NEURAL_NETWORKS.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "NEURAL NETWORKS",
      "provenance": [],
      "authorship_tag": "ABX9TyOQRfqW4p21kirxxE40wZNx",
      "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/NsiriRoua/Artificial_Neural_Network/blob/main/NEURAL_NETWORKS.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hypJxq0xOfZb"
      },
      "source": [
        "# **Basic Feed-forward Network**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FMrc-adeOoCW"
      },
      "source": [
        "![image.png](data:image/png;base64,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)\r\n",
        "\r\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SswuI-sGOqy2"
      },
      "source": [
        "# **Let's import resources**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Zqk9ZJva3lW6"
      },
      "source": [
        "import numpy as np\r\n",
        "im\r\n",
        "port sklearn\r\n",
        "import seaborn as sns \r\n",
        "import matplotlib.pyplot as plt\r\n",
        "\r\n"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rx9AVBQdPCdT"
      },
      "source": [
        "# **Activation functions**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7gqETMt4PK-n"
      },
      "source": [
        "Below we implement the ReLU function, sigmoid function, and the linear function (which simply returns its input). Let’s also combine these functions into a dictionary so we can identify them with a string argument."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xgZFT2AtPGak"
      },
      "source": [
        "#Activations functions\r\n",
        "def ReLU(h):\r\n",
        "  return np.maximum(h,0)\r\n",
        "\r\n",
        "\r\n",
        "\r\n",
        "def sigmoid(h):\r\n",
        "  return 1/(1+np.exp(-h))\r\n",
        "\r\n",
        "def linear(h):\r\n",
        "  return h\r\n",
        "\r\n",
        "\r\n",
        "#Let's define a dictionary of activations functions\r\n",
        "activation_dictionary={'ReLU':ReLU,'sigmoid':sigmoid,'linear':linear}"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "q5nkrvjojS1_"
      },
      "source": [
        "# **Loss Functions**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ABKucoXajWLu"
      },
      "source": [
        "**Residual sum of Squares (RSS) = Squared loss**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nyFurFVWj3MV"
      },
      "source": [
        "![image.png](data:image/png;base64,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)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_kMFPHHBkQtK"
      },
      "source": [
        "def RSS(y,yhat):\r\n",
        "  return np.sum(pow(y-yhat,2))\r\n"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gDaMUlOBlGDt"
      },
      "source": [
        "**Binary Cross-Entropy / Log Loss**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p16PLyVzkqa8"
      },
      "source": [
        "**![image.png](data:image/png;base64,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)**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nM6jq8cRlRQQ"
      },
      "source": [
        "def log_loss(y,yhat):\r\n",
        "  return np.sum(-(y*np.log(yhat)+(1-y)*np.log(1-yhat)))"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UcoWQMqjWNuj"
      },
      "source": [
        "# **Construction**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hIgmWF3CWl2D"
      },
      "source": [
        "We are going to build one hidden layer , input layer and output layer"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_GI98-d6Wv8e"
      },
      "source": [
        " We are going to build a class for fittiing feed-forward networks"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "L13T7ASLZMIl"
      },
      "source": [
        " we fit a network with the fit() method. This method requires training data, the number of nodes for the hidden layer, an activation function for the first and second layers’ outputs, a loss function, and some parameters for gradient descent. After storing those values, the method randomly instantiates the network’s weights: W1, c1, W2, and c2. It then passes the data through this network to instantiate the output values: h1, z1, h2, and yhat (equivalent to z2)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_pe2gZ95ZWZy"
      },
      "source": [
        "![image.png](data:image/png;base64,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)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Q2Rfkp5UWNRr"
      },
