s24LinearModelNotes.ipynb

{
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  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyMezbnY3rLwoEQ9grVEoheX",
      "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/everestso/Summer22/blob/main/s24LinearModelNotes.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "97aWcAkn-820"
      },
      "source": [
        "# Linear Models"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "O53BTmut-WDE"
      },
      "source": [
        "### Includes\n",
        "# Common imports\n",
        "import numpy as np\n",
        "\n",
        "# to make this notebook's output stable across runs\n",
        "np.random.seed(42)\n",
        "\n",
        "# To plot pretty figures\n",
        "####%matplotlib inline\n",
        "import matplotlib\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "import pandas as pd\n",
        "\n",
        "import math"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0dk6lRzv0pEE",
        "outputId": "89c2a566-efbb-4a2c-9782-1f730161e819",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "import os\n",
        "from google.colab import drive\n",
        "\n",
        "drive.mount('/content/gdrive')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Drive already mounted at /content/gdrive; to attempt to forcibly remount, call drive.mount(\"/content/gdrive\", force_remount=True).\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "Range2 = lambda x, p: (round(x-(10**-p)/2,p+1), round(x,p+1), round(x+(10**-p)/2,p+1))\n",
        "RoundIt = lambda x, e: (round(x-e/2,3), round(x,3), round(x+e/2,3))"
      ],
      "metadata": {
        "id": "-eXTNtt092fG"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cX2Qjzgq_jtN",
        "outputId": "8b24131b-e68b-4ea9-8e31-cd3326dc5720",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        }
      },
      "source": [
        "eps = 10.0\n",
        "coef = (1, 2)\n",
        "w = (0, 0)\n",
        "Noise = lambda eps: np.random.random()*eps - (eps/2)\n",
        "\n",
        "\n",
        "F = lambda w, x: w[0] + w[1]*x\n",
        "X = [-7, -2, 1, 3, 7]\n",
        "Y = [round(F(coef, x) + Noise(eps),2) for x in X]\n",
        "print (Y)\n",
        "\n",
        "plt.plot(X,Y,'.')\n",
        "Hxs = [F(coef, x) for x in X]\n",
        "\n",
        "plt.plot(X, Y, '.')\n",
        "plt.plot(X, Hxs, '-', color=\"green\")\n",
        "plt.show()"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[-14.25, 1.51, 5.32, 7.99, 11.56]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-udX_q-mCBuy",
        "outputId": "9a08967a-79de-44d0-8b2c-5032f2dc3c46",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "# Print Examples:\n",
        "X = [-7, -2, 1, 3, 7]\n",
        "Y = [-14.25, 1.51, 5.32, 7.99, 11.56]\n",
        "Examples = list(zip(X,Y))\n",
        "\n",
        "for p in Examples:\n",
        "  print (p)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(-7, -14.25)\n",
            "(-2, 1.51)\n",
            "(1, 5.32)\n",
            "(3, 7.99)\n",
            "(7, 11.56)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "d5PyjFepD4O0",
        "outputId": "aefb7fff-5bb2-4822-9b45-6af16408ae43",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        }
      },
      "source": [
        "# Plot Model\n",
        "def PlotModel(X, Y, model):\n",
        "  Hxs = [F(model, x) for x in X]\n",
        "\n",
        "  plt.plot(X, Y, '.')\n",
        "  plt.plot(X, Hxs, '-', color=\"red\")\n",
        "  plt.show()\n",
        "\n",
