mystery-planet-99-8-cnn.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {
    "_cell_guid": "a1e11ceb-ecb4-e83c-9571-dee02a834580",
    "_uuid": "595424eb4c5c162239022da0cd17e6635986556c"
   },
   "outputs": [],
   "source": [
    "# A 1D convolutional net in Keras\n",
    "Very little preprocessing was needed. Batch normalization made a huge difference, and made it possible to achieve perfect classification within the Kaggle kernel."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "_cell_guid": "61aec30a-f65c-02dd-77b0-67aec83e8632",
    "_execution_state": "idle",
    "_uuid": "6ce895e9b32b7216d59f64c276b7d69068b287e8"
   },
   "outputs": [],
   "source": [
    "#We import libraries for linear algebra, graphs, and evaluation of results\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.metrics import roc_curve, roc_auc_score\n",
    "from scipy.ndimage.filters import uniform_filter1d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "_cell_guid": "d4f7e51a-b964-8eaf-220b-7a924aa7932e",
    "_execution_state": "idle",
    "_uuid": "3dab37c32ac2c1edef4bae4fc3534b92355911ae"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "#Keras is a high level neural networks library, based on either tensorflow or theano\n",
    "from keras.models import Sequential, Model\n",
    "from keras.layers import Conv1D, MaxPool1D, Dense, Dropout, Flatten, \\\n",
    "BatchNormalization, Input, concatenate, Activation\n",
    "from keras.optimizers import Adam"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {
    "_cell_guid": "b3da338c-5beb-d12c-9cb4-088c1eb86069",
    "_uuid": "68a1f6dba3b023e7eb59c6983fdde57851c030ce"
   },
   "outputs": [],
   "source": [
    "## Load the data"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {
    "_execution_state": "idle",
    "_uuid": "68ec0ee6eb9d8256998b7c15d37ec62b3e61eb5b",
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "As the data format is so simple, we do not need pandas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "_cell_guid": "2763eb6d-1867-7254-7278-099e63ddd562",
    "_execution_state": "idle",
    "_uuid": "1cfdd50387bac260912e23444d1234540d5c1b02"
   },
   "outputs": [],
   "source": [
    "INPUT_LIB = '../input/'\n",
    "raw_data = np.loadtxt(INPUT_LIB + 'exoTrain.csv', skiprows=1, delimiter=',')\n",
    "x_train = raw_data[:, 1:]\n",
    "y_train = raw_data[:, 0, np.newaxis] - 1.\n",
    "raw_data = np.loadtxt(INPUT_LIB + 'exoTest.csv', skiprows=1, delimiter=',')\n",
    "x_test = raw_data[:, 1:]\n",
    "y_test = raw_data[:, 0, np.newaxis] - 1.\n",
    "del raw_data"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {
    "_execution_state": "idle",
    "_uuid": "a0b077fb1c89e5afe853f137ded82ffbfcb0449f",
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "Scale each observation to zero mean and unit variance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "_cell_guid": "17cbb5bb-29d7-9a0c-193c-9c132cdea389",
    "_execution_state": "idle",
    "_uuid": "76dd566fee56a9feaf06b9cff2fa54f5239e33cb"
   },
   "outputs": [],
   "source": [
    "x_train = ((x_train - np.mean(x_train, axis=1).reshape(-1,1)) / \n",
    "           np.std(x_train, axis=1).reshape(-1,1))\n",
    "x_test = ((x_test - np.mean(x_test, axis=1).reshape(-1,1)) / \n",
    "          np.std(x_test, axis=1).reshape(-1,1))"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {
    "_execution_state": "idle",
