03_overfitting.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
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   },
   "source": [
    "## Overfitting\n",
    "\n",
    "We've seen in previous lessons how we can construct neural networks with many neurons arranged into as many layers as we wish. This flexibility is what gives neural networks their power; however, it can also cause practical challenges. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "If we use too complicated of a network to fit a relatively small and simple dataset, the network may \"learn\" the noise present in our data rather than the actual useful patterns that the dataset contains. This phenomenon is called \"overfitting,\" and it can have unfortunate consequences. Overfit models may effectively memorize every detail of the dataset on which they were trained, but they will fail to generalize when presented with new data and cannot be relied upon to yield accurate predictions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "We will now demonstrate how overfitting occurs with a simple example. We'll need these libraries:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import tensorflow as tf\n",
    "from tensorflow import keras\n",
    "from visualization import draw_nn_graph\n",
    "from consistency import remove_randomness\n",
    "remove_randomness()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "We'll work with the simple `x` and `y` training dataset that is loaded and visualized below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PNm23V9XDQ7Z/mN4wyCP0hkJ+9pyrlCTNyazhXlWPAZllm7V9ywXcdM6VSZLeMqcfkKQOMtwlqYMMd0nqIMNdkjrIcJekDjLcJamDDHdJ6iDDXZI6yHCXpA5q9W32duyb8vZqkjRAa8N9x74ptm7fz6lXXwdg6uQptm7fD2DAS3rba223zLadh98I9mmnXn2dbTsPj6kiSVo6Whvux06emlO7JL2dtDbcV65YPqd2SXo7aW24b9m4juXLzpvRtnzZeWzZuG5MFUnS0tHaC6rTF00dLSNJZ2ptuEMv4A1zSTpTa7tlJEnDGe6S1EGGuyR10KzhnmR1kkeTHExyIMnNTfvvJHk6yZNJvpVkZdOeJF9JcqRZf/VCvwhJ0kyjnLm/BtxaVVcB1wI3JbkK2FZVf6eq3gf8d+DfNtt/DLii+doMfHX+y5Yknc2s4V5Vx6tqb7P8MnAIWFVVL/Vt9rNANcubgK9Xz+PAiiSXznPdkqSzmNNQyCRrgfXArub5HcCngBeBDzebrQJe6NvtaNN2/LTvtZnemT1r1qyZc+GSpOFGvqCa5ELgQeCW6bP2qvrtqloN3A/85lx+cFXdW1WTVTU5MTExl10lSbMYKdyTLKMX7PdX1fYBm9wPfKJZngJW9627rGmTJC2SUUbLBLgPOFRVd/e1X9G32Sbg2Wb5IeBTzaiZa4EXq2pGl4wkaWGN0ue+AbgR2J/kyabtduDXk6wDfgr8NfAbzbqHgeuAI8CPgc/Oa8WawbtRSRpk1nCvqseADFj18JDtC7jpHOvSCLwblaRh/IRqi3k3KknDGO4t5t2oJA1juLeYd6OSNIzhfpod+6bYcOd3uPy2P2PDnd9hx76lO4rTu1FJGqbVN+uYb227QOndqCQNY7j3OdsFyqUamN6NStIgdsv08QKlpK4w3Pt4gVJSVxjufbxAKakr7HPv4wVKSV1huJ/GC5SSusBuGUnqIMNdkjrIcJekDjLcJamDDHdJ6qD07q0x5iKSE/Tu5vRWXQz8aJ7KWWjWunDaVG+baoV21dumWuHc6v1bVTUxaMWSCPdzlWR3VU2Ou45RWOvCaVO9baoV2lVvm2qFhavXbhlJ6iDDXZI6qCvhfu+4C5gDa104baq3TbVCu+ptU62wQPV2os9dkjRTV87cJUl9DHdJ6qDWhXuS55PsT/Jkkt1N288neSTJ95rHnxt3nTC01m1Jnk3ydJJvJlkx7jqnDaq3b92tSSrJxeOqr9+wWpN8vnl/DyS5a5w19hvyf+F9SR6fbktyzbjrBEiyIsmfNu/joSR/d6keYzC03iV5nA2qtW/d/B5jVdWqL+B54OLT2u4CbmuWbwN+d9x1nqXWjwLnN8u/u1RqHVZv074a2Envg2ZnrF8qtQIfBr4NXNA8v2Tcdc5S77eAjzXL1wH/Y9x1NrX8Z+BfNsvvAFYs1WPsLPUuyeNsUK3N8rwfY607cx9iE703jebx+jHWclZV9a2qeq15+jhw2TjrGdGXgd8ClvrV988Bd1bVKwBV9cMx1zObAt7ZLL8LODbGWgBI8i7g7wP3AVTVT6rqJEv0GBtW71I8zs7y3sICHGNtDPcCvpVkT5LNTdu7q+p4s/x94N3jKe0Mg2rt92vAny9yTWdzRr1JNgFTVfXUeEs7w6D39krgQ0l2JfnLJB8YY32nG1TvLcC2JC8AXwK2jq26N10OnAD+MMm+JH+Q5GdZusfYsHr7LZXjbGCtC3aMjfvPlLfwZ82q5vES4Cl6vwlPnrbN/x13ncNq7Vv328A3aYajLoWvIe/tLuBdTfvzLJ1umUG1PgP8ByDANcBzS+X9HVLvV4BPNO2fBL69BOqcBF4DPtg8vwf4nSV8jA2st2/9kjnOhtS6baGOsdaduVfVVPP4Q3r/aNcAP0hyKUDzuCT+HB9SK0k+A/xj4F9U8y+6FAyo95fpnW08leR5en/a7k3yC2MrsjHkvT0KbK+eJ4Cf0puUaeyG1PtpYHuzyZ80beN2FDhaVbua538KXM0SPcYYXu9SPM6G1bogx1irwr35E+ai6WV6F02eAR6id6DQPP7X8VT4pmG1JvkVen1rv1pVPx5njf2G1PvdqrqkqtZW1Vp6/zmvrqrvj7HUs/0/2EHvoipJrqR3wWrsswOepd5j9H6BAnwE+N54KnxT82/7QpJ1TdM/BA6yBI8xGF7vUjzOhtS6d6GOsbbdIPvdwDeTQK/2/1JVf5Hku8ADSX6d3tXmT46xxmnDaj0CXAA80qx7vKp+Y3xlvmFgveMtaahh7+07gK8leQb4CfDpJXLGNqze/wfck+R84G+AQddlxuHzwP3N+/m/gc/SOxFcasfYtEH1fpeleZwNqnVBOP2AJHVQq7plJEmjMdwlqYMMd0nqIMNdkjrIcJekDjLcJamDDHdJ6qD/D+pXoMJ94+50AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# load data\n",
    "x_train = np.loadtxt(\"data/overfit_example_x_train.csv\", delimiter=\",\")\n",
    "y_train = np.loadtxt(\"data/overfit_example_y_train.csv\", delimiter=\",\")\n",
    "plt.scatter(x_train, y_train)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "## Building a Simple Model (Not Overfit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "As you can see, the  data above looks like a (noisy) line. We'd expect a simple linear model like the one below to give accurate predictions for the values in this dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 15 samples\n",
      "Epoch 1/20\n",
      "15/15 [==============================] - 0s 27ms/sample - loss: 41601.9883\n",
      "Epoch 2/20\n",
      "15/15 [==============================] - 0s 218us/sample - loss: 5064.6592\n",
      "Epoch 3/20\n",
      "15/15 [==============================] - 0s 202us/sample - loss: 683.7819\n",
      "Epoch 4/20\n",
      "15/15 [==============================] - 0s 164us/sample - loss: 158.5091\n",
      "Epoch 5/20\n",
      "15/15 [==============================] - 0s 167us/sample - loss: 95.5280\n",
      "Epoch 6/20\n",
      "15/15 [==============================] - 0s 151us/sample - loss: 87.9766\n",
      "Epoch 7/20\n",
      "15/15 [==============================] - 0s 152us/sample - loss: 87.0711\n",
      "Epoch 8/20\n",
      "15/15 [==============================] - 0s 113us/sample - loss: 86.9625\n",
      "Epoch 9/20\n",
      "15/15 [==============================] - 0s 185us/sample - loss: 86.9495\n",
      "Epoch 10/20\n",
      "15/15 [==============================] - 0s 204us/sample - loss: 86.9480\n",
      "Epoch 11/20\n",
      "15/15 [==============================] - 0s 170us/sample - loss: 86.9478\n",
      "Epoch 12/20\n",
      "15/15 [==============================] - 0s 94us/sample - loss: 86.9477\n",
      "Epoch 13/20\n",
      "15/15 [==============================] - 0s 159us/sample - loss: 86.9478\n",
      "Epoch 14/20\n",
      "15/15 [==============================] - 0s 114us/sample - loss: 86.9477\n",
      "Epoch 15/20\n",
      "15/15 [==============================] - 0s 104us/sample - loss: 86.9478\n",
      "Epoch 16/20\n",
      "15/15 [==============================] - 0s 104us/sample - loss: 86.9478\n",
      "Epoch 17/20\n",
      "15/15 [==============================] - 0s 100us/sample - loss: 86.9478\n",