        "PlotModel( X, Y , (0,0))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "j8t8XSMbYfTe"
      },
      "source": [
        "SquaredError = lambda X, Y, w : sum([(y-F(w, x))**2 for x,y in zip(X,Y)])\n",
        "SquaredErrorLogistic = lambda X, Y, w : sum([(y-G(F(w, x)))**2 for x,y in zip(X,Y)])\n"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "p631BhDHLcT6",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "6755bb41-9db2-498f-cc7e-40ef65191b83"
      },
      "source": [
        "print (\"X=\", X)\n",
        "print (\"Y=\", Y)\n",
        "w= (0,0)\n",
        "w=(0,1)\n",
        "w=(0,0)\n",
        "Predicts = [F(w, x) for x in X]\n",
        "Errors = [x*(y-F(w, x)) for x, y in zip(X,Y)]\n",
        "print (\"Predicts = \", Predicts)\n",
        "print (\"Errors=\", Errors, sum(Errors), sum(Errors)/len(X))\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "X= [-7, -2, 1, 3, 7]\n",
            "Y= [-14.25, 1.51, 5.32, 7.99, 11.56]\n",
            "Predicts =  [0, 0, 0, 0, 0]\n",
            "Errors= [99.75, -3.02, 5.32, 23.97, 80.92] 206.94 41.388\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kR-25-bGZSIa",
        "outputId": "6efc9b12-0721-412c-ee1f-8ff91024c028",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "ws= [(0,0), (0,1), (1,0), (1,1), (1,2)]\n",
        "for model in ws:\n",
        "  print (f\"{model=}, {SquaredError(X, Y, model)=}\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "model=(0, 0), SquaredError(X, Y, model)=431.1187\n",
            "model=(0, 1), SquaredError(X, Y, model)=129.2387\n",
            "model=(1, 0), SquaredError(X, Y, model)=411.8587\n",
            "model=(1, 1), SquaredError(X, Y, model)=113.97870000000002\n",
            "model=(1, 2), SquaredError(X, Y, model)=40.098699999999994\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "g1UAIRzrbFry",
        "outputId": "4e71aa75-b59b-4e07-ded3-5cd273026148",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "## Average Gradients\n",
        "w = [0,0]\n",
        "data = [(x,y) for x, y in zip(zip(np.ones(len(X)), X), Y)]\n",
        "Gradients = np.array([ ( (y-F(w,x[1]))*x[0], (y-F(w,x[1]))*x[1] ) for (x, y) in data ])\n",
        "print(Gradients)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[-14.25  99.75]\n",
            " [  1.51  -3.02]\n",
            " [  5.32   5.32]\n",
            " [  7.99  23.97]\n",
            " [ 11.56  80.92]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "O0PAHyDXjVsf",
        "outputId": "12210518-7423-471c-9633-fdffc456fa1a",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "GradientBatch = np.array([0.0, 0.0])\n",
        "for g in Gradients:\n",
        "  GradientBatch += g\n",
        "GradientBatch = GradientBatch/len(Gradients)\n",
        "print (GradientBatch)\n",
        "for g in GradientBatch:\n",
        "  print (f\"{g=}\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[ 2.426 41.388]\n",
            "g=2.426\n",
            "g=41.388\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-5fjGr8AkdzX",
        "outputId": "91cc5463-4c00-44fb-997f-1dfe8effbe03",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "## Try Different Learning Rates\n",
        "print (f\"{w=}, {SquaredError(X, Y, w)=}\")\n",
        "for learningRate, model in [(learningRate, np.add(w, GradientBatch*learningRate)) for learningRate in (0.01, 0.1, 1.0)]:\n",
        "  print (f\"{model=}, {learningRate=}, {SquaredError(X, Y, model)=}\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "w=[0, 0], SquaredError(X, Y, w)=431.1187\n",
