{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "WSW9BmePM7zZ"
   },
   "source": [
    "# Exercise 5.3: Neural Networks in Keras - Solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "t02FemO-M7za"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# See https://keras.io/\n",
    "# for extennsive documentation\n",
    "import tensorflow as tf\n",
    "from tensorflow import keras\n",
    "\n",
    "from keras.models import Sequential\n",
    "from keras.layers import Dense"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "IrvyHKHTM7ze"
   },
   "source": [
    "Let us visit the problem of wine quality prediction previously encountered in Exercises 3.2 and 4.1 one final time. After linear regression and a self-made network, we can now explore the comfort provided by the Keras library."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "-H-L5egsM7ze",
    "outputId": "82d3f95f-59b1-43e3-e8d7-4d939ea7eec6"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "/bin/sh: wget: command not found\r\n"
     ]
    }
   ],
   "source": [
    "# The code snippet below is responsible for downloading the dataset to\n",
    "# Google. You can directly download the file using the link\n",
    "# if you work with a local anaconda setup\n",
    "!wget https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-white.csv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "mDToshKJNWGY",
    "outputId": "8cce4ba8-392b-43a1-d659-26aa95d21113"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "data: (4898, 12)\n",
      "First example:\n",
      "Features: [7.0000e+00 3.1000e-01 3.5000e-01 1.6000e+00 6.3000e-02 1.3000e+01\n",
      " 1.1900e+02 9.9184e-01 3.2200e+00 5.0000e-01 1.0700e+01]\n",
      "Quality: 5.0\n"
     ]
    }
   ],
   "source": [
    "# load all examples from the file\n",
    "data = np.genfromtxt('winequality-white.csv',delimiter=\";\",skip_header=1)\n",
    "\n",
    "print(\"data:\", data.shape)\n",
    "\n",
    "# Prepare for proper training\n",
    "np.random.shuffle(data) # randomly sort examples\n",
    "\n",
    "# take the first 3000 examples for training\n",
    "X_train = data[:3000,:11] # all features except last column\n",
    "y_train = data[:3000,11]  # quality column\n",
    "\n",
    "# and the remaining examples for testing\n",
    "X_test = data[3000:,:11] # all features except last column\n",
    "y_test = data[3000:,11] # quality column\n",
    "\n",
    "print(\"First example:\")\n",
    "print(\"Features:\", X_train[0])\n",
    "print(\"Quality:\", y_train[0])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "VXx8BXB_M7zi"
   },
   "source": [
    "Below is the simple network from exercise 4.1 implemented using Keras. In addition to the network we define the loss function and optimiser."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "id": "Z0HMdw9eM7zi"
   },
   "outputs": [],
   "source": [
    "# See: https://keras.io/api/models/sequential/ and \n",
    "# https://keras.io/api/layers/core_layers/dense/\n",
    "# We can use the Sequential class to very easiliy\n",
    "# build a simple architecture\n",
    "model = Sequential()\n",
    "# 11 inputs, 20 outputs, relu\n",
    "model.add(Dense(20, input_dim=11, activation='relu')) \n",
    "model.add(Dense(20, activation='relu')) \n",
    "model.add(Dense(20, activation='relu')) \n",
    "# 20 inputs (automatically detected by Keras), 1 output, linear activation\n",
    "model.add(Dense(1, activation='linear'))\n",
    "\n",
    "\n",
    "# Set loss function and optimiser algorithm\n",
    "# Remove comments from of these versions:\n",
    "\n",
    "# Initial:\n",
    "#model.compile(loss='mse',  # mean squared error\n",
    "#              optimizer='sgd'# stochastic gradient descent\n",
    "#             ) \n",
    "#\n",
    "# sgd with mometum\n",
    "# instead of passing a string, we can explicitely construct the optimizer object\n",
    "# this gives us more control over its properties\n",
    "#opt = keras.optimizers.SGD(momentum=0.8) \n",
    "#model.compile(loss='mse',  # mean squared error\n",
    "#              optimizer='sgd'\n",
    "#             ) \n",
    "#\n",
    "# Adam:\n",
    "opt = keras.optimizers.Adam(learning_rate=0.0005) \n",
    "model.compile(loss='mse',  # mean squared error\n",
    "              optimizer=opt\n",
    "             ) \n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "I98jdZcqM7zm"
   },
   "source": [
    "# Training and evaluation below\n",
    "\n",
    "The code below trains the network for 5 epochs using the loss function and optimiser defined above. Each example is individually passed to the network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/70\n",
      "300/300 [==============================] - 1s 2ms/step - loss: 46.4118 - val_loss: 3.1073\n",
      "Epoch 2/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 2.7097 - val_loss: 2.1891\n",
      "Epoch 3/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 1.9155 - val_loss: 0.9903\n",
      "Epoch 4/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.8393 - val_loss: 0.7024\n",
      "Epoch 5/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.6665 - val_loss: 0.6581\n",
      "Epoch 6/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.7041 - val_loss: 0.6317\n",
      "Epoch 7/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.6754 - val_loss: 0.6689\n",
      "Epoch 8/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.6605 - val_loss: 0.6133\n",
      "Epoch 9/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.6512 - val_loss: 0.6183\n",
      "Epoch 10/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.6678 - val_loss: 0.6162\n",
      "Epoch 11/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.6542 - val_loss: 0.5944\n",
      "Epoch 12/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.6498 - val_loss: 0.6002\n",
      "Epoch 13/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.6381 - val_loss: 0.5874\n",
      "Epoch 14/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.6452 - val_loss: 0.6921\n",
      "Epoch 15/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.6827 - val_loss: 0.6189\n",
      "Epoch 16/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5984 - val_loss: 0.7090\n",
      "Epoch 17/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.6073 - val_loss: 0.5954\n",
      "Epoch 18/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.6351 - val_loss: 0.6501\n",
      "Epoch 19/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.6004 - val_loss: 0.5765\n",
