ],
   "source": [
    "for k,v in dump_dict.items():\n",
    "    if type(v) is np.ndarray:\n",
    "        print(f\"{k} is shape: {v.shape}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Norm of Gradient')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(dump_dict['norms']) # plot norms of gradients\n",
    "plt.xlabel('Iteration', fontsize=16)\n",
    "plt.ylabel('Norm of Gradient', fontsize=16)\n",
    "#plt.savefig('grad_norm.pdf')\n",
    "#plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Loss')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "i_axis = np.arange(dump_dict['EPOCHS']) # abscissa for plots of loss & accuracy\n",
    "\n",
    "# plot loss each epoch\n",
    "loss_min = min(min(dump_dict['trng_loss']),\n",
    "               min(dump_dict['test_loss'])\n",
    "               ) # min of vertical dashed line\n",
    "loss_max = max(max(dump_dict['trng_loss']),\n",
    "               max(dump_dict['test_loss'])\n",
    "               ) # max of vertical dashed line\n",
    "\n",
    "plt.plot(i_axis, dump_dict['trng_loss'], 'b--', label='Train') # plot loss\n",
    "plt.plot(i_axis, dump_dict['test_loss'], 'r--', label='Test')\n",
    "plt.plot((240+dump_dict['best_ind'], 240+dump_dict['best_ind']), (loss_min, loss_max), 'g--')\n",
    "plt.legend()\n",
    "plt.xlabel('Epoch', fontsize=16)\n",
    "plt.ylabel('Loss', fontsize=16)\n",
    "#plt.savefig('loss.pdf')\n",
    "#plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# defining my activation functions\n",
    "def relu(x):\n",
    "    '''the Relu activation function'''\n",
    "    return np.maximum(0,x)\n",
    "\n",
    "def softmax(x):\n",
    "    '''the softmax activation function applied to each column'''\n",
    "    temp = x - np.amax(x, axis=0, keepdims=True) # to avoid overflow\n",
    "    # softmax(z_k) = exp(z_k)/sum_k' {exp(z_k')}\n",
    "    return np.exp(temp)/np.sum(np.exp(temp), axis=0, keepdims=True)\n",
    "  \n",
    "def cross_ent1(p, q):\n",
    "  \n",
    "    return -1*(p * np.log(q)).sum(axis=0)\n",
    "  \n",
    "def cross_ent2(p, xw):\n",
    "  \n",
    "    temp = np.log( np.sum( np.exp(xw), axis=0 ) ) - xw\n",
    "  \n",
    "    return np.sum( temp * p, axis=0 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "xw1 = np.random.randint(low=-9, high=10, size=(3,5))\n",
    "xw2 = np.random.randint(low=-9, high=10, size=(3,5))\n",
    "p1 = softmax(xw1)\n",
    "p2 = softmax(xw2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.49904690e-03, 3.34092779e+00, 3.56155146e+00, 6.84220745e-03,\n",
       "       1.52310077e+00])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cross_ent1(p1, p2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.49904690e-03, 3.34092779e+00, 3.56155146e+00, 6.84220745e-03,\n",
       "       1.52310077e+00])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cross_ent2(p1, xw2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model(W1,W10,W2,W20):\n",
    "  \n",
    "    def f(x):\n",
    "        H1 = relu(np.tensordot(np.transpose(W1),x, axes=1) + W10)\n",
    "        XW = np.tensordot(np.transpose(W2),H1, axes=1) + W20\n",
    "        \n",
    "        return XW\n",
    "      \n",
    "    return f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def grad(W1,W10,W2,W20):\n",
    "  \n",
    "    N1, K = W2.shape\n",
    "    BATCH_SIZE = 1\n",
    "  \n",
    "    pdRelu1 = np.zeros((BATCH_SIZE, N1, N1)) # partial relu1(z)/partial z\n",
    "    pdSigma = np.zeros((BATCH_SIZE, K, K)) # partial softmax(z)/partial z\n",
    "  \n",
    "    def g(xbatch, ybatch):\n",
    "      \n",
    "        # FORWARD PROP\n",
    "        H1 = relu(np.tensordot(np.transpose(W1),xbatch, axes=1) + W10)\n",