            "model=array([0.02426, 0.41388]), learningRate=0.01, SquaredError(X, Y, model)=278.461828946\n",
            "model=array([0.2426, 4.1388]), learningRate=0.1, SquaredError(X, Y, model)=635.0997745999998\n",
            "model=array([ 2.426, 41.388]), learningRate=1.0, SquaredError(X, Y, model)=175525.90795999998\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Hk--iezR7JQQ",
        "outputId": "bd403c98-35b5-4a64-96ac-8062577d437a",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "print (SquaredError(X, Y, (0.018, 0.452)))\n",
        "print (SquaredError(X, Y, (0.18, 4.52)))\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "266.524472\n",
            "847.6354999999999\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Algorithm Test\n",
        "learningRate = 0.01\n",
        "w = [0,0]\n",
        "data = [(x,y) for x, y in zip(zip(np.ones(len(X)), X), Y)]\n",
        "Iterations = 0\n",
        "print (f\"{Iterations=}, {w=}  {SquaredError(X, Y, w)=}\")"
      ],
      "metadata": {
        "id": "I5OawmFDNxLA",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "270a8562-29b0-4546-f465-ca3d5ca88479"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iterations=0, w=[0, 0]  SquaredError(X, Y, w)=431.1187\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "Iterations = Iterations + 1\n",
        "GradientBatch = np.array([0.0, 0.0])\n",
        "Gradients = np.array([ ( (y-F(w,x[1]))*x[0], (y-F(w,x[1]))*x[1] ) for (x, y) in data ])\n",
        "for g in Gradients:\n",
        "  GradientBatch += g\n",
        "GradientBatch = GradientBatch/len(Gradients)\n",
        "print (GradientBatch)\n",
        "w = np.add(w, GradientBatch*learningRate)\n",
        "print (f\"{Iterations=}, {w=}  {SquaredError(X, Y, w)=}\")\n",
        "#print ( {SquaredError(X, Y, w)=})"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rpOomy-uO2xK",
        "outputId": "2164c619-fce7-4ece-8939-3154fbd0c14d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[ 2.426 41.388]\n",
            "Iterations=1, w=array([0.02426, 0.41388])  SquaredError(X, Y, w)=278.461828946\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4SzviiEwmEF4",
        "outputId": "7659eac1-ced5-4287-fa3a-997f088c109e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        }
      },
      "source": [
        "PlotModel(X, Y, w)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "cv = np.cov(X, Y, bias=True, rowvar=False)\n",
        "w1 = round(cv[1][0]/cv[0][0], 2)\n",
        "w0 = round(np.mean(Y) - w1*np.mean(X), 2)\n",
        "model = (w0, w1)\n",
        "print (f\"{model=}\")\n",
        "PlotModel(X, Y, model)\n",
        "print (X, Y)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 465
        },
        "id": "dCfgjCsfokIR",
        "outputId": "f8e80b6b-6443-4ce9-d8f7-857296bd7e70"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "model=(1.7, 1.82)\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[-7, -2, 1, 3, 7] [-14.25, 1.51, 5.32, 7.99, 11.56]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "learningRate = 0.01\n",
        "w = [0,0]\n",
        "data = [(x,y) for x, y in zip(zip(np.ones(len(X)), X), Y)]\n",
        "totalIterations = 5000\n",
        "print (f\"{Iterations=}, {w=}  {SquaredError(X, Y, w)=}\")\n",
        "for i in range(totalIterations):\n",
        "  GradientBatch = np.array([0.0, 0.0])\n",
        "  Gradients = np.array([ ( (y-F(w,x[1]))*x[0], (y-F(w,x[1]))*x[1] ) for (x, y) in data ])\n",
        "  for g in Gradients:\n",
        "    GradientBatch += g\n",
        "  GradientBatch = GradientBatch/len(Gradients)\n",
