ML4DM_Lab_1.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "ML4DM_Lab_1.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "TPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/nishi1612/Machine-Learning-For-Data-Mining/blob/master/ML4DM_Lab_1.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "I2DI6ohig2KK",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import pandas as pd\n",
        "import math"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "q7yudYUfAx7z",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def graph():\n",
        "  plt.xlabel('$x$')\n",
        "  plt.ylabel('$y$')\n",
        "  plt.show()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6CWeUlPNgyYK",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "N = 50\n",
        "M = 2"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VS6CM-YIg5-a",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def generate_input(N,M):\n",
        "  mu = np.random.random((M,1))\n",
        "  sigma = np.random.random((M,1))\n",
        "  X = np.ones((N,M+1))\n",
        "  for i in range(M):\n",
        "     X[:,i] = np.random.normal(mu[i],sigma[i],N)\n",
        "  return X"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Q-OLZflMOAsN",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def predict_output(X,weight):\n",
        "  return np.matmul(X,weight)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "a2wBXtI8kyeO",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def generate_output(X,M):\n",
        "  weight = np.random.random((M+1,1))\n",
        "  Y = predict_output(X,weight)\n",
        "  return weight, Y"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YM1BiR04nXjI",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def add_noise(Y,N):\n",
        "  noise = np.random.random((N,1))\n",
        "  Y_noise = Y+noise\n",
        "  return Y_noise"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "znVSseT4nrDa",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def closed_form(X,Y_noise):\n",
        "  a = np.linalg.inv(np.matmul(X.transpose(),X))\n",
        "  b = np.matmul(a,X.transpose())\n",
        "  weight_predicted = np.matmul(b,Y_noise)\n",
        "  return weight_predicted"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wOLhsly9u3RI",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def calculate_mse(y_predicted,y,N):\n",
        "  mse = np.sum((y_predicted - y)**2)\n",
        "  return mse/N"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9tdUc-u9jBqv",
        "colab_type": "text"
      },
      "source": [
        "**Closed form solution**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4BANM5cKroK-",
        "colab_type": "code",
        "outputId": "2df0f673-29a8-46b7-b817-f490e24ff16a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "X = generate_input(N,M)\n",
        "weight, Y = generate_output(X,M)\n",
        "Y_noise = add_noise(Y,N)\n",
        "weight_predicted = closed_form(X,Y_noise)\n",
        "y_predicted = predict_output(X,weight_predicted)\n",
        "mse = calculate_mse(y_predicted,Y_noise,N)\n",
        "mse"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.06779247294855101"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cS78HzjXp-cY",
        "colab_type": "code",
        "outputId": "6b805b23-737e-4f99-d6d0-ffcba3dad664",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "X.shape, weight.shape"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "((50, 3), (3, 1))"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 28
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kHcsjNzPy9ny",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def gradient_descent(X,Y):\n",
        "  epochs = 1000000\n",
        "  alphas = [0.0000001]\n",
        "  for alpha in alphas:\n",