    "        XW = np.tensordot(np.transpose(W2),H1, axes=1) + W20\n",
    "        Yhat = softmax(XW)\n",
    "      \n",
    "        # BACK PROP - compute the gradients, working backwards\n",
    "        gradYhat = -ybatch/Yhat # gradient of output\n",
    "\n",
    "        # partial softmax(z)/partial z\n",
    "        for b in range(BATCH_SIZE):\n",
    "            pdSigma[b,:,:] = np.matmul(\n",
    "                np.diag(Yhat[:,b]),\n",
    "                    np.identity(K) - Yhat[:,b]\n",
    "                    )\n",
    "\n",
    "        gradW2 = (\n",
    "            np.matmul(\n",
    "                np.matmul(\n",
    "                    np.expand_dims(np.transpose(H1),axis=2), # col vecs\n",
    "                    np.expand_dims(np.transpose(gradYhat),axis=1) # row vecs\n",
    "                    ), # outer product, effectively\n",
    "                pdSigma\n",
    "                )\n",
    "            )\n",
    "\n",
    "        gradW20 = (\n",
    "            np.matmul(\n",
    "                pdSigma,\n",
    "                np.expand_dims(np.transpose(gradYhat),axis=2), # col vecs\n",
    "                )\n",
    "            )\n",
    "\n",
    "        gradH1 = (\n",
    "            np.matmul(\n",
    "                W2,\n",
    "                np.matmul(\n",
    "                    pdSigma,\n",
    "                    np.expand_dims(np.transpose(gradYhat),axis=2), # col vecs\n",
    "                    )\n",
    "                )\n",
    "            )\n",
    "\n",
    "        # partial Relu(z)/partial z for H1\n",
    "        for b in range(BATCH_SIZE):\n",
    "            pdRelu1[b,:,:] = np.diag(np.sign(H1[:,b]))\n",
    "\n",
    "        gradW1 = (\n",
    "            np.matmul(\n",
    "                np.matmul(\n",
    "                    np.expand_dims(np.transpose(xbatch),axis=2), # col vecs\n",
    "                    np.swapaxes(gradH1,1,2) # row vecs\n",
    "                    ), # outer product, effectively\n",
    "                pdRelu1\n",
    "                )\n",
    "            )\n",
    "\n",
    "        gradW10 = (\n",
    "            np.matmul(\n",
    "                pdRelu1,\n",
    "                gradH1 # col vecs\n",
    "                )\n",
    "            )\n",
    "        \n",
    "        return gradW1, gradW10, gradW2, gradW20\n",
    "  \n",
    "    return g"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# loss (-LCL)\n",
    "def loss(y, XW): \n",
    "  \n",
    "    L = (\n",
    "        -np.sum(np.transpose(y) *\n",
    "                (XW -\n",
    "                 np.log(\n",
    "                     np.sum(np.exp(XW),\n",
    "                            axis=0, \n",
    "                            keepdims=True\n",
    "                            )\n",
    "                     )\n",
    "                 )\n",
    "                )\n",
    "        )/XW.shape[1]\n",
    "    return L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# total accuracy\n",
    "def accuracy(y, XW):\n",
    "  \n",
    "    return np.sum(y == np.argmax(XW, axis=0))/XW.shape[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shapes of weights and biases:\n",
      "(512, 128)\n",
      "(128, 1)\n",
      "(128, 10)\n",
      "(10, 1)\n",
      "\n",
      "\n",
      "Shapes of data:\n",
      "(512, 400)\n",
      "(512, 400)\n",
      "(10, 400)\n",
      "(10, 400)\n"
     ]
    }
   ],
   "source": [
    "W1_D = dump_dict['W1_last'].copy()\n",
    "W10_D = (dump_dict['W10_last'].copy())[:,None]\n",
    "W2_D = dump_dict['W2_last'].copy()\n",
    "W20_D = (dump_dict['W20_last'].copy())[:,None]\n",