      "Epoch 18/20\n",
      "15/15 [==============================] - 0s 196us/sample - loss: 86.9478\n",
      "Epoch 19/20\n",
      "15/15 [==============================] - 0s 125us/sample - loss: 86.9478\n",
      "Epoch 20/20\n",
      "15/15 [==============================] - 0s 180us/sample - loss: 86.9478\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<tensorflow.python.keras.callbacks.History at 0x7fc3783519b0>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# build model\n",
    "model = keras.Sequential(\n",
    "    [\n",
    "        keras.layers.Dense(\n",
    "            name=\"output\",\n",
    "            units=1,\n",
    "            input_shape=(1,),\n",
    "            kernel_initializer=tf.keras.initializers.ones,\n",
    "            bias_initializer=tf.keras.initializers.zeros\n",
    "        )\n",
    "    ]\n",
    ")\n",
    "\n",
    "# configure for training\n",
    "model.compile(\n",
    "    optimizer=tf.keras.optimizers.SGD(learning_rate=1e-4),\n",
    "    loss=\"mean_squared_error\"\n",
    ")\n",
    "\n",
    "# train\n",
    "model.fit(x_train,y_train,epochs=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "Generating predicted `y` values from our model reveals that the predictions it has produced are reasonable:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# visualize to demonstrate that our optimizer has found the best-fit line\n",
    "y_pred_train = model.predict(x_train)\n",
    "plt.scatter(x_train, y_train)\n",
    "plt.plot(x_train, y_pred_train, c=\"r\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "## Overfitting the Linear Trend\n",
    "\n",
    "Let's now load a much more complicated model that has been trained against this same dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:No training configuration found in save file: the model was *not* compiled. Compile it manually.\n"
     ]
    }
   ],
   "source": [
    "model_overfit = tf.keras.models.load_model(\"models/relu_overfit.h5\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "This model has a very large hidden layer consisting of many neurons:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "draw_nn_graph(model_overfit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "When we use this overfit model to predict the `y` values on which it was trained, it appears to have more predictive power than our original linear model. The predicted values from the overfit model (the green points) perfectly overlap the blue points from the actual dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 1152x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# model appears better\n",
    "plt.figure(figsize=(16,10))\n",
    "y_pred_train_overfit = model_overfit.predict(x_train)\n",
    "plt.scatter(x_train, y_train, marker=\"*\", alpha=1.0, s=150)\n",
    "plt.scatter(x_train, y_pred_train, c=\"r\", alpha=0.5)\n",
    "plt.scatter(x_train, y_pred_train_overfit, c=\"g\", alpha=0.67, s=100, marker=\"v\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "Does this mean that the overfit model is better? Absolutely not - as we can see below, the overfit model has learned the oscillatory pattern of the noise in our dataset rather than the underlying linear trend:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "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": [
