training_a_neural_network.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "training_a_neural_network.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyPpU/o1I64S8GlkWMeS7f6F",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/sayarghoshroy/Intro_to_DL_tutorial/blob/master/training_a_neural_network.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MbEbYlfUYQnL",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import pandas as pd\n",
        "from matplotlib import cm\n",
        "from mpl_toolkits.mplot3d import Axes3D\n",
        "\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.neural_network import MLPRegressor"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jOsI9zIyamjH",
        "colab_type": "text"
      },
      "source": [
        "## *Example 4: Train a Neural Network on a Real World Dataset*\n",
        "\n",
        "### $ Predict\\ Concrete\\ Compressive\\ Strength.$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "l0mcHgP4aiWD",
        "colab_type": "code",
        "outputId": "157c8155-d276-4137-dab8-f24c24d176d0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "# loading the data\n",
        "data_read = pd.read_excel('./Concrete_Data.xls')\n",
        "data = data_read.values\n",
        "# the last column of the data is what we are trying to predict\n",
        "\n",
        "print(\"Dimensions of the Dataset: \" + str(np.shape(data)))"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Dimensions of the Dataset: (1030, 9)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NCPnanyEa-H4",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Splitting the Data into Training and Testing Sets\n",
        "X_train, X_test, y_train, y_test = train_test_split(data[:, 0:8], data[:, 8], test_size = 0.3, random_state = 2020)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Awx63jZ5bcmr",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Data Normalization\n",
        "# Note that we are only observing our training set\n",
        "\n",
        "train_mean = np.mean(X_train, axis = 0)\n",
        "train_var = np.var(X_train, axis = 0)\n",
        "\n",
        "X_train = (X_train -  train_mean) / np.sqrt(train_var)\n",
        "X_test = (X_test - train_mean) / np.sqrt(train_var)\n",
        "# Pre-processing Step"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tdRXBevvb2Pc",
        "colab_type": "text"
      },
      "source": [
        "#### $ Building\\ Neural\\ Network\\ and\\ defining\\ Gradients$\n",
        "\n",
        "$ y' = W_2.f(W_1^TX)$\n",
        "\n",
        "$ Neural\\ Network\\ with\\ one\\ hidden\\ layer,\\ eight\\ inputs,\\ and\\ one\\ output. $\n",
        "\n",
        "$where:$\n",
        "\n",
        "- $\\ W_1\\ is\\ of\\ size\\ 8\\ \\times\\ n\\_nodes$\n",
        "\n",
        "- $\\ W_2\\ is\\ of\\ size\\ 1\\ \\times\\ n\\_nodes$\n",
        "\n",
        "- $\\ f\\ is\\ the\\ activation\\ for\\ the\\ hidden\\ layer$\n",
        "\n",
        "- $\\ X\\ is\\ the\\ data\\ matrix\\ of\\ size\\ 8\\times [batch\\ size]$\n",
        "\n",
        "<br>\n",
        "\n",
        "$ Mean\\ Squared\\ Error = \\frac{1}{N}(y - y')^T (y - y') $\n",
        "\n",
        "$ = \\frac{1}{N} (y^Ty - y^Ty' - y'^Ty +y'^Ty') = L$\n",
        "\n",
        "<br>\n",
        "\n",
        "$ \\frac{\\partial L}{\\partial W_2} = \\frac{1}{N}(2y'.\\frac{\\partial y'}{\\partial W_2} - 2y. \\frac{\\partial y'}{\\partial W_2})$\n",
        "\n",
        "$= \\frac{2}{N}(y' - y).f(W_1^TX)$\n",
        "\n",
        "<br>\n",
        "\n",
        "$ \\frac{\\partial L}{\\partial W_1} = \\frac{2}{N}(y' - y) \\frac{\\partial y'}{\\partial W_1}$\n",
        "\n",
        "$ = \\frac{2}{N}(y' - y).W_2 \\odot f'(W_1^T X).X^T$\n",
        "\n",
        "<br>\n",
        "\n",
        "$ -\\ where\\ f'\\ is\\ the\\ derivative\\ of\\ the\\ activation\\ function$\n",
        "\n",
        "<br>\n",
        "\n",
        "$ NOTE:\\ No\\ biases\\ have\\ been\\ used\\ so\\ far.$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iUCVObw4blyK",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "batch_size = 200\n",
        "\n",
        "def forward(X, W_1, W_2, f):\n",