    "_uuid": "e2aa36f3133a1fad819e48dc60e120aed6283ce2",
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "This is our only preprocessing step: We add an input corresponding to the running average over\n",
    "200 time steps. This helps the net ignore high frequency noise and instead look at non-local\n",
    "information. Look at the graphs below to see what it does."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "_cell_guid": "2c006e96-8688-72e4-6abe-65d5d8f22fc6",
    "_execution_state": "busy",
    "_uuid": "f4d354b6d9d6b2fb5c788355c99e61a62699323c"
   },
   "outputs": [],
   "source": [
    "x_train = np.stack([x_train, uniform_filter1d(x_train, axis=1, size=200)], axis=2)\n",
    "x_test = np.stack([x_test, uniform_filter1d(x_test, axis=1, size=200)], axis=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {
    "_cell_guid": "c90d56a7-dec3-65a3-cac3-32e36c6bf31c",
    "_uuid": "6651259e2b8bab4c98f4649263e583201e494e45"
   },
   "outputs": [],
   "source": [
    "## Train the model"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {
    "_execution_state": "idle",
    "_uuid": "a6eeb9020d7eae0925578490c692217659cd4a6b",
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "With the Sequential API for Keras, we only need to add the layers one at a time. Each 1D convolutional layers corresponds to a local filter, and then a pooling layer reduces the data length by approximately a factor 4. At the end, there are two dense layers, just as we would in a typical image classifier. Batch normalization layers speed up convergence. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "_cell_guid": "3637a7be-c21b-3b78-b6b6-9146332f3972",
    "_execution_state": "busy",
    "_uuid": "bbbee746cbd798b62d349a2b4d828e2fb889e164"
   },
   "outputs": [],
   "source": [
    "model = Sequential()\n",
    "model.add(Conv1D(filters=8, kernel_size=11, activation='relu', input_shape=x_train.shape[1:]))\n",
    "model.add(MaxPool1D(strides=4))\n",
    "model.add(BatchNormalization())\n",
    "model.add(Conv1D(filters=16, kernel_size=11, activation='relu'))\n",
    "model.add(MaxPool1D(strides=4))\n",
    "model.add(BatchNormalization())\n",
    "model.add(Conv1D(filters=32, kernel_size=11, activation='relu'))\n",
    "model.add(MaxPool1D(strides=4))\n",
    "model.add(BatchNormalization())\n",
    "model.add(Conv1D(filters=64, kernel_size=11, activation='relu'))\n",
    "model.add(MaxPool1D(strides=4))\n",
    "model.add(Flatten())\n",
    "model.add(Dropout(0.5))\n",
    "model.add(Dense(64, activation='relu'))\n",
    "model.add(Dropout(0.25))\n",
    "model.add(Dense(64, activation='relu'))\n",
    "model.add(Dense(1, activation='sigmoid'))"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {
    "_execution_state": "idle",
    "_uuid": "5d25c5ad8a6ddd1319af7c56075a05fbfec8749b",
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "The data here is extremely unbalanced, with only a few positive examples. To correct for this, I use the positive examples a lot more often, so that the net sees 50% of each over each bats. Also, I generate new examples by rotation them randomly in time. This is called augmentation and is similar to when we rotate/shift examples in image classification."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "_cell_guid": "4ba8b520-7302-747c-7f84-8a816508e651",
    "_execution_state": "busy",
    "_uuid": "0604716b9a92c9113dcd16631b6fc48ff006fd53"
   },
   "outputs": [],
   "source": [