    "# but this is all a lie - as we can see, the model has fit itself to the noise\n",
    "x_spacing = x_train[1] - x_train[0]\n",
    "x_fine_grain = np.arange(x_train[0], x_train[-1], x_spacing/10)\n",
    "y_pred_overfit_fine_grain = model_overfit.predict(x_fine_grain)\n",
    "plt.plot(x_fine_grain, y_pred_overfit_fine_grain, c=\"g\")\n",
    "plt.scatter(x_train, y_train)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "We can see the downfall of this approach when we extrapolate further in the future. Let's load some additional data points, which we'll call the \"test\" dataset, to demonstrate how our overfit model fails to generalize to new data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD4CAYAAAAXUaZHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAYC0lEQVR4nO3df5BdZX3H8feHJMIGLKuyatgkbFTEokhCrzEWf4xQ5Ec7DTJasahI68QfsRVltIAzVpxmoGJ1pB3jpEIHnCAihJhRrNKStjJTkm7IDwgRjQZI1iiLNiANognf/nGelZtl795zd+/Ze8/Zz2tmZ899znPOPg+H/e6T73nOcxQRmJlZtRzW6QaYmVn7ObibmVWQg7uZWQU5uJuZVZCDu5lZBc3sdAMAjjnmmBgYGOh0M8zMSmXTpk2PRkTfWPu6IrgPDAwwODjY6WaYmZWKpIca7XNaxsysghzczcwqyMHdzKyCHNzNzCrIwd3MrIIc3M3MKsjB3cysghzczcym0q7VsHYAbjws+75rdSE/piseYjIzmxZ2rYaNy+Dg/uzz/oeyzwALLmjrj/LI3cxsqmz95DOBfcTB/Vl5mzUN7pKOkLRR0lZJ2yVdkcolaYWkH0raIemv68qvkbRT0jZJp7S91WZmZbT/4dbKJyFPWuYp4LSIeELSLOAuSd8Bfh+YB7wiIp6W9MJU/2zg+PT1WmBl+m5mNr3Nnp+lYsYqb7OmI/fIPJE+zkpfAXwQ+ExEPJ3qPZLqLAVuSMfdDfRKmtP2lpuZlc3JK2DG7EPLZszOytssV85d0gxJW4BHgDsiYgPwUuAdkgYlfUfS8al6P7C77vA9qWz0OZelYweHh4cn1wszs07LMwtmwQWweBXMPg5Q9n3xqrbfTIWcs2Ui4iCwUFIvcJukVwGHA7+OiJqk84DrgDfk/cERsQpYBVCr1aLllpuZdYtWZsEsuKCQYD5aS7NlImIfsB44i2xEvibtug14ddoeIsvFj5ibyszMqmkKZ8HklWe2TF8asSOpBzgD+AGwFnhzqvYm4Idpex3wnjRrZgnwWETsbXvLzcy6xRTOgskrT1pmDnC9pBlkfwxujohvSboLWC3po8ATwPtS/duBc4CdwH7govY328ysi0zhLJi8mgb3iNgGLBqjfB/wx2OUB7C8La0zMyuDk1ccmnOHwmbB5OUnVM3MJmsKZ8Hk5bVlzMzaYYpmweTlkbuZWQU5uJuZVZCDu5lZBTm4m5lVkIO7mVkFObibmVWQg7uZWQU5uJuZVZCDu5lZBTm4m5lVkIO7mVkFObibmVWQg7uZWQU5uJuZVZCDu5lZBTm4m5lVkIO7mVkFObibmVVQ0+Au6QhJGyVtlbRd0hWj9l8j6Ym6z4dL+rqknZI2SBpof7PNzGw8eUbuTwGnRcTJwELgLElLACTVgOeNqv+XwP9GxMuALwB/38b2mplNnV2rYe0A3HhY9n3X6k63KLemwT0yIyPzWekrJM0ArgY+MeqQpcD1afsW4HRJalN7zcymxq7VsHEZ7H8IiOz7xmWlCfC5cu6SZkjaAjwC3BERG4APA+siYu+o6v3AboCIOAA8BrxgjHMukzQoaXB4eHgyfTAza7+tn4SD+w8tO7g/Ky+BXME9Ig5GxEJgLrBY0huBtwP/ONEfHBGrIqIWEbW+vr6JnsbMrBj7H26tvMu0NFsmIvYB64E3Ay8Ddkp6EJgtaWeqNgTMA5A0Ezga+EW7GmxmNml5cumz5499bKPyLpNntkyfpN603QOcAWyKiBdHxEBEDAD70w1UgHXAhWn7bcCdERHtb7qZ2QTkzaWfvAJmzD60bMbsrLwE8ozc5wDrJW0D/ocs5/6tcepfC7wgjeQ/Blw6+WaambVJ3lz6ggtg8SqYfRyg7PviVVl5CcxsViEitgGLmtQ5qm7712T5eDOz7tNKLn3BBaUJ5qP5CVUzm15KnkvPy8HdzKaXkufS83JwN7PppeS59Lya5tzNzCqnxLn0vDxyN7Pu1sr6LiVeC6bdPHI3s+41Mid9ZOriyJx0ePbIu5W604BH7mbWvVpZ36Xka8G0m4O7mXWvVuakl3wtmHZzcDez7tXKnPRpMn89Lwd3M+tercxJnybz1/NycDez7tXKnPRpMn89L3XDgo21Wi0GBwc73Qwzs1KRtCkiamPt88jdzKyCHNzNzCrIwd3MrIIc3M3MKsjB3cysghzczax9vHBX1/DCYWbWHl64q6s0HblLOkLSRklbJW2XdEUqXy3pAUn3SbpO0qxULknXSNopaZukU4ruhJl1AS/c1VXypGWeAk6LiJOBhcBZkpYAq4FXACcBPcD7Uv2zgePT1zJgZbsbbWZdyAt3dZWmwT0yT6SPs9JXRMTtaV8AG4G5qc5S4Ia0626gV9KcIhpvZl3EC3d1lVw3VCXNkLQFeAS4IyI21O2bBbwb+NdU1A/srjt8Tyobfc5lkgYlDQ4PD0+0/WbWLbxwV1fJFdwj4mBELCQbnS+W9Kq63V8C/isivt/KD46IVRFRi4haX19fK4eaWTfywl1dpaXZMhGxT9J64CzgPkl/C/QB76+rNgTMq/s8N5WZWdVNgxdPl0We2TJ9knrTdg9wBvADSe8DzgTeGRFP1x2yDnhPmjWzBHgsIvYW0HYzM2sgz8h9DnC9pBlkfwxujohvSToAPAT8tySANRHxGeB24BxgJ7AfuKiQlpuZWUNNg3tEbAMWjVE+5rFp9szyyTfNzMwmyssPmJlVkIO7mVkFObibmVWQg7uZWQU5uJtZZ3h54EJ5yV8zm3peHrhwHrmb5eWRZvt4eeDCeeRulodHmu3l5YEL55G7WR4eabaXlwcunIO7WR5VHGm2kmZqd0rKywMXzsHdLI+qjTRH0kz7HwLimTTTWEG7lbp5eXngwilbCqazarVaDA4OdroZZo2NzrlDNtIsa0BaO5CC9Sizj4NzH5x4XZtSkjZFRG2sfR65m+VRtZFmK2mmKqakpgHPljHLq0ovopg9v8FofIw0Uyt1rWt45G5WhLw3IIuYO5/nnK3c0PTNz1LyyN2s3fLOiS9i7nzec45sb/1kll6ZPT8L1mP93FbqWtfwDVWzdst7A7KIG5W++Tmt+Iaq2VTKewOyiBuVvvlpiYO7WbvlnRPfytz5vLn5qs3HtwlzcDdrt7w3IPPWa+UhIt/8tKRpcJd0hKSNkrZK2i7pilS+QNIGSTslfV3Sc1L54enzzrR/oNgumHWZvHPi89ZrZV2bqs3HtwlrekNVkoAjI+IJSbOAu4CPAB8D1kTETZK+DGyNiJWSPgS8OiI+IOl84K0R8Y7xfoZvqJqN48bDgLF+TwV//vRUt8a6yKRuqEbmifRxVvoK4DTgllR+PXBu2l6aPpP2n57+QJjZRDiPbhOQK+cuaYakLcAjwB3Aj4F9EXEgVdkD9KftfmA3QNr/GPCCMc65TNKgpMHh4eHJ9cKsypxHtwnIFdwj4mBELATmAouBV0z2B0fEqoioRUStr69vsqczqy7n0W0CWnpCNSL2SVoPvA7olTQzjc7nAkOp2hAwD9gjaSZwNPCLNrbZbPqp0ro2NiXyzJbpk9SbtnuAM4AdwHrgbanahcA30/a69Jm0/87ohsdgbVpZu3mIU6+6kwWXfptTr7qTtZuHmh9kViF5Ru5zgOslzSD7Y3BzRHxL0v3ATZL+DtgMXJvqXwt8VdJO4JfA+QW026yhtZuHuGzNvTz524MADO17ksvW3AvAuYv6xzvUrDKaBveI2AYsGqP8J2T599Hlvwbe3pbWmU3A1d994HeBfcSTvz3I1d99wMHdpg0/oWqV89N9T7ZUblZFDu5WOcf29rRUblZFDu5WOR8/8wR6Zs04pKxn1gw+fuYJHWqR2dTzyzqsckby6ld/9wF+uu9Jju3t4eNnnuB8u00rDu5WSecu6ncwt2nNaRkzswpycDczqyAHdzOzCnJwNzOrIAd3M7MKcnA3M6sgB3czswryPHeb9tZuHvIDT1Y5Du42rXl5YKsqp2VsWhtveWCzMnNwt2nNywNbVTktY4UpQy772N4ehsYI5F4e2MrOI3crxEgue2jfkwTP5LK77V2mXh7YqsrB3QpRllz2uYv6ufK8k+jv7UFAf28PV553Utf9C8OsVU7LWCHKlMv28sBWRU1H7pLmSVov6X5J2yV9JJUvlHS3pC2SBiUtTuWSdI2knZK2STql6E7Y5K3dPMSpV93Jgku/zalX3Tnp9IlfdWfWWXnSMgeASyLiRGAJsFzSicBngSsiYiHwqfQZ4Gzg+PS1DFjZ9lZbWxWRH3cu26yzmgb3iNgbEfek7V8BO4B+IIDfS9WOBn6atpcCN0TmbqBX0py2t9zapoj8uHPZZp3VUs5d0gCwCNgAXAx8V9LnyP5I/GGq1g/srjtsTyrbO+pcy8hG9syfP7/1llvbFJUfdy7brHNyz5aRdBRwK3BxRDwOfBD4aETMAz4KXNvKD46IVRFRi4haX19fK4damzk/blY9uYK7pFlkgX11RKxJxRcCI9vfABan7SFgXt3hc1OZdSnnx82qp2laRpLIRuU7IuLzdbt+CrwJ+A/gNOBHqXwd8GFJNwGvBR6LiENSMtZdRlIneZ4mLeKp0zI8yWpWNoqI8StIrwe+D9wLPJ2KLwceB75I9gfi18CHImJT+mPwT8BZwH7googYHO9n1Gq1GBwct4p1gdErKEI2wp/MjdIizmk2XUjaFBG1sfY1HblHxF2AGuz+gzHqB7C8pRZaKYw3q2aigbiIc5qZlx+wFhQxq6ZMT7KalYmDu+VWxKwaz9QxK4aDu+VWxKwaz9QxK4YXDrPcWplV08lzmlmO2TJTwbNlLC9PmzR7xqRmy5h1C7/M2iw/59ytNMryAhCzbuDgbqXhaZNm+Tm4W2l42qRZfg7uVhqeNmmWn2+oWml42qRZfg7uVip+AYhZPk7LmJlVkIO7mVkFObibmVWQg7uZWQU5uJuZVZCDu5lZBTm4m5lVUNPgLmmepPWS7pe0XdJH6vb9laQfpPLP1pVfJmmnpAcknVlU483MbGx5HmI6AFwSEfdIei6wSdIdwIuApcDJEfGUpBcCSDoROB94JXAs8G+SXh4RBxuc38zM2qzpyD0i9kbEPWn7V8AOoB/4IHBVRDyV9j2SDlkK3BQRT0XELmAnsLiIxpuZ2dhayrlLGgAWARuAlwNvkLRB0n9Kek2q1g/srjtsTyozM7MpknttGUlHAbcCF0fE45JmAs8HlgCvAW6W9JIWzrcMWAYwf/78lhpdVX6FnJm1S66Ru6RZZIF9dUSsScV7gDWR2Qg8DRwDDAHz6g6fm8oOERGrIqIWEbW+vr7J9KESRl4hN7TvSYJnXiG3dvOz/tOZmTWVZ7aMgGuBHRHx+bpda4E3pzovB54DPAqsA86XdLikBcDxwMZ2N7xq/Ao5M2unPGmZU4F3A/dK2pLKLgeuA66TdB/wG+DCiAhgu6SbgfvJZtos90yZ5op6hZxTPWbTU9PgHhF3AWqw+10NjlkBrJhEu6adY3t7GBojkE/mFXIjqZ6RfxGMpHoAB3izivMTql2iiFfIOdVjNn35TUxdoohXyBWV6jGz7ufg3kXa/Qq5IlI9ZlYOTstUWBGpHjMrB4/cK6yIVI+ZlYODe8W1O9VjZuXgtIyZWQV55F7HD/yYWVU4uCd+4MfMqsRpmcQP/JhZlTi4J37gx8yqxME9