        "    theta = np.ones((X.shape[1],1))\n",
        "    h = predict_output(X,theta)\n",
        "    cost = np.zeros((epochs,1))\n",
        "    for i in range(epochs):\n",
        "        theta[0] = theta[0] - alpha*np.sum(h-Y)/X.shape[0]\n",
        "        for j in range(1,X.shape[1]):\n",
        "          theta[j] = theta[j] - alpha/X.shape[0] * np.sum((h-Y)*X[:,j])\n",
        "          h = predict_output(X,theta)\n",
        "        cost[i] = calculate_mse(Y,h,X.shape[0])\n",
        "        if(i>0 and cost[i]>cost[i-1]):\n",
        "          epochs = i\n",
        "          break\n",
        "        if(i%50000==0):\n",
        "          print(\"Epoch : \" , i , \" Cost : \" , cost[i])\n",
        "    plt.plot(np.arange(epochs),cost[:epochs])\n",
        "    plt.xlabel('Epochs')\n",
        "    plt.ylabel('Cost')\n",
        "    plt.title('Cost v/s Epoch for gradient descent')\n",
        "    plt.show()\n",
        "    if(alpha==0.0000001):\n",
        "      return theta"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jVqbwxnIjIL4",
        "colab_type": "text"
      },
      "source": [
        "**Gradient Descent Method for multi variable linear regression**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jGDa8pi8IK_X",
        "colab_type": "code",
        "outputId": "e405b2ad-586c-484f-8bc8-14ea05c53401",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 652
        }
      },
      "source": [
        "weight_predicted = gradient_descent(X,Y_noise)\n",
        "y_predicted = predict_output(X,weight_predicted)\n",
        "mse = calculate_mse(y_predicted,Y_noise,N)\n",
        "mse"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Epoch :  0  Cost :  [1.12145015]\n",
            "Epoch :  50000  Cost :  [0.61337244]\n",
            "Epoch :  100000  Cost :  [0.36072773]\n",
            "Epoch :  150000  Cost :  [0.2344388]\n",
            "Epoch :  200000  Cost :  [0.17085471]\n",
            "Epoch :  250000  Cost :  [0.13852735]\n",
            "Epoch :  300000  Cost :  [0.12187705]\n",
            "Epoch :  350000  Cost :  [0.11315618]\n",
            "Epoch :  400000  Cost :  [0.10849162]\n",
            "Epoch :  450000  Cost :  [0.10593307]\n",
            "Epoch :  500000  Cost :  [0.10448878]\n",
            "Epoch :  550000  Cost :  [0.10364785]\n",
            "Epoch :  600000  Cost :  [0.10314259]\n",
            "Epoch :  650000  Cost :  [0.1028298]\n",
            "Epoch :  700000  Cost :  [0.10263086]\n",
            "Epoch :  750000  Cost :  [0.10250142]\n",
            "Epoch :  800000  Cost :  [0.10241559]\n",
            "Epoch :  850000  Cost :  [0.10235785]\n",
            "Epoch :  900000  Cost :  [0.10231858]\n",
            "Epoch :  950000  Cost :  [0.10229163]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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zKwSuABbEBzCzU4FbiMJBl+UcoeMnj+X+j57PB86bzo+eeIWL//0RHtbehIgc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\n/x+f6pjewdkZKwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.10227304034479473"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 30
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MndHx1anc-EE",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def sigmoid(z):\n",
        "  return 1/(1+np.exp(-z))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ddDDpm-QdFnm",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def logistic_cost(y_actual,y_predicted):\n",
        "  return np.sum(((-y_actual*np.log(y_predicted)) - ((1-y_actual)*np.log(1-y_predicted))))/y_predicted.shape[0]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KimtELtPd5ZS",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def logistic_output(X,theta):\n",
        "  t = sigmoid(np.dot(X,theta))\n",
        "  for i in range(t.shape[0]):\n",
        "    if(t[i]<0.5):\n",