    "def batch_generator(x_train, y_train, batch_size=32):\n",
    "    \"\"\"\n",
    "    Gives equal number of positive and negative samples, and rotates them randomly in time\n",
    "    \"\"\"\n",
    "    half_batch = batch_size // 2\n",
    "    x_batch = np.empty((batch_size, x_train.shape[1], x_train.shape[2]), dtype='float32')\n",
    "    y_batch = np.empty((batch_size, y_train.shape[1]), dtype='float32')\n",
    "    \n",
    "    yes_idx = np.where(y_train[:,0] == 1.)[0]\n",
    "    non_idx = np.where(y_train[:,0] == 0.)[0]\n",
    "    \n",
    "    while True:\n",
    "        np.random.shuffle(yes_idx)\n",
    "        np.random.shuffle(non_idx)\n",
    "    \n",
    "        x_batch[:half_batch] = x_train[yes_idx[:half_batch]]\n",
    "        x_batch[half_batch:] = x_train[non_idx[half_batch:batch_size]]\n",
    "        y_batch[:half_batch] = y_train[yes_idx[:half_batch]]\n",
    "        y_batch[half_batch:] = y_train[non_idx[half_batch:batch_size]]\n",
    "    \n",
    "        for i in range(batch_size):\n",
    "            sz = np.random.randint(x_batch.shape[1])\n",
    "            x_batch[i] = np.roll(x_batch[i], sz, axis = 0)\n",
    "     \n",
    "        yield x_batch, y_batch"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {
    "_execution_state": "idle",
    "_uuid": "fd043b67ebf19352b1b8ec2a063ad8a50765e70d",
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "The hyperparameters here are chosen to finish training within the Kernel, rather than to get optimal results. On a GPU, I might have chosen a smaller learning rate, and perhaps SGD instead of Adam. As it turned out, results were brilliant anyway."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "_cell_guid": "fe6afcb2-7e0a-501d-bf19-759c0b3fda77",
    "_execution_state": "idle",
    "_uuid": "c8844e546b1d4677b3be321cbc203c8c617ef7c4"
   },
   "outputs": [],
   "source": [
    "#Start with a slightly lower learning rate, to ensure convergence\n",
    "model.compile(optimizer=Adam(1e-5), loss = 'binary_crossentropy', metrics=['accuracy'])\n",
    "hist = model.fit_generator(batch_generator(x_train, y_train, 32), \n",
    "                           validation_data=(x_test, y_test), \n",
    "                           verbose=0, epochs=5,\n",
    "                           steps_per_epoch=x_train.shape[1]//32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "_cell_guid": "964bdbf2-a325-11da-98c8-4dd56b31c9ad",
    "_execution_state": "busy",
    "_uuid": "6030dfe0cb763066fdecf81a27dff897cce69af4"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/40\n",
      "12s - loss: 0.6343 - acc: 0.6540 - val_loss: 0.6017 - val_acc: 0.7982\n",
      "Epoch 2/40\n",
      "12s - loss: 0.5701 - acc: 0.7124 - val_loss: 0.5056 - val_acc: 0.8368\n",
      "Epoch 3/40\n",
      "13s - loss: 0.5271 - acc: 0.7547 - val_loss: 0.4880 - val_acc: 0.7895\n",
      "Epoch 4/40\n",
      "12s - loss: 0.4788 - acc: 0.7759 - val_loss: 0.4772 - val_acc: 0.7789\n",
      "Epoch 5/40\n",
      "12s - loss: 0.4473 - acc: 0.7914 - val_loss: 0.5052 - val_acc: 0.7439\n",
      "Epoch 6/40\n",
      "12s - loss: 0.4156 - acc: 0.8103 - val_loss: 0.4922 - val_acc: 0.7456\n",
      "Epoch 7/40\n",
      "12s - loss: 0.3886 - acc: 0.8213 - val_loss: 0.4836 - val_acc: 0.7368\n",
      "Epoch 8/40\n",
      "12s - loss: 0.3544 - acc: 0.8501 - val_loss: 0.4153 - val_acc: 0.8070\n",
      "Epoch 9/40\n",