afRgjx/4MbMycnBP/MCPmVWJb6gmRT3w4xk4ZtYJDu512v3Aj2fgmFmnOC1TIM/AMbNO8ci9QH67kpl1ikfuBSpiBo5fpG1meTi4F8hvVzKzTnFapkB+u5KZdUrT4C5pHnAD8CIggFUR8cW6/ZcAnwP6IuJRSQK+CJwD7AfeGxH3FNH4MvDblcysE/KkZQ4Al0TEicASYLmkE+F3gf8twMN19c8Gjk9fy4CVbW3xNOeHrcwsj6bBPSL2joy8I+JXwA5gZCj6BeATZCP6EUuBGyJzN9AraU57mz19nbuonyvPO4n+3h4E9Pf2cOV5J3m2jJkdoqWcu6QBYBGwQdJSYCgitmaZmN/pB3bXfd6TyvaOOtcyspE98+fPb7Xd05rfrmRmzeSeLSPpKOBW4GKyVM3lwKcm+oMjYlVE1CKi1tfXN9HTmJnZGHIFd0mzyAL76ohYA7wUWABslfQgMBe4R9KLgSFgXt3hc1OZmZlNkabBPc1+uRbYERGfB4iIeyPihRExEBEDZKmXUyLiZ8A64D3KLAEei4i9jc5vZmbtlyfnfirwbuBeSVtS2eURcXuD+reTTYPcSTYV8qJJt9LMzFrSNLhHxF2AmtQZqNsOYPmkW2ZmZhNW6idUvYCWmdnYShvcvVa6mVljpV04zAtomZk1Vtrg7gW0zMwaK21wL2KtdDOzqihtcPcCWmZmjZX2hmoRa6WbmVVFaYM7eAEtM7NGSpuWMTOzxhzczcwqqNRpmU7y07Fm1s0c3CfAT8eaWbebFsG93aPs8Z6OdXA3s25Q+eBexCjbT8eaWber/A3VItag8dOxZtbtKh/cixhl++lYM+t2lQ/uRYyyz13Uz5XnnUR/bw8C+nt7uPK8k5xvN7OuUfmc+8fPPOGQnDu0Z5Ttp2PNrJtVPrh7DRozm44qH9zBo2wzm36a5twlzZO0XtL9krZL+kgqv1rSDyRtk3SbpN66Yy6TtFPSA5LOLLIDZmb2bHluqB4ALomIE4ElwHJJJwJ3AK+KiFcDPwQuA0j7zgdeCZwFfEnSjDHPbGZmhWga3CNib0Tck7Z/BewA+iPiexFxIFW7G5ibtpcCN0XEUxGxC9gJLG5/083MrJGWpkJKGgAWARtG7foL4Dtpux/YXbdvTyobfa5lkgYlDQ4PD7fSDDMzayJ3cJd0FHArcHFEPF5X/kmy1M3qVn5wRKyKiFpE1Pr6+lo51MzMmsg1W0bSLLLAvjoi1tSVvxf4E+D0iIhUPATMqzt8bipraNOmTY9KeqiFdo92DPDoJI7vNu5Pd3N/ul/V+tSoP8c1OkDPxOQGFSQB1wO/jIiL68rPAj4PvCkihuvKXwncSJZnPxb4d+D4iDh0gZc2kjQYEbWizj/V3J/u5v50v6r1aSL9yTNyPxV4N3CvpC2p7HLgGuBw4I4s/nN3RHwgIrZLuhm4nyxds7zIwG5mZs/WNLhHxF2Axth1+zjHrABWTKJdZmY2CVVZOGxVpxvQZu5Pd3N/ul/V+tRyf5rm3M3MrHyqMnI3M7M6Du5mZhVUuuAu6UFJ90raImkwlT1f0h2SfpS+P6/T7cyrQX8+LWkolW2RdE6n25mXpF5Jt6RF5XZIel2Zrw807FMpr5GkE+ravEXS45IuLus1Gqc/pbw+AJI+mhZpvE/S1yQdIWmBpA1pQcavS3pO0/OULecu6UGgFhGP1pV9lmwe/lWSLgWeFxF/06k2tqJBfz4NPBERn+tUuyZK0vXA9yPiK+l/wNlkU2dLeX2gYZ8upqTXaERa0G8IeC2wnBJfI3hWfy6ihNdHUj9wF3BiRDyZppXfDpwDrImImyR9GdgaESvHO1fpRu4NLCV70Ir0/dwOtmXaknQ08EbgWoCI+E1E7KPE12ecPlXB6cCPI+IhSnyN6tT3p8xmAj2SZpINJPYCpwG3pP25rk8Zg3sA35O0SdKyVPaiiNibtn8GvKgzTZuQsfoD8OG0Vv51ZfknMrAAGAb+RdJmSV+RdCTlvj6N+gTlvEb1zge+lrbLfI1G1PcHSnh9ImII+BzwMFlQfwzYBOyrW4V3zMUYRytjcH99RJwCnE22tvwb63emNW7KlGsaqz8rgZcCC8ku8D90sH2tmAmcAqyMiEXA/wGX1lco4fVp1KeyXiMAUnrpT4FvjN5Xwms0Vn9KeX3SH6GlZIOKY4Ejyd6L0bLSBff0l42IeAS4jWwNm59LmgOQvj/SuRa2Zqz+RMTPI+JgRDwN/DPlWQ9/D7AnIkaWhL6FLDCW9vrQoE8lvkYjzgbuiYifp89lvkYwqj8lvj5/BOyKiOGI+C2whmwJmN6UpoEcizFCyYK7pCMlPXdkG3gLcB+wDrgwVbsQ+GZnWtiaRv0Z+SVL3krWx64XET8Ddks6IRWdTrbGUCmvDzTuU1mvUZ13cmgKo7TXKDmkPyW+Pg8DSyTNliSe+R1aD7wt1cl1fUo1W0bSS8hGt5D9c/nGiFgh6QXAzcB84CHgzyLilx1qZm7j9OerZP+cDOBB4P11+dCuJmkh8BXgOcBPyGYtHEYJr8+IBn26hvJeoyPJgshLIuKxVFbK3yFo2J8y/w5dAbyDbOHFzcD7yHLsNwHPT2Xvioinxj1PmYK7mZnlU6q0jJmZ5ePgbmZWQQ7uZmYV5OBuZlZBDu5mZhXk4G5mVkEO7mZmFfT/k8jmFHJoJVIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_test = np.loadtxt(\"data/overfit_example_x_test.csv\", delimiter=\",\")\n",
    "y_test = np.loadtxt(\"data/overfit_example_y_test.csv\", delimiter=\",\") \n",
    "plt.scatter(x_train, y_train)\n",
    "plt.scatter(x_test, y_test, c=\"orange\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "Our simple model performs well on the test set, as it has captured the underlying linear trend:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "# raw data\n",
    "plt.scatter(x_train, y_train)\n",