      "source": [
        "class FeedForwardNeuralNetwork:\r\n",
        "    \r\n",
        "    def fit(self, X, y, n_hidden, f1 = 'ReLU', f2 = 'linear', loss = 'RSS', lr = 1e-5, n_iter = 1e3, seed = None):\r\n",
        "        \r\n",
        "        ## Store Information\r\n",
        "        self.X = X\r\n",
        "        self.y = y.reshape(len(y), -1)\r\n",
        "        self.N = len(X)\r\n",
        "        self.D_X = self.X.shape[1]\r\n",
        "        self.D_y = self.y.shape[1]\r\n",
        "        self.D_h = n_hidden\r\n",
        "        self.f1, self.f2 = f1, f2\r\n",
        "        self.loss = loss\r\n",
        "        self.lr = lr\r\n",
        "        self.n_iter = int(n_iter)\r\n",
        "        self.seed = seed\r\n",
        "        \r\n",
        "        ## Instantiate Weights\r\n",
        "        np.random.seed(self.seed)\r\n",
        "        self.W1 = np.random.randn(self.D_h, self.D_X)/5\r\n",
        "        self.c1 = np.random.randn(self.D_h, 1)/5\r\n",
        "        self.W2 = np.random.randn(self.D_y, self.D_h)/5\r\n",
        "        self.c2 = np.random.randn(self.D_y, 1)/5\r\n",
        "        \r\n",
        "        ## Instantiate Outputs\r\n",
        "        self.h1 = np.dot(self.W1, self.X.T) + self.c1\r\n",
        "        self.z1 = activation_dictionary[f1](self.h1)\r\n",
        "        self.h2 = np.dot(self.W2, self.z1) + self.c2\r\n",
        "        self.yhat = activation_dictionary[f2](self.h2)\r\n",
        "        \r\n",
        "        ## Fit Weights\r\n",
        "        for iteration in range(self.n_iter):\r\n",
        "            \r\n",
        "            dL_dW2 = 0\r\n",
        "            dL_dc2 = 0\r\n",
        "            dL_dW1 = 0\r\n",
        "            dL_dc1 = 0\r\n",
        "            \r\n",
        "            for n in range(self.N):\r\n",
        "                \r\n",
        "                # dL_dyhat\r\n",
        "                if loss == 'RSS':\r\n",
        "                    dL_dyhat = -2*(self.y[n] - self.yhat[:,n]).T # (1, D_y)\r\n",
        "                elif loss == 'log':\r\n",
        "                    dL_dyhat = (-(self.y[n]/self.yhat[:,n]) + (1-self.y[n])/(1-self.yhat[:,n])).T # (1, D_y)\r\n",
        "                \r\n",
        "        \r\n",
        "                ## LAYER 2 ## \r\n",
        "                # dyhat_dh2 \r\n",
        "                if f2 == 'linear':\r\n",
        "                    dyhat_dh2 = np.eye(self.D_y) # (D_y, D_y)\r\n",
        "                elif f2 == 'sigmoid':\r\n",
        "                    dyhat_dh2 = np.diag(sigmoid(self.h2[:,n])*(1-sigmoid(self.h2[:,n]))) # (D_y, D_y)\r\n",
        "                    \r\n",
        "                # dh2_dc2\r\n",
        "                dh2_dc2 = np.eye(self.D_y) # (D_y, D_y)\r\n",
        "                \r\n",
        "                # dh2_dW2 \r\n",
        "                dh2_dW2 = np.zeros((self.D_y, self.D_y, self.D_h)) # (D_y, (D_y, D_h)) \r\n",
        "                for i in range(self.D_y):\r\n",
        "                    dh2_dW2[i] = self.z1[:,n] \r\n",
        "                \r\n",
        "                # dh2_dz1\r\n",
        "                dh2_dz1 = self.W2 # (D_y, D_h)\r\n",
        "                \r\n",
        "                \r\n",
        "                ## LAYER 1 ##\r\n",
        "                # dz1_dh1\r\n",
        "                if f1 == 'ReLU':\r\n",
        "                    dz1_dh1 = 1*np.diag(self.h1[:,n] > 0) # (D_h, D_h)                \r\n",
        "                elif f1 == 'linear':\r\n",
        "                    dz1_dh1 = np.eye(self.D_h) # (D_h, D_h)\r\n",
        "\r\n",
        "                \r\n",
        "                # dh1_dc1 \r\n",
        "                dh1_dc1 = np.eye(self.D_h) # (D_h, D_h)\r\n",
        "                \r\n",
        "                # dh1_dW1\r\n",
        "                dh1_dW1 = np.zeros((self.D_h, self.D_h, self.D_X)) # (D_h, (D_h, D_X))\r\n",
        "                for i in range(self.D_h):\r\n",
        "                    dh1_dW1[i] = self.X[n]\r\n",
        "                \r\n",
        "                \r\n",
        "                ## DERIVATIVES W.R.T. LOSS ## \r\n",
        "                dL_dh2 = dL_dyhat @ dyhat_dh2\r\n",
        "                dL_dW2 += dL_dh2 @ dh2_dW2\r\n",
        "                dL_dc2 += dL_dh2 @ dh2_dc2\r\n",
        "                dL_dh1 = dL_dh2 @ dh2_dz1 @ dz1_dh1\r\n",