      "13s - loss: 0.3279 - acc: 0.8598 - val_loss: 0.3917 - val_acc: 0.7895\n",
      "Epoch 10/40\n",
      "12s - loss: 0.2781 - acc: 0.8936 - val_loss: 0.3358 - val_acc: 0.8228\n",
      "Epoch 11/40\n",
      "12s - loss: 0.2583 - acc: 0.9015 - val_loss: 0.3141 - val_acc: 0.8316\n",
      "Epoch 12/40\n",
      "12s - loss: 0.2243 - acc: 0.9104 - val_loss: 0.3647 - val_acc: 0.8175\n",
      "Epoch 13/40\n",
      "12s - loss: 0.2018 - acc: 0.9148 - val_loss: 0.3201 - val_acc: 0.8544\n",
      "Epoch 14/40\n",
      "12s - loss: 0.2001 - acc: 0.9214 - val_loss: 0.2251 - val_acc: 0.8930\n",
      "Epoch 15/40\n",
      "13s - loss: 0.1832 - acc: 0.9255 - val_loss: 0.2077 - val_acc: 0.9018\n",
      "Epoch 16/40\n",
      "12s - loss: 0.1507 - acc: 0.9400 - val_loss: 0.1683 - val_acc: 0.9228\n",
      "Epoch 17/40\n",
      "12s - loss: 0.1572 - acc: 0.9422 - val_loss: 0.1265 - val_acc: 0.9474\n",
      "Epoch 18/40\n",
      "12s - loss: 0.1463 - acc: 0.9426 - val_loss: 0.1291 - val_acc: 0.9509\n",
      "Epoch 19/40\n",
      "12s - loss: 0.1172 - acc: 0.9580 - val_loss: 0.1195 - val_acc: 0.9561\n",
      "Epoch 20/40\n",
      "12s - loss: 0.1242 - acc: 0.9555 - val_loss: 0.0965 - val_acc: 0.9649\n",
      "Epoch 21/40\n",
      "12s - loss: 0.1162 - acc: 0.9586 - val_loss: 0.1055 - val_acc: 0.9649\n",
      "Epoch 22/40\n",
      "12s - loss: 0.1027 - acc: 0.9634 - val_loss: 0.1041 - val_acc: 0.9667\n",
      "Epoch 23/40\n",
      "12s - loss: 0.0831 - acc: 0.9729 - val_loss: 0.0823 - val_acc: 0.9772\n",
      "Epoch 24/40\n",
      "12s - loss: 0.1000 - acc: 0.9684 - val_loss: 0.0934 - val_acc: 0.9737\n",
      "Epoch 25/40\n",
      "12s - loss: 0.0914 - acc: 0.9669 - val_loss: 0.0938 - val_acc: 0.9737\n",
      "Epoch 26/40\n",
      "13s - loss: 0.0768 - acc: 0.9744 - val_loss: 0.0706 - val_acc: 0.9754\n",
      "Epoch 27/40\n",
      "13s - loss: 0.0723 - acc: 0.9757 - val_loss: 0.0626 - val_acc: 0.9842\n",
      "Epoch 28/40\n",
      "12s - loss: 0.0777 - acc: 0.9744 - val_loss: 0.0642 - val_acc: 0.9860\n",
      "Epoch 29/40\n",
      "13s - loss: 0.0714 - acc: 0.9763 - val_loss: 0.0630 - val_acc: 0.9842\n",
      "Epoch 30/40\n",
      "13s - loss: 0.0687 - acc: 0.9766 - val_loss: 0.0694 - val_acc: 0.9807\n",
      "Epoch 31/40\n",
      "13s - loss: 0.0701 - acc: 0.9751 - val_loss: 0.0644 - val_acc: 0.9860\n",
      "Epoch 32/40\n",
      "13s - loss: 0.0676 - acc: 0.9773 - val_loss: 0.0682 - val_acc: 0.9842\n",
      "Epoch 33/40\n",
      "12s - loss: 0.0580 - acc: 0.9826 - val_loss: 0.0671 - val_acc: 0.9825\n",
      "Epoch 34/40\n",
      "13s - loss: 0.0626 - acc: 0.9804 - val_loss: 0.0659 - val_acc: 0.9825\n",
      "Epoch 35/40\n",
      "12s - loss: 0.0577 - acc: 0.9798 - val_loss: 0.0610 - val_acc: 0.9877\n",
      "Epoch 36/40\n",
      "12s - loss: 0.0631 - acc: 0.9792 - val_loss: 0.0615 - val_acc: 0.9877\n",
      "Epoch 37/40\n",
      "13s - loss: 0.0515 - acc: 0.9836 - val_loss: 0.0592 - val_acc: 0.9877\n",
      "Epoch 38/40\n",
      "13s - loss: 0.0434 - acc: 0.9845 - val_loss: 0.0571 - val_acc: 0.9895\n",
      "Epoch 39/40\n",
      "12s - loss: 0.0449 - acc: 0.9867 - val_loss: 0.0500 - val_acc: 0.9912\n",
      "Epoch 40/40\n",
      "12s - loss: 0.0573 - acc: 0.9820 - val_loss: 0.0640 - val_acc: 0.9895\n"
     ]
    }
   ],
   "source": [
    "#Then speed things up a little\n",
    "model.compile(optimizer=Adam(4e-5), loss = 'binary_crossentropy', metrics=['accuracy'])\n",