    "plt.scatter(x_test, y_test, c=\"orange\")\n",
    "\n",
    "# predictions - plot the full range, both train and test\n",
    "x = np.concatenate((x_train, x_test))\n",
    "y_pred = model.predict(x)\n",
    "plt.plot(x, y_pred, c=\"r\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "Our overfit model, by contrast, performs horribly on the test dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "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": [
    "y_pred_overfit_test = model.predict(x_test)\n",
    "# raw data\n",
    "plt.scatter(x_train, y_train)\n",
    "plt.scatter(x_test, y_test, c=\"orange\")\n",
    "\n",
    "# predictions\n",
    "y_pred_overfit = model_overfit.predict(x)\n",
    "plt.plot(x, y_pred_overfit, c=\"r\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "## Train/Test Splits\n",
    "\n",
    "Because overfitting has such dramatic negative consequences for neural network models, you will often see the evaluation process above repeated for many different types of problems. The dataset that you are using to train your model will be split into two pieces - a *training set* and a (usually smaller) *test set*. The model will be trained using only the data in the training set, and then its accuracy will be evaluated against the test set. This allows us to perform a \"fair\" comparison of different models that punishes overly complex models that overfit the training data. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "In the subsequent lessons, you should observe that we take this approach, and always work with two different data subsets: `(X_train, y_train)` and `(X_test, y_test)`, due to the concerns discussed in this lesson. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "A common way to split a dataset into train and test subsets is to use the `train_test_split` function from `sklearn`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "We can pass this function a `test_size`  argument indicating how many values to extract into the test set - typically, this is set to around `0.2` or `0.25`; we can see how this works using the demonstration below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_demo = np.arange(0,100)\n",
    "y_demo = 2* x_demo + 5\n",
    "x_demo_train, x_demo_test, y_demo_train, y_demo_test = train_test_split(\n",
    "    x_demo, \n",
    "    y_demo, \n",
    "    test_size=0.2,\n",
    "    random_state=1337\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "Note that the test set size is the specified fraction of the full set size:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "full size: 100\n",
      "test size: 20\n"
     ]
    }
   ],
   "source": [
    "print(\"full size:\", len(x_demo))\n",
    "print(\"test size:\", len(x_demo_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "We also set the `random_state` argument to seed the random number generator so that we get the same (randomly chosen) result every tiem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "<span style=\"color:blue;font-weight:bold\">Exercise</span>: Let's practice training a model on the training set and then evaluating it on the test set. Perform the following tasks:\n",
    "\n",