    "\n",
    "N = 400\n",
    "x_D = np.transpose(x_defender[:N,:]) # each sample is stored as a column\n",
    "x_R = np.transpose(x_reserve[:N,:])\n",
    "y_D = np.transpose(y_defender[:N,:]) # each sample is stored as a column\n",
    "y_R = np.transpose(y_reserve[:N,:])\n",
    "\n",
    "print(\"Shapes of weights and biases:\")\n",
    "print(W1_D.shape)\n",
    "print(W10_D.shape)\n",
    "print(W2_D.shape)\n",
    "print(W20_D.shape)\n",
    "print(\"\\n\")\n",
    "print(\"Shapes of data:\")\n",
    "print(x_D.shape)\n",
    "print(x_R.shape)\n",
    "print(y_D.shape)\n",
    "print(y_R.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(400,)\n",
      "(400,)\n"
     ]
    }
   ],
   "source": [
    "digit_D = np.argmax(y_D, axis=0)\n",
    "digit_R = np.argmax(y_D, axis=0)\n",
    "print(digit_D.shape)\n",
    "print(digit_R.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "M_D = model(W1_D,W10_D,W2_D,W20_D)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(512, 800)\n",
      "(10, 800)\n",
      "(1, 800)\n"
     ]
    }
   ],
   "source": [
    "all_data = np.concatenate((x_D,x_R), axis=1)\n",
    "all_lbls = np.concatenate((y_D,y_R), axis=1)\n",
    "all_mem_lbls = np.concatenate( ( np.ones((1,N)), np.zeros((1,N)) ), axis=1 )\n",
    "print(all_data.shape)\n",
    "print(all_lbls.shape)\n",
    "print(all_mem_lbls.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(10, 800)\n"
     ]
    }
   ],
   "source": [
    "M_D_XW_all = M_D(all_data)\n",
    "print(M_D_XW_all.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(10, 800)\n"
     ]
    }
   ],
   "source": [
    "M_D_yhat_all = softmax(M_D_XW_all)\n",
    "print(M_D_yhat_all.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "M_D_grad = grad(W1_D,W10_D,W2_D,W20_D)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(800, 512, 128)\n",
      "(800, 128, 1)\n",
      "(800, 128, 10)\n",
      "(800, 10, 1)\n"
     ]
    }
   ],
   "source": [
    "M_D_grad_all = M_D_grad(all_data, all_lbls)\n",
    "for g in M_D_grad_all:\n",
    "    print(g.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1, 800)\n"
     ]
    }
   ],
   "source": [
    "grad_all_norms = np.zeros((1,2*N))\n",
    "for i in range(2*N):\n",
    "    grad_all_norms[0,i] = np.sqrt(\n",
    "        np.sum((M_D_grad_all[0][i,:,:])**2) +\n",
    "        np.sum((M_D_grad_all[1][i,:,:])**2) +\n",
    "        np.sum((M_D_grad_all[2][i,:,:])**2) +\n",
    "        np.sum((M_D_grad_all[3][i,:,:])**2)\n",
    "    )\n",
    "print(grad_all_norms.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
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       "      <th>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>400.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>22.797307</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>94.300968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.016946</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.344963</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>6.176784</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>17.810517</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1538.750581</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 0\n",
       "count   400.000000\n",
       "mean     22.797307\n",
       "std      94.300968\n",
       "min       0.016946\n",
       "25%       0.344963\n",
       "50%       6.176784\n",
       "75%      17.810517\n",
       "max    1538.750581"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(grad_all_norms[:,:N].T).describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