      "Epoch 20/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.6296 - val_loss: 0.5682\n",
      "Epoch 21/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.6307 - val_loss: 0.5854\n",
      "Epoch 22/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.6311 - val_loss: 0.6989\n",
      "Epoch 23/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5797 - val_loss: 0.6385\n",
      "Epoch 24/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.6446 - val_loss: 0.5486\n",
      "Epoch 25/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.6366 - val_loss: 0.5558\n",
      "Epoch 26/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.6019 - val_loss: 0.5446\n",
      "Epoch 27/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.6299 - val_loss: 0.5682\n",
      "Epoch 28/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5982 - val_loss: 0.5423\n",
      "Epoch 29/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5921 - val_loss: 0.5433\n",
      "Epoch 30/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5791 - val_loss: 0.5554\n",
      "Epoch 31/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5792 - val_loss: 0.6534\n",
      "Epoch 32/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5904 - val_loss: 0.5771\n",
      "Epoch 33/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5871 - val_loss: 0.5595\n",
      "Epoch 34/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5635 - val_loss: 0.5373\n",
      "Epoch 35/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.6022 - val_loss: 0.7051\n",
      "Epoch 36/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5985 - val_loss: 0.5677\n",
      "Epoch 37/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5580 - val_loss: 0.5455\n",
      "Epoch 38/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.6386 - val_loss: 0.5383\n",
      "Epoch 39/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.6253 - val_loss: 0.6117\n",
      "Epoch 40/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5911 - val_loss: 0.5612\n",
      "Epoch 41/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5735 - val_loss: 0.5583\n",
      "Epoch 42/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5878 - val_loss: 0.5711\n",
      "Epoch 43/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5955 - val_loss: 0.5366\n",
      "Epoch 44/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5770 - val_loss: 0.5332\n",
      "Epoch 45/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5794 - val_loss: 0.5375\n",
      "Epoch 46/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.6078 - val_loss: 0.5349\n",
      "Epoch 47/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5853 - val_loss: 0.5300\n",
      "Epoch 48/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.6130 - val_loss: 0.5279\n",
      "Epoch 49/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5680 - val_loss: 0.7001\n",
      "Epoch 50/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5703 - val_loss: 0.6029\n",
      "Epoch 51/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.6161 - val_loss: 0.5407\n",
      "Epoch 52/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5793 - val_loss: 0.5336\n",
      "Epoch 53/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5859 - val_loss: 0.5460\n",
      "Epoch 54/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5511 - val_loss: 0.5384\n",
      "Epoch 55/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5948 - val_loss: 0.5303\n",
      "Epoch 56/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5912 - val_loss: 0.5345\n",
      "Epoch 57/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5816 - val_loss: 0.5278\n",
      "Epoch 58/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5890 - val_loss: 0.5268\n",
      "Epoch 59/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5852 - val_loss: 0.5261\n",
      "Epoch 60/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5851 - val_loss: 0.5566\n",
      "Epoch 61/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.6098 - val_loss: 0.5239\n",
      "Epoch 62/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5671 - val_loss: 0.5541\n",
      "Epoch 63/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5868 - val_loss: 0.5280\n",
      "Epoch 64/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5735 - val_loss: 0.5238\n",
      "Epoch 65/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5701 - val_loss: 0.5417\n",
      "Epoch 66/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5502 - val_loss: 0.5333\n",
      "Epoch 67/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5938 - val_loss: 0.5467\n",
      "Epoch 68/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5668 - val_loss: 0.5323\n",
      "Epoch 69/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5883 - val_loss: 0.5417\n",
      "Epoch 70/70\n",
      "300/300 [==============================] - 0s 1ms/step - loss: 0.5458 - val_loss: 0.5390\n"
     ]
    }
   ],
   "source": [
    "history = model.fit(X_train, y_train, \n",
    "                    validation_data=(X_test, y_test),\n",
    "                    epochs=70, batch_size=10) # changed batch size to 10 \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The history object returned by the model training above \n",
    "# contains the values of the loss function (the mean-squared-error)\n",
    "# at different epochs\n",
    "# We discard the first epoch as the loss value is very high,\n",
    "# obscuring the rest of the distribution\n",
    "train_loss = history.history[\"loss\"][1:]\n",
    "test_loss = history.history[\"val_loss\"][1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "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": [
    "# Prepare and plot loss over time\n",
    "plt.plot(train_loss,label=\"train\")\n",
    "plt.plot(test_loss,label=\"test\")\n",
    "plt.legend()\n",
    "plt.xlabel(\"Epoch-1\")\n",
    "plt.ylabel(\"Loss\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Correlation coefficient: 0.5500396765061618\n"
     ]
    },
    {
     "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": [
    "# After the training:\n",
    "\n",
    "# Prepare scatter plot\n",
    "y_pred = model.predict(X_test)[:,0]\n",
    "\n",
    "print(\"Correlation coefficient:\", np.corrcoef(y_pred,y_test)[0,1])\n",
    "plt.scatter(y_pred,y_test)\n",
    "plt.xlabel(\"Predicted\")\n",
    "plt.ylabel(\"True\")\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "name": "Exercise 6 - Solution",
   "provenance": []
  },
  "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}