        "                dL_dW1 += dL_dh1 @ dh1_dW1\r\n",
        "                dL_dc1 += dL_dh1 @ dh1_dc1\r\n",
        "            \r\n",
        "            ## Update Weights\r\n",
        "            self.W1 -= self.lr * dL_dW1\r\n",
        "            self.c1 -= self.lr * dL_dc1.reshape(-1, 1)           \r\n",
        "            self.W2 -= self.lr * dL_dW2            \r\n",
        "            self.c2 -= self.lr * dL_dc2.reshape(-1, 1)                    \r\n",
        "            \r\n",
        "            ## Update Outputs\r\n",
        "            self.h1 = np.dot(self.W1, self.X.T) + self.c1\r\n",
        "            self.z1 = activation_dictionary[f1](self.h1)\r\n",
        "            self.h2 = np.dot(self.W2, self.z1) + self.c2\r\n",
        "            self.yhat = activation_dictionary[f2](self.h2)\r\n",
        "       \r\n",
        "\r\n",
        "    def predict(self, X_test):\r\n",
        "      self.h1 = np.dot(self.W1, X_test.T) + self.c1\r\n",
        "      self.z1 = activation_dictionary[self.f1](self.h1)\r\n",
        "      self.h2 = np.dot(self.W2, self.z1) + self.c2\r\n",
        "      self.yhat = activation_dictionary[self.f2](self.h2)        \r\n",
        "      return self.yhat\r\n",
        " \r\n",
        "        \r\n",
        "     \r\n",
        "\r\n",
        "\r\n"
      ],
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MeiFWDOC8p99"
      },
      "source": [
        "# **Housing Buston Dataset**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MtAiE7Pb4XnM"
      },
      "source": [
        "Let's try to build a network with this class using the boston housing data\r\n",
        "this network will contain 8 neurons(units) in its hidden layer "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "j3tDWlX_4qc2"
      },
      "source": [
        "from sklearn.datasets import load_boston\r\n",
        "X_boston=load_boston().data\r\n",
        "Y_boston=load_boston().target"
      ],
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "arV0m9Ql5BPU"
      },
      "source": [
        "**Let's split our data to avoid data leakage**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 351
        },
        "id": "ilrfSH1V5G6P",
        "outputId": "c3335b60-2450-4bd0-869a-7dd1b71769b5"
      },
      "source": [
        "from sklearn.model_selection import train_test_split\r\n",
        "x_boston_train,x_boston_test,y_boston_train,y_boston_test=train_test_split(X,Y,test_size=0.2,random_state=0)\r\n",
        "\r\n",
        "#Instance our network\r\n",
        "FFNN=FeedForwardNeuralNetwork()\r\n",
        "#Fit it\r\n",
        "FFNN.fit(x_boston_train,y_boston_train,n_hidden=8)\r\n",
        "#Predict\r\n",
        "yhat=FFNN.predict(x_boston_test)\r\n",
        "\r\n",
        "fig,ax=plt.subplots()\r\n",
        "sns.scatterplot(y_test,yhat[0])\r\n",
        "ax.set(xlabel='y',ylabel='yhat',title='y vs yhat')\r\n",
        "sns.despine()\r\n",
        "\r\n"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/seaborn/_decorators.py:43: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.\n",
            "  FutureWarning\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dkyCUfvS9k_b"
      },
      "source": [
        "**The mean squarred error**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "CRB0RuQ29okh",
        "outputId": "b94a5b32-f6e5-47a2-b00e-7ff2439ea362"
      },
      "source": [
        "from sklearn.metrics import mean_squared_error\r\n",
        "print('the mean squared error:{}'.format(mean_squared_error(y_boston_test,yhat[0])))"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "the mean squared error:81.57699504323507\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YwANBp-i8xzo"
      },
      "source": [
        "# **Breast Cancer Dataset**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kWd4tBm186cU",
        "outputId": "10482d8a-4dfa-415f-fde2-f8dfad4229c0"
      },
      "source": [
        "from sklearn.datasets import load_breast_cancer\r\n",
        "X_breast_cancer=load_breast_cancer().data\r\n",
        "Y_breast_cancer=load_breast_cancer().target\r\n",
        "x_cancer_train,x_cancer_test,y_cancer_train,y_cancer_test=train_test_split(X,Y,test_size=0.2,random_state=0)\r\n",
        "\r\n",
        "#Instanciate our network \r\n",
        "FFNN=FeedForwardNeuralNetwork()\r\n",
        "\r\n",
        "#Fit it \r\n",
        "FFNN.fit(x_cancer_train,y_cancer_train,n_hidden=8,loss='log',f2='sigmoid',seed=123,lr=1e-4)\r\n",