        "      t[i]=0\n",
        "    else:\n",
        "      t[i]=1\n",
        "  return t"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-DoQJFdyP3GL",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def logistic_gradient_descent(X,Y):\n",
        "  epochs = 1000000\n",
        "  alphas = [0.000001]\n",
        "  for alpha in alphas:\n",
        "    theta = np.ones((X.shape[1],1))\n",
        "    h = sigmoid(np.dot(X,theta))\n",
        "    cost = np.zeros((epochs,1))\n",
        "    for i in range(epochs):\n",
        "      theta[0] = theta[0] - alpha*np.sum(h-Y)/X.shape[0]\n",
        "      for j in range(1,X.shape[1]):\n",
        "        theta[j] = theta[j] - alpha/X.shape[0] * np.sum((h-Y)*X[:,j])\n",
        "        h = sigmoid(np.dot(X,theta))\n",
        "      cost[i] = logistic_cost(Y,h)\n",
        "      if(i>0 and cost[i]>cost[i-1]):\n",
        "        epochs = i\n",
        "        break\n",
        "      if(i%50000==0):\n",
        "        print(\"Epoch : \" , i , \" Cost : \" , cost[i])\n",
        "    plt.plot(np.arange(epochs),cost)\n",
        "    plt.xlabel('Epochs')\n",
        "    plt.ylabel('Cost')\n",
        "    plt.title('Cost v/s Epoch for gradient descent')\n",
        "    plt.show()\n",
        "    if(alpha==0.000001):\n",
        "      return theta"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "X_MZN2m0Pa6M",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def prediction_table(y_actual,y_predicted):\n",
        "  table = pd.DataFrame(columns=['Positive','Negative'])\n",
        "  tp = 0\n",
        "  tn = 0\n",
        "  fp = 0\n",
        "  fn = 0\n",
        "  for i in range(y_predicted.shape[0]):\n",
        "    if(y_actual[i]==1):\n",
        "      if(y_predicted[i]==1):\n",
        "        tp+=1\n",
        "      else:\n",
        "        fn+=1\n",
        "    elif(y_actual[i]==0):\n",
        "      if(y_predicted[i]==1):\n",
        "        fp+=1\n",
        "      else:\n",
        "        tn+=1\n",
        "  table.loc['Positive'] = [tp,fp]\n",
        "  table.loc['Negative'] = [fn,tn]\n",
        "  return table"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZMFC-KTIk8Pt",
        "colab_type": "text"
      },
      "source": [
        "**Gradient Descent Solution for multi variable logistic regression**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rpL0BxgEHst_",
        "colab_type": "code",
        "outputId": "612f6bb8-5a54-45f3-abc2-9b5e3f10c300",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        }
      },
      "source": [
        "x = np.random.uniform(-5,5,(100,1))\n",
        "y = np.random.uniform(0,1,(100,1))\n",
        "plt.scatter(x,y)\n",
        "plt.title('Scatter Graph for randomly generated data')\n",
        "graph()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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VB4cBpZKDbNaO98/6GWZyXhncrTSgSc5esPR5/6yXlC+d42wlM7OKFH2RvXaSylaStEzS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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lwxi3K3pKEwm",
        "colab_type": "code",
        "outputId": "72327451-3da9-4b73-b5a1-f5f87676ba22",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        }
      },
      "source": [
        "labels = np.zeros((x.shape[0],1))\n",
        "vals = np.zeros((x.shape[0],1))\n",
        "for i in range(x.shape[0]):\n",
        "  if(y[i]<1/(1 + math.exp(-x[i]))):\n",
        "    labels[i]=0\n",
        "  else:\n",
        "    labels[i]=1\n",
        "for i in range(x.shape[0]):\n",
        "  if(labels[i]==1):\n",
        "    plt.scatter(x[i],y[i],color='red')\n",
        "  else:\n",
        "    plt.scatter(x[i],y[i],color='blue')\n",
        "plt.plot(np.sort(x,axis=0),1/(1+np.exp(-np.sort(x,axis=0))),color='green',label='Logistic function')\n",