    "hist = model.fit_generator(batch_generator(x_train, y_train, 32), \n",
    "                           validation_data=(x_test, y_test), \n",
    "                           verbose=2, epochs=40,\n",
    "                           steps_per_epoch=x_train.shape[1]//32)"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {
    "_execution_state": "busy",
    "_uuid": "31d3be9df5d7387bf68eb9ca2c1c73c1590c8681",
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Evaluate the model"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {
    "_execution_state": "idle",
    "_uuid": "d8a74931a02d8ceb43c03f9f687f934581e11e9d",
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "First we look at convergence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "_cell_guid": "020d5851-762a-d02c-77fa-319c3af6a4af",
    "_execution_state": "idle",
    "_uuid": "6c22b94c662b6b25fd33c85fd05892aca54e5d86"
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD8CAYAAACMwORRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4341ca2ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAD8CAYAAABw1c+bAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\neOJ3zrkU8/8BG3wWicU1c2YAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f43419a9c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(hist.history['loss'], color='b')\n",
    "plt.plot(hist.history['val_loss'], color='r')\n",
    "plt.show()\n",
    "plt.plot(hist.history['acc'], color='b')\n",
    "plt.plot(hist.history['val_acc'], color='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {
    "_execution_state": "idle",
    "_uuid": "62f58f451ef2de7c4895f8bdb449dae44a122871",
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "We then use our trained net to classify the test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "_cell_guid": "8ef32235-eebb-91e2-4571-1b585aa86ad4",
    "_execution_state": "idle",
    "_uuid": "62e80b4160b0bfd27bf1acdb2e5b6baed971fc01"
   },
   "outputs": [],
   "source": [
    "non_idx = np.where(y_test[:,0] == 0.)[0]\n",
    "yes_idx = np.where(y_test[:,0] == 1.)[0]\n",
    "y_hat = model.predict(x_test)[:,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "_cell_guid": "5f37a9af-ceab-8b5a-3f77-fefd6eb38710",
    "_execution_state": "idle",
    "_uuid": "4b002ba89846d5f0c25fd29466c9ceb4801fc7e5"
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAD8CAYAAAB3u9PLAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\natxVH2YAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4341d0cda0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD8CAYAAACMwORRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAE1FJREFUeJzt3X+MHGd9x/HPx+eE9jBtwDlQ6h93bmXaRhXQZBuQitq0\nFcWBqqYSfwSuDURURyxSUfWPYmSVqqr8B5VaIUTAOtEI0F2xKhGKi0JTaGn5AwFel/xygsM1nC82\nKT5+lJac1NT1t3/MnL1e797O7s3e7Dz7fkmr3XlmvPM83tnPPjfzzIwjQgCAtGyrugIAgPIR7gCQ\nIMIdABJEuANAggh3AEgQ4Q4ACSLcASBBhDsAJIhwB4AEba9qxTfeeGPMzMxUtXoAqKVTp059NyKm\nei1XWbjPzMyo2WxWtXoAqCXbZ4ssx24ZAEgQ4Q4ACSLcASBBhDsAJIhwB4AE9Qx32/fbvmD78S7z\nbfuDtpdsP2r7lvKricsWF6WZGWnbtux5cbHqGqFqbBPooEjP/WOSDmww/w5J+/PHnKSPbL5a6Ghx\nUZqbk86elSKy57k5vszjjG0CXfQM94j4kqTvb7DIQUmfiMxXJN1g+6ayKogWR45Ia2tXl62tZeUY\nT2wT6KKMfe67JD3TMn0uL7uG7TnbTdvN1dXVElY9ZlZW+itH+tgm0MWWHlCNiPmIaEREY2qq59mz\naLd3b3/lSB/bBLooI9zPS9rTMr07L0PZjh6VJievLpuczMqRhn4PjrJNoIsywv2EpLvyUTOvkfTD\niHi2hPdFu9lZaX5emp6W7Ox5fj4rR/0NcnCUbQJdOCI2XsD+pKTbJd0o6TuS/lTSdZIUEcdsW9KH\nlI2oWZN0d0T0vCJYo9EILhwGtJiZyQK93fS0tLy81bXBiLJ9KiIavZbreVXIiHhLj/kh6V191A1A\nJxwcRYk4QxUYFRwcRYkId2BUcHAUJSLcgVHBwVGUqLI7MQHoYHaWMEcp6LkDQIIIdwBIEOEOAAki\n3AEgQYQ7ACSIcAeABBHuAJAgwh0AEkS4A0CCCHcASBDhDgAJItwBIEGEOwAkiHAHgAQR7gCQIMId\nABJEuANAggh3AEgQ4Q4ACSLcASBBhDsAJIhwB4AEEe4AkCDCHQASRLgDQIIIdwBIUKFwt33A9hnb\nS7YPd5j/k7b/3vYjtk/bvrv8qgIAiuoZ7rYnJN0n6Q5JN0t6i+2b2xZ7l6QnIuKVkm6X9Je2ry+5\nrgCAgor03G+TtBQRT0fE85KOSzrYtkxIepFtS9oh6fuSLpZaUwBAYUXCfZekZ1qmz+VlrT4k6ecl\nfVvSY5LeHRGXSqkhAKBvZR1Qfb2khyX9lKRXSfqQ7Z9oX8j2nO2m7ebq6mpJqwYAtCsS7ucl7WmZ\n3p2Xtbpb0gORWZL0LUk/1/5GETEfEY2IaExNTQ1aZwBAD0XC/aSk/bb35QdJ75R0om2ZFUm/IUm2\nXybpZyU9XWZFAQDFbe+1QERctH2vpIckTUi6PyJO274nn39M0p9L+pjtxyRZ0nsi4rtDrDcAYAM9\nw12SIuJBSQ+2lR1ref1tSb9ZbtUAAIPiDFUASBDhDgAJItwBIEGEOwAkiHAHgAQR7gCQIMIdABJE\nuANAggh3AEgQ4Q4ACSLcASBBhDsAJIhwB4AEEe7YvMVFaWZG2rYte15crLpGwNgrdMlfoKvFRWlu\nTlpby6bPns2mJWl2trp6AWOOnjs258iRK8G+bm0tKwdQGcIdm7Oy0l85gC1BuGNz9u7trxzAliDc\nsTlHj0qTk1eXTU5m5QAqQ7hXJZURJrOz0vy8ND0t2dnz/DwHU4GKMVqmCqmNMJmdrWe9gYTRc68C\nI0wADBnhXgVGmAAYMsK9CowwATBkhHsVGGEClCOVgQlDQLhXgREmwOatD0w4e1aKuDIwgYCXJDki\nKllxo9GIZrNZyboBJGBmJgv0dtPT0vLyVtdmy9g+FRGNXsvRcwdQTwxM2BDhDqCeGJiwIcIdQD0x\nMGFDhDuAemJgwoYKhbvtA7bP2F6yfbjLMrfbftj2adv/Wm41AaCD2dns4OmlS9kzwX5Zz2vL2J6Q\ndJ+k10k6J+mk7RMR8UTLMjdI+rCkAxGxYvulw6owAKC3Ij332yQtRcTTEfG8pOOSDrYt81ZJD0TE\niiRFxIVyqwkA6EeRcN8l6ZmW6XN5WauXS3qx7X+xfcr2XZ3eyPac7abt5urq6mA1BgD0VNYB1e2S\nbpX0Rkmvl/Qntl/evlBEzEdEIyIaU1NTJa0aANCuyPXcz0va0zK9Oy9rdU7S9yLiOUnP2f6SpFdK\neqqUWgIA+lKk535S0n7b+2xfL+lOSSfalvmMpNfa3m57UtKrJT1ZblUBAEX17LlHxEXb90p6SNKE\npPsj4rTte/L5xyLiSdv/IOlRSZckfTQiHh9mxQEA3XHhMACoES4cBgBjjHAHgAQR7gCQIMIdABJE\nuANAggh3AEgQ4Q4ACSLcASBBhDsAJIhwB4AEEe4AkCDCHQASRLgDQIIIdwBIEOEOAAki3AEgQYQ7\nACSIcAeABBHuAJAgwh0AEkS4A0CCCHcASBDhDgAJItwBIEGEOwAkiHAHgAQR7gCQIMIdQP0sLkoz\nM9K2bdnz4mLVNRo526uuAAD0ZXFRmpuT1tay6bNns2lJmp2trl4jhp47gHo5cuRKsK9bW8vKcVmh\ncLd9wPYZ20u2D2+w3C/Zvmj7zeVVEQBarKz0Vz6meoa77QlJ90m6Q9LNkt5i++Yuy71f0j+WXUkA\nuGzv3v7Kx1SRnvttkpYi4umIeF7ScUkHOyz3B5I+JelCifUDgKsdPSpNTl5dNjmZleOyIuG+S9Iz\nLdPn8rLLbO+S9DuSPlJe1QCgg9lZaX5emp6W7Ox5fp6DqW3KGi3zAUnviYhLtrsuZHtO0pwk7eVP\nKACDmp0lzHso0nM/L2lPy/TuvKxVQ9Jx28uS3izpw7bf1P5GETEfEY2IaExNTQ1YZaAEjJNG4or0\n3E9K2m97n7JQv1PSW1sXiIh9669tf0zSZyPi70qsJ1AexkljDPTsuUfERUn3SnpI0pOS/jYiTtu+\nx/Y9w64gUDrGSWMMOCIqWXGj0Yhms1nJujHmtm2TOm33tnTp0tbXB+iD7VMR0ei1HGeoYvwwThpj\ngHDH+GGcNMYA4Y7xwzhpjAGuConxxDhpJI6eOwAkiHAHgAQR7gCQIMIdABJEuANAggh3AEgQ4Q4A\nCSLcASBBhDsAJIhwB4AEpRfu3GEHABK7tgx32AEASan13LfiDjv8ZQCgBtLqua+s9FfeL/4yAFAT\nafXch32HHe69CaAm0gr3Yd9hZ9h/GQBASdIK92HfYYd7bwKoibTCXcqCfHk5u4v98nK5+8K59yaA\nmkgv3IeJe28CqIm0RstsBe69CaAG6LkDQIIId4weThQDNo3dMhgtnCgGlIKeO0YLJ4oBpSDcMVo4\nUQwoBeGO0cKJYkApCHeMFk4UA0pRKNxtH7B9xvaS7cMd5s/aftT2Y7a/bPuV5VcVY4ETxYBS9Bwt\nY3tC0n2SXifpnKSTtk9ExBMti31L0q9GxA9s3yFpXtKrh1FhjAFOFAM2rUjP/TZJSxHxdEQ8L+m4\npIOtC0TElyPiB/nkVyTtLreaAIB+FAn3XZKeaZk+l5d18w5Jn+s0w/ac7abt5urqavFaAgD6UuoB\nVdu/pizc39NpfkTMR0QjIhpTU1NlrhoA0KLIGarnJe1pmd6dl13F9iskfVTSHRHxvXKqBwAYRJGe\n+0lJ+23vs329pDslnWhdwPZeSQ9I+r2IeKr8agIA+tGz5x4RF23fK+khSROS7o+I07bvyecfk/Q+\nSTslfdi2JF2MiMbwqg0A2Eihfe4R8WBEvDwifiYijuZlx/JgV0T8fkS8OCJelT8I9rrjyoxArXFV\nSFyLKzMCtcflB3AtrswI1B7hjmtxZUag9gh3XGscrszIMQUkjnDHtVK/MuP6MYWzZ6WIK8cUCHgM\nYkQ7CoQ7rpX6lRk5poCyjHBHgXBHZ7Oz0vKydOlS9pxKsEscU8DG+umJj3BHgXDH+BmHYwoYTL89\n8RHuKBDuGD+pH1PA4PrtiRfpKFS0T55wx/hJ/ZgCBtdvT7xXR6HCffKOiKGvpJNGoxHNZrOSdQNA\nRzMzWQC3m57Ojj11sriY9exXVrIe+9GjVzoKg7xfD7ZPFbnECz13AFg3yC67jQYfVLhPnnAHgHVl\n77Kr8OA94Q4ArcocBlzhwXvCHQAGUWQUTIUH77nkLwD0q5/LYs/OVjISi547+jOi19EAttQIn5m6\njp47iuMmHkBmhM9MXUfPHcXVoLcCbIkaXMKCcEdxNeitoCB2r21ODS5hQbijuBr0VlDACF+mtjZq\ncAkLwr0bejbXqkFvBQWwe60cI35ZbMK9k63u2dTlh6QGvRUUUPfda3X5vlQtIip53HrrrbHlFhYi\npqcj7Ox5YaHzctPTEVmsX/2Ynh5OnSYnr17P5GT3utVB0f9nVGMrt++ypfh96ZOkZhTI2PEJ9342\nik4bvpSFVdnq8kUrGth8+UZfnT+junxfhohwb1d0o1hYyAJsqzagbusaxg9JN72Cu58w4MtXD3X9\n62oUvi8VI9zbFd0ouoWTPZwvQFlhuP5llSImJq68R686Fwnufuo4Dl++ugZjCug8EO7XKLpRdAsn\naTj16hauhw4VD5BO71H0z+0i/y8b/Z+01y31L1+dd2mkYND//35+kEf8x5twb1d0oygSTmV/+O3v\nd+hQfxtwtzoXCdYiPe1e799at6rDb9hfzNR/vOqg38+4n22y6u23AMK9kyIbRa8Pdys+/H4DZKOe\nda9dIkXWdehQ73UM88evqK34bDb6fxjRnt7IK3LMp9v8Ittat218YuLaf1eDH+9Sw13SAUlnJC1J\nOtxhviV9MJ//qKRber3npsO914d66NCVfc8TE9n0Zt97YeHKe5b94beuc6MQbd2fvr7rZqPle9Vt\nkB+zfn5AFhYidu68stzOnd1/VNfbv3Nn9uj3sy37+EWn9be2pchfMv28d9n6GeG0UXi2t7nbZzho\nHQftTBX9Me/1nWr9d2UdMxri51xauEuakPTvkn5a0vWSHpF0c9syb5D0uTzkXyPpq73ed6BwX1iI\neOELe39QPHjw4DHqjx07Bgr9ouFe5AzV2yQtRcTTEfG8pOOSDrYtc1DSJ/J1f0XSDbZv6u90qh4W\nF6W77pKee67UtwWASvzoR9Lb3z60M2yLhPsuSc+0TJ/Ly/pdZnOOHMmu4QAAqbh4cWjX9NnSa8vY\nnrPdtN1cXV3t7x/X5boXANCPIWVbkXA/L2lPy/TuvKzfZRQR8xHRiIjG1NRUfzXlsrIAUjSkbCsS\n7icl7be9z/b1ku6UdKJtmROS7nLmNZJ+GBHPllrTo0ezq8ABQCq2bx/aJbN73kM1Ii7avlfSQ8pG\nztwfEadt35PPPybpQWUjZpYkrUm6u/Sarl9W9p3v5KAqgPrbsUM6dmxol8x2PpRxyzUajWg2m5Ws\nGwDqyvapiGj0Wo79HACQIMIdABJEuANAggh3AEgQ4Q4ACapstIztVUlnB/znN0r6bonVGRW0q15o\nV72k0q7piOh5Fmhl4b4ZtptFhgLVDe2qF9pVL6m2qxt2ywBAggh3AEhQXcN9vuoKDAntqhfaVS+p\ntqujWu5zBwBsrK49dwDABmoX7rYP2D5je8n24arr0w/b99u+YPvxlrKX2P687W/mzy9umffevJ1n\nbL++mlr3ZnuP7S/afsL2advvzstr2zbbP2b7a7Yfydv0Z3l5bdvUyvaE7a/b/mw+Xft22V62/Zjt\nh20387Lat2tgRW60OioPFbhZ9yg/JP2KpFskPd5S9heSDuevD0t6f/765rx9L5C0L2/3RNVt6NKu\nmyTdkr9+kaSn8vrXtm3Kbva+I399naSvKrv5e23b1Na+P5L0N5I+m9B2uCzpxray2rdr0Efdeu5F\nbtY9siLiS5K+31Z8UNLH89cfl/SmlvLjEfE/EfEtZdfKv21LKtqniHg2Iv4tf/3fkp5Udg/d2rYt\nMj/KJ6/LH6Eat2md7d2S3ijpoy3FtW9XF6m2q6e6hfvwb8S99V4WV+5a9R+SXpa/rmVbbc9I+kVl\nPd1aty3fdfGwpAuSPh8RtW9T7gOS/lhS6x3nU2hXSPqC7VO25/KyFNo1kJ53YsLWiYiwXdvhS7Z3\nSPqUpD+MiP+yfXleHdsWEf8n6VW2b5D0adu/0Da/dm2y/VuSLkTEKdu3d1qmju3KvTYiztt+qaTP\n2/5G68wat2sgdeu5F7oRd818x/ZNkpQ/X8jLa9VW29cpC/bFiHggL06ibRHxn5K+KOmA6t+mX5b0\n27aXle3W/HXbC6p/uxQR5/PnC5I+rWw3S+3bNai6hXuRm3XXzQlJb8tfv03SZ1rK77T9Atv7JO2X\n9LUK6teTsy76X0t6MiL+qmVWbdtmeyrvscv2j0t6naRvqMZtkqSIeG9E7I6IGWXfn3+OiN9Vzdtl\n+4W2X7T+WtJvSnpcNW/XplR9RLffh7IbcT+l7Oj2karr02fdPynpWUn/q2wf3zsk7ZT0T5K+KekL\nkl7SsvyRvJ1nJN1Rdf03aNdrle3vfFTSw/njDXVum6RXSPp63qbHJb0vL69tmzq08XZdGS1T63Yp\nG0H3SP44vZ4NdW/XZh6coQoACarbbhkAQAGEOwAkiHAHgAQR7gCQIMIdABJEuANAggh3AEgQ4Q4A\nCfp/9CKIzH3bXT8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f434108d3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot([y_hat[i] for i in yes_idx], 'bo')\n",
    "plt.show()\n",
    "plt.plot([y_hat[i] for i in non_idx], 'ro')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {
    "_execution_state": "idle",
    "_uuid": "ffabc4d6783302adc67cf15ac6ca038030ff8842",
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "These graphs show that the five positive examples all get 0.95-1.00 score. Also, almost all negative examples get score close to zero, except a few in the 0.9-1.0 range. This is encouraging."
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {
    "_execution_state": "idle",
    "_uuid": "088fa46309212bf4a02766ea44e918d561643718",
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "We now choose an optimal cutoff score for classification. Sklearn can help us with this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "_cell_guid": "3d10d764-1a5f-7315-ea45-9e9481261ea4",