        "\r\n",
        "#Let's predict \r\n",
        "yhat=FFNN.predict(x_cancer_test)\r\n",
        "\r\n",
        "\r\n"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:45: RuntimeWarning: invalid value encountered in true_divide\n",
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:45: RuntimeWarning: divide by zero encountered in true_divide\n",
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:85: RuntimeWarning: invalid value encountered in matmul\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xln8EumERUf3"
      },
      "source": [
        "# **Let's make the calculation more faster using tensors**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Indryp32Rc8P"
      },
      "source": [
        "class FeedForwardNeuralNetwork:\r\n",
        "    \r\n",
        "    \r\n",
        "    def fit(self, X, Y, n_hidden, f1 = 'ReLU', f2 = 'linear', loss = 'RSS', lr = 1e-5, n_iter = 5e3, seed = None):\r\n",
        "        \r\n",
        "        ## Store Information\r\n",
        "        self.X = X\r\n",
        "        self.Y = Y.reshape(len(Y), -1)\r\n",
        "        self.N = len(X)\r\n",
        "        self.D_X = self.X.shape[1]\r\n",
        "        self.D_Y = self.Y.shape[1]\r\n",
        "        self.Xt = self.X.T\r\n",
        "        self.Yt = self.Y.T\r\n",
        "        self.D_h = n_hidden\r\n",
        "        self.f1, self.f2 = f1, f2\r\n",
        "        self.loss = loss\r\n",
        "        self.lr = lr\r\n",
        "        self.n_iter = int(n_iter)\r\n",
        "        self.seed = seed\r\n",
        "        \r\n",
        "        ## Instantiate Weights\r\n",
        "        np.random.seed(self.seed)\r\n",
        "        self.W1 = np.random.randn(self.D_h, self.D_X)/5\r\n",
        "        self.c1 = np.random.randn(self.D_h, 1)/5\r\n",
        "        self.W2 = np.random.randn(self.D_Y, self.D_h)/5\r\n",
        "        self.c2 = np.random.randn(self.D_Y, 1)/5\r\n",
        "        \r\n",
        "        ## Instantiate Outputs\r\n",
        "        self.H1 = (self.W1 @ self.Xt) + self.c1\r\n",
        "        self.Z1 = activation_function_dict[self.f1](self.H1)\r\n",
        "        self.H2 = (self.W2 @ self.Z1) + self.c2\r\n",
        "        self.Yhatt = activation_function_dict[self.f2](self.H2)\r\n",
        "        \r\n",
        "        ## Fit Weights\r\n",
        "        for iteration in range(self.n_iter):\r\n",
        "            \r\n",
        "            # Yhat #\r\n",
        "            if self.loss == 'RSS':\r\n",
        "                self.dL_dYhatt = -(self.Yt - self.Yhatt) # (D_Y x N)\r\n",
        "            elif self.loss == 'log':\r\n",
        "                self.dL_dYhatt = (-(self.Yt/self.Yhatt) + (1-self.Yt)/(1-self.Yhatt)) # (D_y x N)\r\n",
        "            \r\n",
        "            # H2 #\r\n",
        "            if self.f2 == 'linear':\r\n",
        "                self.dYhatt_dH2 = np.ones((self.D_Y, self.N))\r\n",
        "            elif self.f2 == 'sigmoid':\r\n",
        "                self.dYhatt_dH2 = sigmoid(self.H2) * (1- sigmoid(self.H2))\r\n",
        "            self.dL_dH2 = self.dL_dYhatt * self.dYhatt_dH2 # (D_Y x N)\r\n",
        "\r\n",
        "            # c2 # \r\n",
        "            self.dL_dc2 = np.sum(self.dL_dH2, 1) # (D_y)\r\n",
        "            \r\n",
        "            # W2 # \r\n",
        "            self.dL_dW2 = np.tensordot(self.dL_dH2, self.Z1, (1,1)) # (D_Y x D_h)\r\n",
        "            \r\n",
        "            # Z1 #\r\n",
        "            self.dL_dZ1 = np.tensordot(self.W2, self.dL_dH2, (0, 0)) # (D_h x N)\r\n",
        "            \r\n",
        "            # H1 #\r\n",
        "            if self.f1 == 'ReLU':\r\n",
        "                self.dL_dH1 = self.dL_dZ1 * np.maximum(self.H1, 0) # (D_h x N)\r\n",
        "            elif self.f1 == 'linear':\r\n",
        "                self.dL_dH1 = self.dL_dZ1 # (D_h x N)\r\n",
        "            \r\n",
        "            # c1 #\r\n",
        "            self.dL_dc1 = np.sum(self.dL_dH1, 1) # (D_h)\r\n",
        "            \r\n",
        "            # W1 # \r\n",
        "            self.dL_dW1 = np.tensordot(self.dL_dH1, self.Xt, (1,1)) # (D_h, D_X)\r\n",
        "            \r\n",
        "            ## Update Weights\r\n",
        "            self.W1 -= self.lr * self.dL_dW1\r\n",
        "            self.c1 -= self.lr * self.dL_dc1.reshape(-1, 1)           \r\n",