        "  w = np.add(w, GradientBatch*learningRate)\n",
        "print (f\"{totalIterations=}, {w=}  {SquaredError(X, Y, w)=}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "og1uowb2qGC6",
        "outputId": "bc1f25ed-6495-4808-e6a7-f8c9673a8380"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iterations=1, w=[0, 0]  SquaredError(X, Y, w)=431.1187\n",
            "totalIterations=5000, w=array([1.69906475, 1.81733813])  SquaredError(X, Y, w)=34.42909208633094\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nd7eLKfx0wkL"
      },
      "source": [
        "# Logistic Regression"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "G = lambda xIn: 1/(1+np.e**(-xIn))"
      ],
      "metadata": {
        "id": "Yv7arskBjGIZ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7E8nsibXrfwR",
        "outputId": "c9484bb6-12b0-4550-d06b-9e43dcd10a35",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "Predict = lambda x: 1.0 if x > 0.5 else 0.0\n",
        "w = (0,0)\n",
        "Y = [Predict(G(F(coef, x))) for x in X]\n",
        "for x, y in zip(X, Y):\n",
        "  print (x, y)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "-7 0.0\n",
            "-2 0.0\n",
            "1 1.0\n",
            "3 1.0\n",
            "7 1.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0THLfoDtnq9T",
        "outputId": "81b26e04-aa53-4ad9-d4c9-716d445cde82",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        }
      },
      "source": [
        "def PlotLogisticData(X, Y, model):\n",
        "  posX = []\n",
        "  posY = []\n",
        "  negX = []\n",
        "  negY = []\n",
        "  for x, y in zip(X,Y):\n",
        "    if y:\n",
        "      posX += [x]\n",
        "      posY += [Predict(G(F(model,x)))]\n",
        "    else:\n",
        "      negX += [x]\n",
        "      negY += [Predict(G(F(model,x)))]\n",
        "  plt.plot(posX, posY, '+', color='green')\n",
        "  plt.plot(negX, negY, 'o', color='red')\n",
        "  plt.show()\n",
        "PlotLogisticData(X, Y, w)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PCgj7bHLPvyM",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "acee4c70-5526-4f2a-9822-045400dbf929"
      },
      "source": [
        "print (\"X=\", X)\n",
        "print (\"Y=\", Y)\n",
        "w= (0,0)\n",
        "w=(0,1)\n",
        "w=(0,0)\n",
        "Predicts = [F(w, x) for x in X]\n",
        "Errors = [x*(y-G(F(w, x))) for x, y in zip(X,Y)]\n",
        "print (\"Predicts = \", Predicts)\n",
        "print (\"Errors=\", Errors, sum(Errors), sum(Errors)/len(X))\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "X= [-7, -2, 1, 3, 7]\n",
            "Y= [0.0, 0.0, 1.0, 1.0, 1.0]\n",
            "Predicts =  [0, 0, 0, 0, 0]\n",
            "Errors= [3.5, 1.0, 0.5, 1.5, 3.5] 10.0 2.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VTCTItCC2fgJ",
        "outputId": "af331f1d-1d8b-4357-e5ee-4724aeac0552",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "ws= [(0,0), (0,1), (1,0), (1,1), (1,2)]\n",
        "for model in ws:\n",
        "  print (model, SquaredErrorLogistic(X, Y, model), RoundIt(SquaredErrorLogistic(X, Y, model),0.1) )"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(0, 0) 1.25 (1.2, 1.25, 1.3)\n",
            "(0, 1) 0.0887896982223366 (0.039, 0.089, 0.139)\n",
            "(1, 0) 1.2858817551625858 (1.236, 1.286, 1.336)\n",
            "(1, 1) 0.0868685548209095 (0.037, 0.087, 0.137)\n",
            "(1, 2) 0.004499256912790766 (-0.046, 0.004, 0.054)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kFEoYgJztCvn",