        "    y_prime = np.matmul(W_2, f(np.matmul(W_1.T, X.T)))\n",
        "    return y_prime\n",
        "\n",
        "def convergence(losses):\n",
        "    if len(losses) > 1 and np.abs(losses[-1] - losses[-2]) < 1e-4:\n",
        "        return True\n",
        "    return False\n",
        "\n",
        "def plot_losses(errors):\n",
        "    fig = plt.figure(figsize=(9, 9))\n",
        "    p = fig.add_subplot('111')\n",
        "    p.set_title('Error v/s Epoch')\n",
        "    p.set_xlabel('Epoch Number')\n",
        "    p.set_ylabel('Error')\n",
        "    losses = [x for x in errors]\n",
        "    p.plot(list(range(1, len(losses))), losses[1:])\n",
        "    plt.show()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "izuPNAticNXs",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def batch_backprop_train(nodes, f, f_prime, random_seed = 2020, max_iter = int(1e4)):\n",
        "    np.random.seed(seed = random_seed)\n",
        "    W_1 = np.random.random_sample((8, nodes))\n",
        "    np.random.seed(seed = random_seed)\n",
        "    W_2 = np.random.random_sample((1, nodes))\n",
        "\n",
        "    eta = 1e-4 * 5\n",
        "    \n",
        "    iteration = 0\n",
        "\n",
        "    train_loss = []\n",
        "\n",
        "    while iteration < max_iter and convergence(train_loss) == False:\n",
        "        # random batch selection\n",
        "        indices = np.random.randint(0, X_train.shape[0], batch_size)\n",
        "        sample = X_train[indices]\n",
        "        y = y_train[indices]\n",
        "\n",
        "        train_loss.append(np.power(np.linalg.norm(y_train - forward(X_train, W_1, W_2, f)), 2) / np.shape(y_train)[0])\n",
        "\n",
        "        y_prime = forward(sample, W_1, W_2, f)\n",
        "\n",
        "        partial_L_W_1 = (2 / batch_size) * (np.multiply( (np.asmatrix(y_prime - y).T @ W_2).T, f_prime(W_1.T @ sample.T)) @ sample).T\n",
        "        partial_L_W_2 = (2 / batch_size) * np.matmul(np.asmatrix(y_prime - y), f(np.matmul(W_1.T, sample.T).T))\n",
        "\n",
        "        W_1 = W_1 - eta * partial_L_W_1\n",
        "        W_2 = W_2 - eta * partial_L_W_2\n",
        "        \n",
        "        iteration += 1\n",
        "    \n",
        "    test_error = np.power(np.linalg.norm(y_test - forward(X_test, W_1, W_2, f)), 2) / np.shape(y_test)[0]\n",
        "    return train_loss, test_error, W_1, W_2"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Mx69Fgmzcg_d",
        "colab_type": "code",
        "outputId": "bdf61f93-73f1-4ea3-9168-ae98fd0b438a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "source": [
        "activations = ['relu', 'tanh']\n",
        "\n",
        "get_f = {'tanh' : (lambda x: np.tanh(x)), 'relu': (lambda x: np.maximum(0, x))}\n",
        "get_f_prime = {'tanh': (lambda x: 1 - np.power(np.tanh(x), 2)), 'relu': (lambda x: np.greater(x, 0))}\n",
        "\n",
        "for active in activations:\n",
        "    train_loss, test_error, _, _ = batch_backprop_train(64, get_f[active], get_f_prime[active])\n",
        "    print(\"Hidden Layer Activation = \" + str(active))\n",
        "    print(\"MSE on Train Set: \" + str(train_loss[-1]))\n",
        "    print(\"MSE on Test Set: \" + str(test_error))\n",
        "    plot_losses(train_loss)"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Hidden Layer Activation = relu\n",
            "MSE on Train Set: 148.62573587283686\n",
            "MSE on Test Set: 174.13285193540767\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 648x648 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Hidden Layer Activation = tanh\n",
            "MSE on Train Set: 201.7388019547476\n",
            "MSE on Test Set: 271.9911446153087\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 648x648 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yPebYkB6gTQ4",
        "colab_type": "text"
      },
      "source": [
        "---\n",
        "$ How\\ scikit-learn\\ makes\\ our\\ life\\ easier $\n",
        "\n",
        "---"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-zpjnaUPdMv9",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Using sklearn's implementation of SGD with 10000 iterations\n",