    "_execution_state": "busy",
    "_uuid": "38e7322f333dc2afa38186f208e5b96f4bd83fb9"
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD8CAYAAACMwORRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4341c1a470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Crossover at 0.97 with specificity 0.99\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD8CAYAAACMwORRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n1CDjLkkNMu6S1CDjLkkNMu6S1KD/Bh+nlf0E+ODlAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4340cdceb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ROC area under curve is 1.00\n"
     ]
    }
   ],
   "source": [
    "y_true = (y_test[:, 0] + 0.5).astype(\"int\")\n",
    "fpr, tpr, thresholds = roc_curve(y_true, y_hat)\n",
    "plt.plot(thresholds, 1.-fpr)\n",
    "plt.plot(thresholds, tpr)\n",
    "plt.show()\n",
    "crossover_index = np.min(np.where(1.-fpr <= tpr))\n",
    "crossover_cutoff = thresholds[crossover_index]\n",
    "crossover_specificity = 1.-fpr[crossover_index]\n",
    "print(\"Crossover at {0:.2f} with specificity {1:.2f}\".format(crossover_cutoff, crossover_specificity))\n",
    "plt.plot(fpr, tpr)\n",
    "plt.show()\n",
    "print(\"ROC area under curve is {0:.2f}\".format(roc_auc_score(y_true, y_hat)))"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {
    "_cell_guid": "67e27578-3029-3e51-448f-bc2b7a8f24ab",
    "_uuid": "d15012aa5570172dee9f99f79dc962a06aedd63c"
   },
   "outputs": [],
   "source": [
    "Let's take a look at the misclassified data (if any):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "_cell_guid": "28f895b0-597b-4f46-1a7f-7377d97ade05",
    "_execution_state": "idle",
    "_uuid": "ce60fdc5bcf2b2d08f68c22d581116383d6b6c45"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "124\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYAAAAD8CAYAAAB+UHOxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4340c70080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "347\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAD8CAYAAAB0IB+mAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nkMAXQgiDkMAXQgiD+H+5wnkapr0PXgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4341014240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "372\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXYAAAD8CAYAAABjAo9vAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f43410c3ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "false_positives = np.where(y_hat * (1. - y_test) > 0.5)[0]\n",
    "for i in non_idx:\n",
    "    if y_hat[i] > crossover_cutoff:\n",
    "        print(i)\n",
    "        plt.plot(x_test[i])\n",
    "        plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {
    "_cell_guid": "3c3c8bbf-9638-8f4f-050e-695a66a8b84a",
    "_uuid": "84ee7f7a1f17f0c2d5f309fa957a0cb8bbcd38ba"
   },
   "outputs": [],
   "source": [
    "It seems NASA missed one planet. I take this opportunity to claim it, and hereby name it Kaggle alpha :)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "_cell_guid": "0bebfd57-3ff5-90d1-79a2-4fb500116cc6",
    "_execution_state": "idle",
    "_uuid": "0e60c2111bc64417f9320ecb5f6adab298423606"
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "_change_revision": 0,
  "_is_fork": false,
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}