        "outputId": "b93a6b66-9202-432a-99cf-2f0aa8d17161",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "## Average Gradients\n",
        "w = ws[0]\n",
        "data = [(x,y) for x, y in zip(zip(np.ones(len(X)), X), Y)]\n",
        "Gradients = np.array([ ( (y-G(F(w,x[1])))*x[0], (y-G(F(w,x[1])))*x[1] ) for (x, y) in data ])\n",
        "print(Gradients)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[-0.5  3.5]\n",
            " [-0.5  1. ]\n",
            " [ 0.5  0.5]\n",
            " [ 0.5  1.5]\n",
            " [ 0.5  3.5]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ap9AZTZatT_n",
        "outputId": "0e28c338-f1f4-4227-e802-caa298b362d7",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "GradientBatch = np.array([0.0, 0.0])\n",
        "for g in Gradients:\n",
        "  GradientBatch += g\n",
        "GradientBatch = GradientBatch/len(Gradients)\n",
        "print (GradientBatch)\n",
        "print (X, Y)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[0.1 2. ]\n",
            "[-7, -2, 1, 3, 7] [0.0, 0.0, 1.0, 1.0, 1.0]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UPCCYrMdtZsf",
        "outputId": "45dbfa65-9d62-4b86-9a63-d9574a0765c9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "wNew = np.add(w, GradientBatch*learningRate)\n",
        "print (wNew)\n",
        "print (w)\n",
        "print (SquaredErrorLogistic(X, Y, (0,0)))\n",
        "print (w, SquaredErrorLogistic(X, Y, w))\n",
        "for model in [np.add(w, GradientBatch*learningRate) for learningRate in (1, 1)]:\n",
        "  print (model, SquaredErrorLogistic(X, Y, model))\n",
        "  print (model, RoundIt(model[0],0.1), RoundIt(model[1],1.0))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[0.001 0.02 ]\n",
            "(0, 0)\n",
            "1.25\n",
            "(0, 0) 1.25\n",
            "[0.1 2. ] 0.012300762094024014\n",
            "[0.1 2. ] (0.05, 0.1, 0.15) (1.5, 2.0, 2.5)\n",
            "[0.1 2. ] 0.012300762094024014\n",
            "[0.1 2. ] (0.05, 0.1, 0.15) (1.5, 2.0, 2.5)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rrjzRLN6xo-0",
        "outputId": "12fcec27-6b50-49db-eb49-154ce8e55d46",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        }
      },
      "source": [
        "PlotLogisticData(X, Y, (0.1, 2))\n",
        "print (np.log10(2))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.3010299956639812\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PyZ1eIhaRt8T",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7264aa7b-6609-416a-eac5-1030e450a4cb"
      },
      "source": [
        "print (G(14.1))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.9999992476022669\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# More Logistic Regression\n"
      ],
      "metadata": {
        "id": "VQuS2A7RweWX"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "F2 = lambda w, x: x[1] - w[0] - w[1]*x[0]\n",
        "eps = 30.0\n",
        "coef = (1, 2)\n",
        "w = (0, 0)\n",
        "Noise = lambda eps: np.random.random()*eps - (eps/2)\n",
        "\n",
        "\n",
        "X1 = range(-6, 7, 1)\n",
        "X2 = [round(F(coef, x) + Noise(eps),2) for x in X1]\n",
        "Y = [1 if F2(coef,x) > 0 else 0 for x in zip(X1, X2)]\n",
        "print (Y)\n",
        "\n",
        "plt.plot(X1, X2,'.')\n",
        "Hxs = [F(coef, x) for x in X1]\n",
        "\n",
        "plt.plot(X1, Hxs, '-', color=\"green\")\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "id": "8zqGDfEjwhSt",