    "* Create a model named `my_model` containing a single layer with one neuron. Use the following argument in the creation of this neuron to help the training process along:\n",
    "\n",
    "```\n",
    "kernel_initializer=keras.initializers.constant(2)\n",
    "```\n",
    "\n",
    "* Compile your model for training using a `loss` value of `mean_squared_error` and an optimizer created as follows: `keras.optimizers.Adam(lr=0.01)`\n",
    "* `fit` your model for `50` epochs on the datsets `x_demo_train` and `y_demo_train`\n",
    "* Create a variable `y_pred_my_model` and assign it the value produced by calling `my_model.predict` on the argument `x_demo_test`\n",
    "* Make a scatter plot of `x_demo_test` vs. `y_demo_test`\n",
    "* Overlay a line plot of your predictions `y_pred_my_model` \n",
    "\n",
    "Be careful not to delete the `remove_randomness` call at the top of the cell."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "tags": [
     "exercise"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fc343353c50>]"
      ]
     },
     "execution_count": 40,
     "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": [
    "remove_randomness()\n",
    "\n",
    "my_model = tf.keras.Sequential([\n",
    "    tf.keras.layers.Dense(units=1,\n",
    "                          kernel_initializer=keras.initializers.constant(2))\n",
    "])\n",
    "\n",
    "my_model.compile(optimizer=keras.optimizers.Adam(lr=0.01), loss=\"mean_squared_error\")\n",
    "history = my_model.fit(x_demo_train, y_demo_train, epochs=50, verbose=0)\n",
    "\n",
    "y_pred_my_model = my_model.predict(x_demo_test)\n",
    "\n",
    "plt.scatter(x_demo_test, y_demo_test)\n",
    "plt.plot(x_demo_test, y_pred_my_model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "deletable": false,
    "editable": false,
    "scrolled": true,
    "strategicml": {
     "execution_time": 1584779897311,
     "exercise_id": "dc0514e4-4931-42c3-acfc-eb898820b8bc",
     "points": 4
    },
    "tags": [
     "test"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"background-color:#e8fcef\n",
       ";color:#333333;padding:10px;border-style:solid;border-width:2px;border-color:#038c33\">\n",
       "<div style=\"font-weight:bold\">Correct!</div>\n",
       "</div>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "check_variable_definition(\"my_model\")\n",
    "assert str(type(my_model)) ==  \"<class 'tensorflow.python.keras.engine.sequential.Sequential'>\", \"Your variable <code>my_model</code> does not contain an object of the right type - did you create it using <code>keras.Seqential()</code>?\"\n",
    "assert len(my_model.layers) == 1, \"Your model does not contain the correct number of layers.\"\n",
    "assert abs(y_pred_my_model[5] - 116.31786) < 0.01, \"Your <code>y_pred_my_model</code> values are incorrect - check your training configuration\"\n",
    "success()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fc3504d12e8>]"
      ]
     },
     "execution_count": 49,
     "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"
     },
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   "metadata": {},
   "outputs": [],
   "source": []
  }
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