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       "      <th>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>400.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>1080.197127</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>15483.974429</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.017448</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.745258</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>7.341540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>23.592551</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>307693.750741</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   0\n",
       "count     400.000000\n",
       "mean     1080.197127\n",
       "std     15483.974429\n",
       "min         0.017448\n",
       "25%         0.745258\n",
       "50%         7.341540\n",
       "75%        23.592551\n",
       "max    307693.750741"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(grad_all_norms[:,N:].T).describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.55960625\n"
     ]
    }
   ],
   "source": [
    "auroc = metrics.roc_auc_score(all_mem_lbls[0,:], -1*grad_all_norms[0,:])\n",
    "print(auroc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5799999999999986\n"
     ]
    }
   ],
   "source": [
    "pair_accuracy = 0\n",
    "for i in range(N):\n",
    "    if grad_all_norms[0,i] < grad_all_norms[0,N+i]: pair_accuracy += 1/N\n",
    "print(pair_accuracy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "kde_D = stats.gaussian_kde(grad_all_norms[0,:N].T)\n",
    "kde_R = stats.gaussian_kde(grad_all_norms[0,:N].T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7ff2c6b13580>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "grid = np.linspace(np.min(grad_all_norms), np.max(grad_all_norms), 50)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(5,3))\n",
    "ax.plot(grid, kde_D(grid), c='r', label = \"D grad norms\")\n",
    "ax.plot(grid, kde_R(grid), c='b', label = \"R grad norms\")\n",
    "\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xylims = np.linspace(min(np.min(grad_all_norms[:,:N].T), np.min(grad_all_norms[:,:N].T)),\n",
    "                     max(np.max(grad_all_norms[:,:N].T), np.max(grad_all_norms[:,:N].T)))\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = plt.gca()\n",
    "ax.scatter(grad_all_norms[:,:N].T,grad_all_norms[:,N:].T, c='b', alpha=0.3)\n",
    "ax.plot(xylims,xylims, c='k', linestyle='--')\n",
    "ax.set_yscale('log')\n",
    "ax.set_xscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(800, 800, 3, 2)\n"
     ]
    }
   ],
   "source": [
    "etas = [1e-8,1e-6]\n",
    "all_distances = np.zeros((2*N,2*N,3,len(etas)))\n",
    "print(all_distances.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "i = 0\n",
      "i = 80\n",
      "i = 160\n",
      "i = 240\n",
      "i = 320\n",
      "i = 400\n",
      "i = 480\n",
      "i = 560\n",
      "i = 640\n",
      "i = 720\n"
     ]
    }
   ],
   "source": [
    "for i in range(2*N):\n",
    "    for j, eta in enumerate(etas):\n",
    "        W1_i = W1_D + eta*M_D_grad_all[0][i,:,:]\n",
    "        W10_i = W10_D + eta*M_D_grad_all[1][i,:,:]\n",
    "        W2_i = W2_D + eta*M_D_grad_all[2][i,:,:]\n",
    "        W20_i = W20_D + eta*M_D_grad_all[3][i,:,:]\n",
    "        \n",
    "        M_i = model(W1_i,W10_i,W2_i,W20_i)\n",
    "        M_i_XW_all = M_i(all_data)\n",
    "        M_i_yhat_all = softmax(M_i_XW_all)\n",
    "        \n",
    "        # 2norm on predictions\n",
    "        all_distances[i,:,0,j] = np.linalg.norm(M_D_yhat_all - M_i_yhat_all, axis=0)\n",
    "        all_distances[i,:,1,j] = np.linalg.norm(M_D_XW_all - M_i_XW_all, axis=0)\n",
    "        all_distances[i,:,2,j] = cross_ent2(M_D_yhat_all, M_i_XW_all)\n",
    "        \n",