        "outputId": "861fe65b-45d4-4c5b-953d-978fdba19537"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def Separate(Data):\n",
        "  pos = []\n",
        "  neg = []\n",
        "  for i in range(len(Data)):\n",
        "    if Data[i][1]==0:\n",
        "      neg.append(Data[i])\n",
        "    else:\n",
        "      pos.append(Data[i])\n",
        "  return neg, pos"
      ],
      "metadata": {
        "id": "KzYyAPwMzM_Q"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "X = list(zip(X1, X2))\n",
        "Data = list(zip(X, Y))\n",
        "neg, pos = Separate(Data)\n",
        "print (f\"{neg=} {pos=}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3I9axAqhza_u",
        "outputId": "40952ede-40bf-4d0b-9ce2-a0e76a6a6225"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "neg=[((-6, -21.32), 0), ((-5, -22.26), 0), ((-1, -15.38), 0), ((2, -3.63), 0), ((3, -2.55), 0), ((4, -0.5), 0), ((5, 5.13), 0)] pos=[((-4, 3.99), 1), ((-3, -1.97), 1), ((-2, 3.24), 1), ((0, 15.1), 1), ((1, 12.97), 1), ((6, 13.74), 1)]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "negatives, positives = Separate(Data)\n",
        "dataX1pos = [x[0] for x,y in positives]\n",
        "dataX2pos = [x[1] for x,y in positives]\n",
        "dataX1neg = [x[0] for x,y in negatives]\n",
        "dataX2neg = [x[1] for x,y in negatives]\n",
        "\n",
        "iteration = 0\n",
        "plt.plot(dataX1pos, dataX2pos, \"g+\")\n",
        "plt.plot(dataX1neg, dataX2neg, \"r.\")\n",
        "\n",
        "Hxs = [F(coef, x) for x in X1]\n",
        "plt.plot(X1, Hxs, '-', color=\"yellow\")\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "ImDQcNw40DOY",
        "outputId": "7737fa27-bdb2-40a8-d550-60eb8c0bf1b6"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Example\n"
      ],
      "metadata": {
        "id": "b7W5KjFDd_0s"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "sigmoid = lambda y: 1/(1+math.exp(-y))\n",
        "classify = lambda y: 1 if y>0.5 else 0\n",
        "F = lambda W, X: sum([w*x for w,x in zip(W,X)])\n",
        "Fx2 = lambda W, X: (W[0]*X[0]+W[1]*X[1])/(-1*W[2])\n",
        "data = [((1,2,3),0), ((1,3,4),0), ((1,4,5),0), ((1,5,6),1), ((1,6,7),1), ((1,8,9),1) ]\n",
        "data = [((1, -7, 10), 0), ((1, -3, 4), 0), ((1, 8, 7), 1), ((1, 1, 16), 0), ((1, 8, -4), 1), ((1, 9, 5), 1), ((1, -4, 14), 0), ((1, -1, -8), 1), ((1, -8, 0), 0), ((1, 8, 3), 1)] ## data2## data2\n",
        "\n",
        "X = [(d[0], d[1], d[2]) for d,_ in data]\n",
        "Y = [y for _, y in data]"
      ],
      "metadata": {
        "id": "TALfxTWufV8M"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "data = [((1, 5.1, 3.5), 0), ((1, 4.9, 3.0), 0), ((1, 4.7, 3.2), 0), ((1, 4.6, 3.1), 0), ((1, 5.0, 3.6), 0), ((1, 5.4, 3.9), 0), ((1, 4.6, 3.4), 0),\n",
        "         ((1, 5.0, 3.4), 0), ((1, 4.4, 2.9), 0), ((1, 4.9, 3.1), 0), ((1, 5.4, 3.7), 0), ((1, 4.8, 3.4), 0), ((1, 4.8, 3.0), 0), ((1, 4.3, 3.0), 0),\n",
        "         ((1, 5.8, 4.0), 0), ((1, 5.7, 4.4), 0), ((1, 5.4, 3.9), 0), ((1, 5.1, 3.5), 0), ((1, 5.7, 3.8), 0), ((1, 5.1, 3.8), 0), ((1, 5.4, 3.4), 0),\n",
        "         ((1, 5.1, 3.7), 0), ((1, 4.6, 3.6), 0), ((1, 5.1, 3.3), 0), ((1, 4.8, 3.4), 0), ((1, 5.0, 3.0), 0), ((1, 5.0, 3.4), 0), ((1, 5.2, 3.5), 0),\n",
        "         ((1, 5.2, 3.4), 0), ((1, 4.7, 3.2), 0), ((1, 4.8, 3.1), 0), ((1, 5.4, 3.4), 0), ((1, 5.2, 4.1), 0), ((1, 5.5, 4.2), 0), ((1, 4.9, 3.1), 0),\n",
        "         ((1, 5.0, 3.2), 0), ((1, 5.5, 3.5), 0), ((1, 4.9, 3.6), 0), ((1, 4.4, 3.0), 0), ((1, 5.1, 3.4), 0), ((1, 5.0, 3.5), 0), ((1, 4.5, 2.3), 0),\n",