        "            self.W2 -= self.lr * self.dL_dW2            \r\n",
        "            self.c2 -= self.lr * self.dL_dc2.reshape(-1, 1)                    \r\n",
        "            \r\n",
        "            ## Update Outputs\r\n",
        "            self.H1 = (self.W1 @ self.Xt) + self.c1\r\n",
        "            self.Z1 = activation_function_dict[self.f1](self.H1)\r\n",
        "            self.H2 = (self.W2 @ self.Z1) + self.c2\r\n",
        "            self.Yhatt = activation_function_dict[self.f2](self.H2)  \r\n",
        "            \r\n",
        "    def predict(self, X_test):\r\n",
        "        X_testt = X_test.T\r\n",
        "        self.h1 = (self.W1 @ X_testt) + self.c1\r\n",
        "        self.z1 = activation_function_dict[self.f1](self.h1)\r\n",
        "        self.h2 = (self.W2 @ self.z1) + self.c2\r\n",
        "        self.Yhatt = activation_function_dict[self.f2](self.h2)        \r\n",
        "        return self.Yhatt"
      ],
      "execution_count": 63,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "t2mSaPvpW_O8"
      },
      "source": [
        "# **Implementation**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8tcZG4RcXEBR"
      },
      "source": [
        "import tensorflow as tf\r\n",
        "from sklearn import datasets\r\n",
        "import matplotlib.pyplot as plt\r\n",
        "import seaborn as sns\r\n"
      ],
      "execution_count": 16,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tuuawvV8beyR",
        "outputId": "a57b4106-febd-4d76-833d-c370d9c01692"
      },
      "source": [
        "#Instanciate the model\r\n",
        "model=tf.keras.models.Sequential()\r\n",
        "\r\n",
        "#Let's add Layers \r\n",
        "model.add(tf.keras.layers.Dense(units=8,activation='relu',input_shape=(X_boston.shape[1],),name='hidden'))\r\n",
        "model.add(tf.keras.layers.Dense(units=1,activation='linear',name='output'))\r\n",
        "\r\n",
        "#Let's compile out model\r\n",
        "model.compile(optimizer='adam',loss='mse')\r\n",
        "#Let's summarize our model\r\n",
        "model.summary()"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Model: \"sequential_1\"\n",
            "_________________________________________________________________\n",
            "Layer (type)                 Output Shape              Param #   \n",
            "=================================================================\n",
            "hidden (Dense)               (None, 8)                 112       \n",
            "_________________________________________________________________\n",
            "output (Dense)               (None, 1)                 9         \n",
            "=================================================================\n",
            "Total params: 121\n",
            "Trainable params: 121\n",
            "Non-trainable params: 0\n",
            "_________________________________________________________________\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "IDq7jYNX84-l",
        "outputId": "686b46d5-3657-416f-8df3-ea2d19689c5c"
      },
      "source": [
        "#Let's fit our model , and we should define the epochs and the Batch size,validation size\r\n",
        "model.fit(X_boston,Y_boston,epochs=100,batch_size=1,validation_split=0.2,verbose=0)\r\n"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tensorflow.python.keras.callbacks.History at 0x7fe5fcf02250>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 21
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 321
        },
        "id": "6v74sUME9eDl",
        "outputId": "e4e7b34a-cb1b-4244-ff03-87bdf7e33a1a"
      },
      "source": [
        "#Let's predict\r\n",
        "yhat_boston=model.predict(X_boston)[:,0]\r\n",
        "fig, ax = plt.subplots()\r\n",
        "sns.scatterplot(Y_boston, yhat_boston)\r\n",
        "sns.despine()\r\n"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/seaborn/_decorators.py:43: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.\n",
            "  FutureWarning\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wtoMGiKP9we3",
        "outputId": "273ce4c4-bf55-4621-c2c6-4d55fc522c4c"
      },
      "source": [
        "from sklearn.metrics import mean_squared_error\r\n",
        "print('the mean squared error:{}'.format(mean_squared_error(Y_boston,yhat_boston)))"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "the mean squared error:42.57954713676986\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}