    "    if i % 80 == 0:\n",
    "        print(f\"i = {i}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(800, 3, 2)\n"
     ]
    }
   ],
   "source": [
    "dist_to_Mi_Ui = np.zeros((2*N,3,len(etas)))\n",
    "for i in range(2*N):\n",
    "    dist_to_Mi_Ui[i,:,:] = all_distances[i,i,:,:]\n",
    "print(dist_to_Mi_Ui.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For distance function 0:\n",
      "\tAUC for eta= 1e-08: 0.55938125\n",
      "\tAUC for eta= 1e-06: 0.5593999999999999\n",
      "\n",
      "\n",
      "For distance function 1:\n",
      "\tAUC for eta= 1e-08: 0.56021875\n",
      "\tAUC for eta= 1e-06: 0.5602125\n",
      "\n",
      "\n",
      "For distance function 2:\n",
      "\tAUC for eta= 1e-08: 0.5650000000000001\n",
      "\tAUC for eta= 1e-06: 0.5660499999999999\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for i in range(3):\n",
    "    print(f\"For distance function {i}:\")\n",
    "    for j, eta in enumerate(etas):\n",
    "        auc = metrics.roc_auc_score(all_mem_lbls[0,:], -1*dist_to_Mi_Ui[:,i,j])\n",
    "        print(f\"\\tAUC for eta={eta: .0e}: {auc}\")\n",
    "    print(\"\\n\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(800, 3, 2)\n"
     ]
    }
   ],
   "source": [
    "dist_to_Mi_all = np.mean(all_distances, axis=1)\n",
    "\n",
    "print(dist_to_Mi_all.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For distance function 0:\n",
      "\tAUC for eta= 1e-08: 0.5603374999999999\n",
      "\tAUC for eta= 1e-06: 0.5603374999999999\n",
      "\n",
      "\n",
      "For distance function 1:\n",
      "\tAUC for eta= 1e-08: 0.56135625\n",
      "\tAUC for eta= 1e-06: 0.56135625\n",
      "\n",
      "\n",
      "For distance function 2:\n",
      "\tAUC for eta= 1e-08: 0.558934375\n",
      "\tAUC for eta= 1e-06: 0.5599500000000001\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for i in range(3):\n",
    "    print(f\"For distance function {i}:\")\n",
    "    for j, eta in enumerate(etas):\n",
    "        auc = metrics.roc_auc_score(all_mem_lbls[0,:], -1*dist_to_Mi_all[:,i,j])\n",
    "        print(f\"\\tAUC for eta={eta: .0e}: {auc}\")\n",
    "    print(\"\\n\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Cross Entropy Loss of Prediction on Point')"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mask_D = (digit_D ==\n",
    "mask_R = \n",
    "xylims = np.linspace(min(np.min(grad_all_norms[0,:]), np.min(dist_to_Mi_Ui[:,2,1])),\n",
    "                     max(np.max(grad_all_norms[0,:]), np.max(dist_to_Mi_Ui[:,2,1])))\n",
    "\n",
    "fig = plt.figure(figsize=(8,8))\n",
    "ax = plt.gca()\n",
    "ax.scatter(grad_all_norms[0,:N], dist_to_Mi_Ui[:N,2,1], c='r', alpha=0.1)\n",
    "ax.scatter(grad_all_norms[0,N:], dist_to_Mi_Ui[N:,2,1], c='b', alpha=0.1)\n",
    "ax.plot(xylims,xylims, c='k', linestyle='--')\n",
    "ax.set_yscale('log')\n",
    "ax.set_xscale('log')\n",
    "ax.set_xlabel(\"Norm of Gradient at Point\", fontsize=14)\n",
    "ax.set_ylabel(\"Cross Entropy Loss of Prediction on Point\", fontsize=14)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "bins = np.linspace(0, 2.2, 100)\n",
    "\n",
    "fig = plt.figure(figsize=(8,8))\n",
    "plt.hist(dist_to_Mi_Ui[:N,2,1], bins, color='r', alpha=0.5, label='Defender')\n",
    "plt.hist(dist_to_Mi_Ui[N:,2,1], bins, color='b', alpha=0.5, label='Reserve')\n",
    "plt.legend(loc='upper right')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([8, 3, 1, 4, 9])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digit_D[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:joe_env]",
   "language": "python",
   "name": "conda-env-joe_env-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}