        "plt.legend(loc=\"upper right\")\n",
        "plt.title('Data classified into two classes with the logistic regression')\n",
        "graph()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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6AqDDOFUQhYOTBbjTS7E59e4i/tOJSNQe+dHyj0zyg8nmnEnnmJLSkqg9R/Ee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\nL/LcHwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DGuDV6CYKvCF",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "X = np.zeros((x.shape[0],2))\n",
        "X[:,1] = x[:,0]\n",
        "X[:,0] = np.ones(x.shape[0])\n",
        "Y = labels"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "e5XHNWJ7MDMw",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def logistic_gradient_descent(X,Y):\n",
        "  epochs = 1000000\n",
        "  alphas = [0.00001]\n",
        "  for alpha in alphas:\n",
        "    theta = np.zeros((X.shape[1],1))\n",
        "    h = sigmoid(np.dot(X,theta))\n",
        "    cost = np.zeros((epochs,1))\n",
        "    for i in range(epochs):\n",
        "      theta[0] = theta[0] - alpha*np.sum(h-Y)/X.shape[0]\n",
        "      for j in range(1,X.shape[1]):\n",
        "        theta[j] = theta[j] - alpha/X.shape[0] * np.sum((h-Y)*X[:,j])\n",
        "        h = sigmoid(np.dot(X,theta))\n",
        "      cost[i] = logistic_cost(Y,h)\n",
        "      if(i>0 and cost[i]>cost[i-1]):\n",
        "        epochs = i\n",
        "        break\n",
        "      if(i%50000==0):\n",
        "        print(\"Epoch : \" , i , \" Cost : \" , cost[i])\n",
        "    plt.plot(np.arange(epochs),cost[:epochs])\n",
        "    plt.xlabel('Epochs')\n",
        "    plt.ylabel('Cost')\n",
        "    plt.title('Cost v/s Epoch for gradient descent')\n",
        "    plt.show()\n",
        "    if(alpha==0.00001):\n",
        "      return theta"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uwAggEzvLS1U",
        "colab_type": "code",
        "outputId": "dea01cbb-01cd-4b3a-9e3f-7fe34a847112",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 618
        }
      },
      "source": [
        "weight_predicted = logistic_gradient_descent(X,Y)\n",
        "y_hat = sigmoid(np.dot(X,weight_predicted))\n",
        "cost = logistic_cost(Y,y_hat)\n",
        "y_predicted = logistic_output(X,weight_predicted)\n",
        "cost"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Epoch :  0  Cost :  [0.6931429]\n",
            "Epoch :  50000  Cost :  [0.53650005]\n",
            "Epoch :  100000  Cost :  [0.45490069]\n",
            "Epoch :  150000  Cost :  [0.41058937]\n",
            "Epoch :  200000  Cost :  [0.38520788]\n",
            "Epoch :  250000  Cost :  [0.36996488]\n",
            "Epoch :  300000  Cost :  [0.36046102]\n",
            "Epoch :  350000  Cost :  [0.3543665]\n",
            "Epoch :  400000  Cost :  [0.3503793]\n",
            "Epoch :  450000  Cost :  [0.34773689]\n",
            "Epoch :  500000  Cost :  [0.34597464]\n",
            "Epoch :  550000  Cost :  [0.34479992]\n",
            "Epoch :  600000  Cost :  [0.34402328]\n",
            "Epoch :  650000  Cost :  [0.34351924]\n",
            "Epoch :  700000  Cost :  [0.34320313]\n",
            "Epoch :  750000  Cost :  [0.34301693]\n",
            "Epoch :  800000  Cost :  [0.3429204]\n",
            "Epoch :  850000  Cost :  [0.34288536]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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abp0FcPdHgEdalH0lNu7ATWGIt/kbMCWdsbWnYmghs+evZcueOkoK8pMKQ0QkYyTdwZ2R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\nERFJSclCRERSUrIQEZGUlCxERCSl/w9IYPcEL2LaagAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.34288370087441594"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 92
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "F0ouCT57ZQML",