        "def train(X, y, n_nodes = 64, active = 'relu'):\n",
        "    reg = MLPRegressor(alpha = 0,\n",
        "                       learning_rate_init = 1e-4 * 5,\n",
        "                       hidden_layer_sizes = (n_nodes),\n",
        "                       random_state = 2020,\n",
        "                       activation = active,\n",
        "                       max_iter = int(1e5),\n",
        "                       solver = 'sgd',\n",
        "                       momentum = 0)\n",
        "    reg.fit(X, y)\n",
        "    return reg\n",
        "    # reg is our trained model\n",
        "    \n",
        "def plot_loss_curve(reg):\n",
        "    fig = plt.figure(figsize=(9, 9))\n",
        "    p = fig.add_subplot('111')\n",
        "    p.set_title('Error v/s Epoch')\n",
        "    p.set_xlabel('Epoch Number')\n",
        "    p.set_ylabel('Error')\n",
        "    errors = reg.loss_curve_\n",
        "    p.plot(list(range(1, len(errors))), errors[1:])\n",
        "    plt.show()\n",
        "\n",
        "def get_train_test_loss(reg):\n",
        "    pred_y_train = reg.predict(X_train)\n",
        "    pred_y_test = reg.predict(X_test)\n",
        "    \n",
        "    train_Loss = np.power(np.linalg.norm(y_train - pred_y_train), 2) / np.shape(y_train)[0]\n",
        "    test_Loss = np.power(np.linalg.norm(y_test - pred_y_test), 2) / np.shape(y_test)[0]\n",
        "\n",
        "    return (train_Loss, test_Loss)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hmZ_QchJg-vD",
        "colab_type": "code",
        "outputId": "4b0f5fd9-028b-49f2-c7c9-bda1546330fb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "source": [
        "# obtaining results using scikit learn\n",
        "\n",
        "for active in activations:\n",
        "    model = train(X_train, y_train, 64, active)\n",
        "    print(\"Hidden Layer Activation = \" + str(active))\n",
        "    loss_train, loss_test = get_train_test_loss(model)\n",
        "    print(\"Error on Train Set: \" + str(loss_train))\n",
        "    print(\"Error on Test Set: \" + str(loss_test))\n",
        "    plot_loss_curve(model)"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Hidden Layer Activation = relu\n",
            "Error on Train Set: 31.31644006134109\n",
            "Error on Test Set: 43.96036471068162\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 648x648 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Hidden Layer Activation = tanh\n",
            "Error on Train Set: 13.418856105181682\n",
            "Error on Test Set: 25.01920654591389\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 648x648 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WtwaQiThhz4h",
        "colab_type": "text"
      },
      "source": [
        "## $ If\\ you're\\ interested\\ in\\ optimization\\ and\\ learning, $\n",
        "### $ try\\ including\\ bias\\ terms\\ in\\ the\\ vanilla\\ model\\ and\\ evaluate\\ the\\ new\\ performance.$\n",
        "\n",
        "#### $ This\\ should\\ give\\ you\\ a\\ head\\ start: $\n",
        "\n",
        "$ if\\ we\\ define\\ our\\ model\\ as: $\n",
        "\n",
        "$ y' = W_2.f(W_1^TX + b_1) + b_2$\n",
        "\n",
        "$where:$\n",
        "\n",
        "- $\\ W_1\\ is\\ of\\ size\\ 8\\ \\times\\ n\\_nodes$\n",
        "\n",
        "- $\\ W_2\\ is\\ of\\ size\\ 1\\ \\times\\ n\\_nodes$\n",
        "\n",
        "- $\\ b_1 \\in\\ \\mathbb{R}^{n\\_nodes}$\n",
        "\n",
        "- $\\ b_2\\ \\in\\ \\mathbb{R}$\n",
        "\n",
        "- $\\ f\\ is\\ the\\ activation\\ for\\ the\\ hidden\\ layer$\n",
        "\n",
        "- $\\ X\\ is\\ the\\ data\\ matrix\\ of\\ size\\ 8\\times [batch\\ size]$\n",
        "\n",
        "$ What\\ else\\ do\\ we\\ need\\ to\\ consider? $\n",
        "\n",
        "#### $ HINT:\\ Think\\ about\\ \\frac{\\partial L}{\\partial b_1}\\ and\\ \\frac{\\partial L}{\\partial b_2}$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sW3ne9K0hNjH",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# ^_^ Thank You"
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}