        "colab_type": "code",
        "outputId": "bea67986-a76d-40f1-9eba-6d3b44d36411",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 111
        }
      },
      "source": [
        "df = prediction_table(Y,y_predicted)\n",
        "df"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Positive</th>\n",
              "      <th>Negative</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>Positive</th>\n",
              "      <td>47</td>\n",
              "      <td>10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Negative</th>\n",
              "      <td>7</td>\n",
              "      <td>36</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "         Positive Negative\n",
              "Positive       47       10\n",
              "Negative        7       36"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 93
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FNdH2tuQZXXx",
        "colab_type": "code",
        "outputId": "45e1fa76-3f6c-40ad-c7a4-98766e8ade0d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 851
        }
      },
      "source": [
        "for i in range(x.shape[0]):\n",
        "  if(labels[i]==1):\n",
        "    plt.scatter(x[i],y[i],color='red')\n",
        "  else:\n",
        "    plt.scatter(x[i],y[i],color='blue')\n",
        "plt.plot(np.sort(x,axis=0),1/(1+np.exp(-np.sort(x,axis=0))),color='green',label='Logistic function')\n",
        "plt.legend(loc=\"upper left\")\n",
        "plt.title('Data classified into two classes with the logistic regression')\n",
        "graph()\n",
        "for i in range(x.shape[0]):\n",
        "  if(y_predicted[i]==1):\n",
        "    plt.scatter(x[i],y[i],color='red')\n",
        "  else:\n",
        "    plt.scatter(x[i],y[i],color='blue')\n",
        "plt.plot(np.sort(x,axis=0),1/(1+np.exp(-np.sort(x,axis=0))),color='green',label='Logistic function')\n",
        "plt.legend(loc=\"upper left\")\n",
        "plt.title('Data classified into two classes with predicted values')\n",
        "graph()\n",
        "for i in range(x.shape[0]):\n",
        "  if(y_predicted[i]==labels[i]):\n",
        "    plt.scatter(x[i],y[i],color='pink')\n",
        "  else:\n",
        "    plt.scatter(x[i],y[i],color='green')\n",
        "plt.plot(np.sort(x,axis=0),1/(1+np.exp(-np.sort(x,axis=0))),color='red',label='Logistic function')\n",
        "plt.legend(loc=\"upper left\")\n",
        "plt.title('Data misclassified data highlighted')\n",
        "graph()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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y45dMvWEqnet3dlokxUE8MY5DCYF46KcXCDd0XneyRedQS+dYwTF6vN+DOevn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\nxaEoiqKEhCoORVEUJSRUcSiKoigh8f8fStuUmZkBmwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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EJS0RkUdE5Cr3sLuA/iLyHTAO6KtBHfSpNMTzTHB+UXwJqqB2H9pN57Gdydid\nwUc9P+LMk870WiTD59jAe34iUqOm+RGvg7shb+8jcDyBfjT4RpCDRw7SeWxnvlj/BZOvm0yXxl28\nFsnwEN/0czCKQVBi3EqCH4K7PWyZedVgOZp9lJ4f9GTW2lm8+fs3TTEYYWPKobRE8qsPSoxbSfCD\n4vNIQXlpUfvbp39j4vKJPNvpWXqe2TP6CRrxQziTPvhx8XyyH9XoTPgTi5lJvJj9xA+TI0V6Jhx/\nJ6svzntRGYLePu326CZkBApsJrgY4NVXXxq8LKS9npLLo3sXyT+biEQvzY9XfqxJQ5P0d2N/p0eO\nHoleQkbgCFc5mEO6NATRgewHx7CXjB0b85F0Y/3Il21bxrn/OZdG1Rsxp98cUpJTIp+IEVjMIR0L\n/GBHLy5+cAx7SQx7H+W4o9atc+oLoUTClZSfu2v3od1c/c7VJCclM7XHVFMMRokx5VAaguhADqJC\nCyChTmhwGpg5CiISwyXk5+TuPyCbi0f0YdWOVbz3x/doUK1B0RcyjAIw5VAagjJISihBVGgBJL+o\nWdVfTUmlzSL5Xf9Aq8dZsG8ST1/2NBemX1i6BIyEx5RDaQnCICmhBFGhBZBoW+/yXOfUj+Hiv8P3\nPRnUZlBkEgkoCdoJPuKYcigNQc2FQVNoASTa1rvjrnPCGrimJ/x8Jg0WvVrkvM9Bzbbh4JdRWuIB\nUw4lxXKhUQjRtt4du365fdD9agAqTJ7I449UKvS8eM+28Tw8WcwJJ97Vj4vn/RyC2MfBiCnR7tbx\n1lvZWun6HsrDoieeNz2s68d7tvWiT0lxCTdfRCv/YJ3gokwQcqER1zw/93llCPro7EfDPifes63f\nlV+4/TCj2V8zXOVgZqWSYiGhhod8u/lb7vzkTjqf2pn7298f9nnxnm39HowXrtnLD+YxUw4lxe+5\n0Ihbdh/aTbf3u1GrUi1GXz2aMnln1C2QeM+2OcF4qam/bqtY0Tt5chNuFJsf+qqacigpFhJqeICq\ncsuHt7Bm5xrGXTOOmpXyzKZbKImSbQ8c+PV/ZqZ/nO7httx80cILx/bkx8Vzn0Os8HqwOsNXvP7t\n68oQ9B+z/+G1KL7Fz36HIPkcPC/kS7okhHLwwzDXhm9YmblSKw+rrBe+fqGNtFoIfne6ByVayUZl\n9TOJPoKqcYzDRw9z/uvnszJzJd/d8p2Nm1QI9tkUjo3KGg/4wStlhE+ursdj//xFxHoiD509lHkb\n5zHyypGmGIog3p3uscKUg5/xhVcqAYjEeBK5uh6PXXceA15qGZGeyP9d918em/MYN7S4gWubXFv8\nCyQYieJ0jzZmVvIzOQVOaMCL6jHHAAAdz0lEQVRzpUqW0yPF2LEwaJATzhJKSZ5xLltGOj+xjvQ8\nhxXXtLH70G6av9Sccknl+Pbmb6lSvkr4JxtGPphZKR6wKlD0yFG8uRUDlKy3US5T33ryb90V1yL4\n14//yobdGxj9+9FRVwzxPCCfUXxMOfgdG0E1OuTXBTWU4pbiuUx9Dcn//OJYBKeumMqoRaO4r919\ntG3QtnjyFJN4H5APTPkVF1MORuHE6xdVVOFfXL9OLi/oMB6gEvuOO6Q4TtFt+7Zx09SbOOuks3i4\nw8PFk6UE+GG4hmiSCMov4oQT7+rHJSH6OXhNPPezKKinVGnuMVdg+phb55QoTj07O1v/8M4ftPw/\nyuv3W74vvhwlwO99A0qLnzvGxRqsn4NRauI5YDw/Zz84g/I8+6yn5rux34+l98Te/LPjP7mn3T0x\nSTOeXzU4Dd/8ijoRx2KbSJhD2ig98dzPIj9n/5gxsH27p4rh570/c/vHt3Nu/XO5q+1dMUs33vsG\nWFR48THlYBRMvH9R+Tn7Pfax3Db9NvZm7WXUVaNIKpMUs3TjPTAu3pVfVAjH9uTHxXwOMSCIPofS\nDEjj8f1OWDqh2JP3GOFjY1g64KeB94BOwApgFXBfAcd0A5YCS4C3i7qmKYcYEaQvqrSFu4deyx37\nd2jtp2tri5dbaNaRrKinZyQu4SqHqJuVRCQJeAHoDDQBeohIk1zHNAbuB9qpalPgjmjLZYRJpPtZ\nRNNsU9p4TA99LHd9chfb9m1j1FWjKJdULurpGUZRxMLncA6wSlXXqGoWMB7omuuY/sALqroTQFW3\nxkAuI9ZEO9i8tIW7Rz6WT1d/yuuLXueedvfQsk7LqKZlGOESC+VQD9gQsp7hbgvlNOA0EflSRL4W\nkU75XUhEBojIfBGZv23btiiJa0SNaPe0Km3h7oHXcm/WXvpP7c9vUn/DQxc+FLV0DKO4+CVaqSzQ\nGOgA9ABeFZHquQ9S1ZGq2lpVW9eqVSvGIhqlJlJmm4JMU6Ut3CMVslMM09kDnz3A+l/W85+r/kOF\nshWKl45hRJNwHBOlWYC2wIyQ9fuB+3Md8zLQL2T9M+C3hV3XHNIBJBIO36Kczl470IvhFP9i3Rcq\nQ0Rvm3ZbsS4flPgAv5LozxC/RCvhtArWAI2A8sB3QNNcx3QC3nT/18QxQ6UWdl1TDgEkEqGifh8H\nIUz5Dhw+oL8Z8RtN+3ea7jm0J6xLBzGy2G/YM/SRcnBkoQvwI7AaGOxuewS4yv0vwDM4oayLgeuK\nuqYph4BS2mqb3wcBClO++2ferwxBZ6yaEfal/a4Xg4A9Q58ph2gsnimHRG+Teo3fv+4w5FuwaYEm\nDU3SfpP6FevSfteLufHjpxK0ZxgNwlUOfnFIBwMb99d7/D4OQhHyHT56mBun3EityrX412X/Ktal\ngzSaiV8/lSA9Q88JR4P4cfGk5eDHWqsfq2fRxu/3XIh8w/47TBmCTlw2sUSXDYq93I+fimqwnmG0\nwMxKUcBvbVLL6YFi6dalWv4f5fWP7/6xxNfwu17MwW+fSihBeYbRIlzlYPM5FAe/DXrvN3mMAsnW\nbC54/QKWbV/G0j8v5aQqJ3ktUlSxrOlfbD6HaOA3e3c8z7cQZ7y64FW+3PAl/7rsX3GvGMB/n4pR\nfEw5FAe/DXpv3rVAsHnPZu6deS8XpV9En7P6eC1OTPDbp2IUHzMrBZn8prqsVMm+Qp/R7b1uTFkx\nhcW3LqZxamOvxTESHDMrJQJWPSucosY4isGsbx/9+BHvLX2Pv1/wd1MMRqCwloMRnxTVqopBq2tv\n1l6avtiUKuWr8O3N31I+qXxErmsYpcFaDkZk8Xhu5WJT1PDg0R4+HHj484dZ/8t6Rl4x0hSDETjK\nei2AEQBy17JzuruCf01YRUVyRTnSa+HmhQyfO5ybW91Mu4btInJNw4gl1nIwiiYGteyIU1QkVxQj\nvY5mH+XmD2+mVqVaPNHxiVJfzzC8wJSDUTRB7E9RVKB9FAPxn5/3PPM3zefZTs9SvUKeOasMIxAU\nqRxE5FMROSsWwhg+JYj9KYqK5IpGpNfYsWxIP4EHp9xB55XQrcOfPffNBM1V5AfsmbkUNb4GcDbw\nOfA6UCecMTlisdh8DjHExnAqmjFjVMuX167XoRUHo2uqu8+pXDnPnpO9tuKTCM+MSA+8B1yDM4vb\nw0DFcM+L1hIY5RAvo3zFy31Ei7Q0nXA6yhD0yfNyjTbn0VCkfh0Z1c8kwjMLVzmE1c9BRARoCpwP\nPAocxJkH+q3It2XCIxD9HKwHc8Kwu4LQ5C9Qcz98MxLKZYfsFIHs7ALPjRZlyjhFW248EicQJMIz\ni1g/BxH5EtgI/BuoB/QFOgDniMjI0okZ5wQxyscoEYO7prApBUZOzaUYwDPfTBBdRV5jz+xXwolW\nGgDUU9VLVfXvqvqhqq5S1duA9lGWL9gEMcon0iSAd29uxlxeaLKXgfPLcM7GXDvLlfNsKFIbGbX4\n2DMLIRzbU0ELcHJpzi/NEgifQyIYMAsjAbx7WUeytPlLzbXev+rpL6NHqqam/nqvqame36u5iopP\nrJ6ZV+8GmwnOByRA4VgoCaAc//nFP5Uh6ISlE7wWxQgQXhYN4SoH6wQXTRJ91NQ4N6ut3rGah2c9\nTNffdOXqM672WhwjQATBHWljK0WbXr0SRxnkpmHD/OeKjAPvnqpy84c3Uz6pPC90ecFrcYyAEYR6\nk7Uc/Eo8OHLj2Ls3+rvRfPbTZzxxyRPUq1rPa3GMgBGEqChTDn4kp3/EunWOOTJnFNSgKYg4Natt\n3beVOz+5k3YN2nFz65u9FscIIEGoN5ly8CNBMEiGS69esHat04No7VpnW8BbRHd8fAd7s/by6pWv\nUkbsEzKKTxDqTeZz8CNBMEiWhCDOC5GLaSunMe6HcQy5cAhn1DrDa3GMAON3d6RVe/xINA2SXvoy\nAt4i2pu1l1s/upUmtZpw3/n3eS2OYUQVUw5+JFoGSa99GQFvET34fw+y4ZcNvHrlqySXTfZaHMPn\nBD2mxJSDH4mWQdLrmnsQQjQKYG7GXJ6b+xy3tr6V8xqc57U4hs/xuh4WCWKiHESkk4isEJFVIlJg\ne1xErhERFZEiRwyMe3I7ciNhnAy35h6tKk8QQjTyIetoFv2n9qduSl0e7/i41+IYAcDrelgkiLpy\nEJEk4AWgM9AE6CEiTfI5LgUYBMyNtkwJSzg192hWeYIQopEPj815jMVbF/PyFS9TNblqTNMOumki\nUQm4BdUhnDE2SrMAbYEZIev348wFkfu44cDvgFlA66KuG4ixlfxGOAO6JMB4SMVh0eZFWvaRstp7\nQu+Yp53oQ3MFGT9/RvhobKV6wIaQ9Qx32zFE5Gyggap+VNiFRGSAiMwXkfnbtm2LvKTxTjg197io\n8kSGw0cP029yP1IrpjL88uExTz8eTBOJSkAtqMfhuUNaRMoAzwB3FXWsqo5U1daq2rpWrVrRFy4e\nKcqXEWCncaR56qun+HbLt7z4uxdJrZQa8/RNTweXgFpQjyMWymEj0CBkvb67LYcUoBkwS0TWAucC\nU8wp7RHxUOWJAEu2LmHo7KF0a9qNP5zxB09kMD0dbKIRUxJLYqEcvgEai0gjESkPXAdMydmpqr+o\nak1VTVfVdOBr4CpV9fkE0XFKPFR5SsmR7CPcMOUGqiZX5fnOz3smh+lpw0uirhxU9QgwEJgBLAPe\nVdUlIvKIiFwV7fSNElCSKk8chdUM/3o48zbOY0TnEdSq7J350vS04SXiOK+DR+vWrXX+fGtc+ILc\nYyaBU8UNYEm2YvsKWrzSgk6ndmJCtwmIiNciGUZEEZEFqlqk2d5zh7QRB0Q6rMajVsiR7CP0ndyX\nSuUq8dLvXjLFYCQ0NiqrUXoiGVbj4citT335FF9nfM24a8ZRu0rtqKZlGH7HWg5G6YlkWI1Hwf3f\n//w9D896mG5Nu3Fds+uimpZhBAFTDkbpiWRYjQfB/YeOHKL3hN7UqFjD5oM2DBdTDkbpKWlYTX6+\nBQ+C+//++d9ZvHUxo7qOomalmlFLxyg9cRQU53/CGWPDj4uNrRRwCho46NZbYzqg0KyfZqkMEb1l\n6i1Rub4ROWysqciAj8ZWMoy8FORbmDYtZsH9uw7u4k+T/sQpNU7h6cuetmqpz7GxpmKL9XMwvKFM\nGafylxsRp/NdlFFVenzQg/eXvs+XN3xJm9mr4qavRrzicZaJG6yfg+FvPB44aPR3o3lnyTs8ctEj\ntKnfxqqlAcDGmootphwMb/Bw4KDVO1YzcPpALky7kHvb3etsjHRfDTNPRRwbayq2mHIwvMGjgYOy\njmZx3QfXUbZMWd66+i2SyiQ5OyJVLY2HyYN9Qm4dCzbWVEwJx2vtx8WilYyS8NeP/6oMQScum3j8\njkiFwvh5CrAAYZFJ0QOLVgoYZoqIHu6znXq68O+v/81t1S7j96f//vhjCmvJFOfd2Aw9EcFcQD4g\nHA3ixyWuWg5WTYoe7rNdXxWtcQ/a8mb0YErF8J9tcd+NtRwigkj+j1HEa8mCD9ZyiDKRrOlbNSl6\nDB7M4YP76f5HyEqCd96D5D0Hwn+2xX035jWNCBaZ5D2mHEpCpJ2OZoqIHuvXc++l8L8G8J8p0HjH\nr9vDPb9Y222GnohgOtZ7TDmUhEjX9K2aFDXeuyCVf7eF27+GbktCdoT7bEvyboI+ebAPMB3rPaYc\nSkKka/pWTYoKi39eTN+L99B2Yxme+jRkR3Gerb0bzzAd6y2mHEpCpGv6Vk2KODsP7OTqd66mWuUa\nfNDuWcrXL+GzjfG7saA1wy/Y2EolIY7mTI5HjmYf5cpxVzJzzUxm9Z3FeQ3O81qksLBsZcQCG1sp\nmlhNPzJEqZo8ZNYQpq+azojOIwKjGKBoV1YQWxVBlNlwCSfe1Y9LXPVzSESi1Ldj3OJxyhD0psk3\naXZ2doSEjQ2FxfYHsStMEGVOBAizn4OZlQxvSE93QoBzk5bmeB9LwBfrv+CS0Zdwbv1z+aT3JySX\nTS6ViLGmsEcCEX9cUScKr9iIAGZWKgpr73pLhCO+VmaupOv4rjSq3oiJ3ScGTjFA4YFRQewK45XM\n9mlHhsRUDn4eOTNRcnYEI762799Ol7e7UEbK8FHPj6hRsUYphfOGwlxZQewK44XMxf20E+VzKxHh\n2J78uJTK5+DX8W8SyUgboXs9cPiAnvef8zT5H8n61fqvoiSs9wQxa3ghc3E+7SA+00hAmD4Hzwv5\nki6lUg5+HdXLr0orWowZ49ybiPNbzK/yaPZR7f5ed2UI+u4P70ZFRD9RysflCbGWuTifdqJ9bjmE\nqxwS0yHtV0+ZTZJbLO6feT9PfPkET3Z8kr+1+5vX4hg+oDifdqJ+buaQLgy/DokQRMOyR7z0zUs8\n8eUT3NzqZu4+726vxTF8QnE+7aB8bp75RcJpXpR2AToBK4BVwH357L8TWAp8D3wGpBV1zVL3c/Bj\nGz1RjaDFZOz3Y1WGiF759pV6+Ohh7wTxYx4ywn4tQfjcoiEjfvE5AEnAauBkoDzwHdAk1zEXAZXc\n/7cC7xR13bjtBGcFTqFMXj5Zk4YmaYc3Ouj+rP3eCRKEksUoEr9/btHwi4SrHKLucxCRtsAQVb3c\nXb/fbbE8XsDxLYHnVbVdYde1TnBRZOxYZ8yG9eudNvawYb4YGmTisol0f787Leu0ZOb1M0lJTvFO\nGL/6rYy4Ihp+ET/5HOoBG0LWM9xtBXEjMD2qEhkF49M+IO8vfZ9u73ejVd1WfNL7E28VAwSzV5oR\nOLz0i/jKIS0ivYHWwFMF7B8gIvNFZP62bdtiK1yi4MMpS8f/MJ7r3r+ONvXaMKP3DKpVqOaZLMcI\nijfTCDRexs7EQjlsBBqErNd3tx2HiHQEBgNXqeqh/C6kqiNVtbWqtq5Vq1ZUhE14fFYjHvP9GHpN\n6EW7hu34uPfHVE2u6okcefBrxJsRV3g5AHQslMM3QGMRaSQi5YHrgCmhB7h+hldwFMPWGMhkFISP\nasRvLHqDP038Ex3SOzCt5zSqlK8ScxkKJM6GbbdhJPyLVzPiRV05qOoRYCAwA1gGvKuqS0TkERG5\nyj3sKaAK8J6ILBKRKQVczog2PqkRv7bwNW6YfAMdT+7I1B5TqVy+ckzTD4s4mcfSp24mw2vCCWny\n4xK3oax+wMP4vuzsbH3qy6eUIWinMZ30wOEDvpIvHknUYSQSFfwSyhotLJQ1/jiafZRBHw/ihW9e\noFvTboz+/ei8Q2/bXJoRJ1GHkUhU/BTKahhFsv/wfq559xpe+OYF7m57N+OuGZf/nAw+jKYKOj5y\nMxk+wpSDUTAx8lJu2buFi9+8mCkrpjCi8wieuuwpykgBWdNn0VTxgE/cTIbPKOu1AIZPyW2+yfFS\nQkTNNws3L6Tr+K7sOLCDCd0n8PvTf1/4CQ0b5t8z2aq5JSbndfqwU7zhIeZzMPInBsNDvLnoTW75\n6BZOrHwik6+bTIvaLYo+yXwOhlEqzOdglI4omm8OHTnELR/eQt/JfWlbvy3f9P8mPMUAcde/wDD8\niimHWBDEHkZR8lL+tPMn2r/enlcWvMJ97e7jk+s/4cTKJxbvInHSv8Aw/Iwph2gT1B5GUfBSjls8\njhavtODHzB+Z2H0ij3d8nLJlzO1lJDZ+rTuacog2QQ29jKD5ZtfBXVw/8Xp6TuhJsxObseiWRUU7\nng0jAfBz3dEc0tEmwXsYTVg2gYHTBrJ131b+fsHfGXzBYGstGIaLF9OChOuQtq802iRo6OXG3RsZ\nOH0gk5ZPomXtlkztMZVWdVt5LZZh+Ao/d9sxs1K0SbAeRtmazUvfvESTF5swY9UMnuz4JPP6zzPF\nYBj54Ofe6aYcok0ChV7+sPUHLnj9Av487c+cU+8cFt+6mL+1+5uZkQyjAPxcd7SvNhb06hWXyiCH\njN0ZPPT5Q7z53ZtUr1CdN7q+wZ/O+hMi4rVohuFr/Nw73ZSDUWJ2HdzFE188wbNznyVbs7mjzR08\n0P4BUiulei2aYQQGv9YdzaxkFJtDRw7xzP+e4ZTnTuHJL5/k2ibXsmLgCv51+b9MMRilwq8x/4mI\nKQcjbPYf3s9zc5/jlOdO4a5P7qJ13dYsvHkhb139FunV070Wz9dYoVc0fo75T0RMOcQjES6JMvdn\n8uh/HyV9eDqDPh7EySeczMzrZzKj94zwx0RKYKzQC4+g9heNV6wTXLwRwVFLf9j6A8/Pe57R343m\nwJEDdD61M/edfx8XpF0QYaHjGy86OgWRBO8vGjNsVNZEpZTVrx0HdvDy/Jdp+5+2nPnSmbyx6A16\nNOvB4lsXM63XNFMMJcDPHZ38hN9i/hPdFGjRSvFGCUqiw0cPM33VdEZ/N5qpP04l62gWzU5sxlOX\nPkW/Fv3MyVxKErSTfLEZNiz/Rq8XMf8xmuvK15hyiDfCLIlUlYWbFzL6u9G8/cPbbN+/nVqVavHn\n1n/mT2f9iRa1W1g/hQjhp0LPz/gp5r+wBrgpByOYFFISHc0+ytcZX/PRyo+YsGwCKzJXUD6pPFf9\n5ir6nNWHy0+5nHJJ5byTPU7xU6Hnd/wS82+mQHNIxydjxx4riTIb12PGX6/ioxN38fGqj9lxYAdJ\nksSF6RfyxyZ/pHvT7pxQ8QSvJTYMXxHPQQQ2KmuCsn3/dr5oVZk5r1zDrHWz+Hbzt+jPL1JrTy2u\nOO0Kftf4d1x2ymVUr1Dda1ENw7eYKdCUQ6A5kn2EZduWsXDzQr7a8BVz1s9h2fZlACQnJXNu/XMZ\n2mEol51yGb+t91vKiAWnGUYOIQ3sPKY+MwWaWSkwHD56mKXblrJg8wIWbl7Igs0L+G7Ldxw4cgCA\nqslVadegHe0btqd9Wnt+W/e3JJdN9ljqCFPY12wYxSCC3YECR7hmJVMOPmNf1j5W7VjFiswVLN++\nnKXblrJk2xJWbF/B4ezDAFQpX4Wz65xNqzqtjv2elnoaSWWSPJY+iiTy1+wT4kk3x7NPoShMOfiU\nfVn7WPfLOtbtWsfaXWtZ94vzm/N/y94tx44VhPTq6TQ9sSlNazWl+UnNaVWnFY1TGyeeiSiRv2Yf\nEG+6OZF7Y5tyiCGqyu5Du/l5389s2buFn/e6v/t+/d28ZzPrf1nPtv3bjju3XJlypFVPI716OmnV\n0mhUvRGNUxtzWuppnJZ6GpXKVSog1QQjkb9mHxBvujne7qc4+CpaSUQ6Ac8CScBrqvpErv3JwGig\nFZAJdFfVtbGQDZzCfW/WXnYf2s0vh35xfg/+Uuj6zoM7ydyfSeaBTLbv387BIwfzXLeMlOHEyidy\nUuWTqF2lNq3qtDqmCHKW2lVqR68VEE92AOtm7ClBjPsvLPtbNFLRRF05iEgS8AJwKZABfCMiU1R1\nachhNwI7VfVUEbkO+CfQPdqy9Zvcj4nLJrInaw/ZWnTtM6V8ClWTq1I1uSo1KtagYbWGtKzTkpoV\na3JSlZOOKYGTqji/qRVTvfMDxFv/f/uaPSVourmo7G/RSEUTdbOSiLQFhqjq5e76/QCq+njIMTPc\nY/4nImWBLUAtLUS4SJiVXp7/Msu2LaNqclWqVah2rOCvllztuG3VkqtRpXyVYDl847HdHE8toYAR\nNJ9DPGb/SOEbn4OIXAt0UtWb3PXrgTaqOjDkmB/cYzLc9dXuMdtzXWsAMACgYcOGrdbl9/YNB7PR\nGxEmSLrZsn/BxOWQ3ao6UlVbq2rrWrVqeS2Ov/Hb+MdG4OnVy6l1Z2c7v35VDGDZPxLEQjlsBBqE\nrNd3t+V7jGtWqobjmDZKyrBhTrs/FLPRGwmCZf/SEwvl8A3QWEQaiUh54DpgSq5jpgB93P/XAv9X\nmL/BCINevRyDcFqa05ZOS/OvgdgwIoxl/9ITk34OItIFGI4TyjpKVYeJyCPAfFWdIiIVgLeAlsAO\n4DpVXVPYNf3Uz8EwDCMo+Kqfg6pOA6bl2vZQyP+DwB9jIYthGIZRNIFySBuGYRixwZSDYRiGkQdT\nDoZhGEYeTDkYhmEYeTDlYBiGYeTBlINhGIaRB1MOhmEYRh4CO9mPiGwDgjryXk1ge5FHxQ+Jdr+Q\nePecaPcLwb3nNFUtcnC6wCqHICMi88PpoRgvJNr9QuLdc6LdL8T/PZtZyTAMw8iDKQfDMAwjD6Yc\nvGGk1wLEmES7X0i8e060+4U4v2fzORiGYRh5sJaDYRiGkQdTDoZhGEYeTDl4iIjcJSIqIjW9liXa\niMhTIrJcRL4XkYkiUt1rmaKBiHQSkRUiskpE7vNanmgjIg1E5HMRWSoiS0RkkNcyxQIRSRKRb0Xk\nQ69liRamHDxCRBoAlwHrvZYlRnwKNFPV5sCPwP0eyxNxRCQJeAHoDDQBeohIE2+lijpHgLtUtQlw\nLvCXBLhngEHAMq+FiCamHLzj38A9QEJEBKjqJ6p6xF39GqjvpTxR4hxglaquUdUsYDzQ1WOZooqq\nblbVhe7/PTgFZj1vpYouIlIf+B3wmteyRBNTDh4gIl2Bjar6ndeyeMQNwHSvhYgC9YANIesZxHlB\nGYqIpOPMAz/XW0miznCcil2214JEk5jMIZ2IiMhMoHY+uwYDD+CYlOKKwu5ZVSe7xwzGMUWMjaVs\nRnQRkSrAB8Adqrrba3mihYhcAWxV1QUi0sFreaKJKYcooaod89suImcCjYDvRAQc88pCETlHVbfE\nUMSIU9A95yAifYErgEs0PjvYbAQahKzXd7fFNSJSDkcxjFXVCV7LE2XaAVeJSBegAlBVRMaoam+P\n5Yo41gnOY0RkLdBaVYM4umPYiEgn4BngQlXd5rU80UBEyuI42y/BUQrfAD1VdYmngkURcWo4bwI7\nVPUOr+WJJW7L4W5VvcJrWaKB+RyMWPE8kAJ8KiKLRORlrwWKNK7DfSAwA8cx+248KwaXdsD1wMXu\ne13k1qqNgGMtB8MwDCMP1nIwDMMw8mDKwTAMw8iDKQfDMAwjD6YcDMMwjDyYcjAMwzDyYMrBMAzD\nyIMpB8MwDCMPphwMI0K48xpc6v5/VERGeC2TYZQUG1vJMCLHw8AjInIizuikV3ksj2GUGOshbRgR\nRERmA1WADu78BoYRSMysZBgRwh1xtw6QZYrBCDqmHAwjAohIHZw5KroCe91RaA0jsJhyMIxSIiKV\ngAk4cykvA/6B438wjMBiPgfDMAwjD9ZyMAzDMPJgysEwDMPIgykHwzAMIw+mHAzDMIw8mHIwDMMw\n8mDKwTAMw8iDKQfDMAwjD/8Pd4fQZ41eh0wAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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lXbsWLrkEjjgCbr01sViSEYDpGlyV7rPRukCTg6pbOn+h6jv5J9OzpXraBue4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\nAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kNImRs0U9bn1",
        "colab_type": "code",
        "outputId": "974ea408-9c4c-44c4-d2f9-bacacc67a528",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "source": [
        "weight_predicted"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0.0937218 ],\n",
              "       [-0.96575395]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 95
        }
      ]
    }
  ]
}