        "         ((1, 4.4, 3.2), 0), ((1, 5.0, 3.5), 0), ((1, 5.1, 3.8), 0), ((1, 4.8, 3.0), 0), ((1, 5.1, 3.8), 0), ((1, 4.6, 3.2), 0), ((1, 5.3, 3.7), 0),\n",
        "         ((1, 5.0, 3.3), 0), ((1, 7.0, 3.2), 1), ((1, 6.4, 3.2), 1), ((1, 6.9, 3.1), 1), ((1, 5.5, 2.3), 1), ((1, 6.5, 2.8), 1), ((1, 5.7, 2.8), 1),\n",
        "         ((1, 6.3, 3.3), 1), ((1, 4.9, 2.4), 1), ((1, 6.6, 2.9), 1), ((1, 5.2, 2.7), 1), ((1, 5.0, 2.0), 1), ((1, 5.9, 3.0), 1), ((1, 6.0, 2.2), 1),\n",
        "         ((1, 6.1, 2.9), 1), ((1, 5.6, 2.9), 1), ((1, 6.7, 3.1), 1), ((1, 5.6, 3.0), 1), ((1, 5.8, 2.7), 1), ((1, 6.2, 2.2), 1), ((1, 5.6, 2.5), 1),\n",
        "         ((1, 5.9, 3.2), 1), ((1, 6.1, 2.8), 1), ((1, 6.3, 2.5), 1), ((1, 6.1, 2.8), 1), ((1, 6.4, 2.9), 1), ((1, 6.6, 3.0), 1), ((1, 6.8, 2.8), 1),\n",
        "         ((1, 6.7, 3.0), 1), ((1, 6.0, 2.9), 1), ((1, 5.7, 2.6), 1), ((1, 5.5, 2.4), 1), ((1, 5.5, 2.4), 1), ((1, 5.8, 2.7), 1), ((1, 6.0, 2.7), 1),\n",
        "         ((1, 5.4, 3.0), 1), ((1, 6.0, 3.4), 1), ((1, 6.7, 3.1), 1), ((1, 6.3, 2.3), 1), ((1, 5.6, 3.0), 1), ((1, 5.5, 2.5), 1), ((1, 5.5, 2.6), 1),\n",
        "         ((1, 6.1, 3.0), 1), ((1, 5.8, 2.6), 1), ((1, 5.0, 2.3), 1), ((1, 5.6, 2.7), 1), ((1, 5.7, 3.0), 1), ((1, 5.7, 2.9), 1), ((1, 6.2, 2.9), 1),\n",
        "         ((1, 5.1, 2.5), 1), ((1, 5.7, 2.8), 1), ((1, 6.3, 3.3), 2), ((1, 5.8, 2.7), 2), ((1, 7.1, 3.0), 2), ((1, 6.3, 2.9), 2), ((1, 6.5, 3.0), 2),\n",
        "         ((1, 7.6, 3.0), 2), ((1, 4.9, 2.5), 2), ((1, 7.3, 2.9), 2), ((1, 6.7, 2.5), 2), ((1, 7.2, 3.6), 2), ((1, 6.5, 3.2), 2), ((1, 6.4, 2.7), 2),\n",
        "         ((1, 6.8, 3.0), 2), ((1, 5.7, 2.5), 2), ((1, 5.8, 2.8), 2), ((1, 6.4, 3.2), 2), ((1, 6.5, 3.0), 2), ((1, 7.7, 3.8), 2), ((1, 7.7, 2.6), 2),\n",
        "         ((1, 6.0, 2.2), 2), ((1, 6.9, 3.2), 2), ((1, 5.6, 2.8), 2), ((1, 7.7, 2.8), 2), ((1, 6.3, 2.7), 2), ((1, 6.7, 3.3), 2), ((1, 7.2, 3.2), 2),\n",
        "         ((1, 6.2, 2.8), 2), ((1, 6.1, 3.0), 2), ((1, 6.4, 2.8), 2), ((1, 7.2, 3.0), 2), ((1, 7.4, 2.8), 2), ((1, 7.9, 3.8), 2), ((1, 6.4, 2.8), 2),\n",
        "         ((1, 6.3, 2.8), 2), ((1, 6.1, 2.6), 2), ((1, 7.7, 3.0), 2), ((1, 6.3, 3.4), 2), ((1, 6.4, 3.1), 2), ((1, 6.0, 3.0), 2), ((1, 6.9, 3.1), 2),\n",
        "         ((1, 6.7, 3.1), 2), ((1, 6.9, 3.1), 2), ((1, 5.8, 2.7), 2), ((1, 6.8, 3.2), 2), ((1, 6.7, 3.3), 2), ((1, 6.7, 3.0), 2), ((1, 6.3, 2.5), 2),\n",
        "         ((1, 6.5, 3.0), 2), ((1, 6.2, 3.4), 2), ((1, 5.9, 3.0), 2)]"
      ],
      "metadata": {
        "id": "Rx2pr-OBeBxL"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "np.random.seed(22)\n",
        "rangeValue = (3,10)\n",
        "sigmoid = lambda y: 1/(1+math.exp(-y))\n",
        "classify = lambda y: 1 if y>0.5 else 0\n",
        "#model = [random.random(),random.random(),random.random()]\n",
        "model=(0.001,0.001,0.001)\n",
        "alpha = 0.1\n",
        "alpha1 = 0.1 ## data 2 alpha\n",
        "alpha2 = 0.1\n",
        "\n",
        "X = [(d[0], d[1], d[2]) for d,_ in data]\n",
        "Y = [y for _, y in data]\n",
        "\n",
        "dataX1 = [x[1] for x,y in data]\n",
        "dataX2 = [x[2] for x,y in data]\n",
        "\n",
        "negatives, positives = Separate(data)\n",
        "dataX1pos = [x[1] for x,y in positives]\n",
        "dataX2pos = [x[2] for x,y in positives]\n",
        "dataX1neg = [x[1] for x,y in negatives]\n",
        "dataX2neg = [x[2] for x,y in negatives]\n",
        "\n",
        "iteration = 0\n",
        "plt.plot(dataX1pos, dataX2pos, \"g+\")\n",
        "plt.plot(dataX1neg, dataX2neg, \"r+\")\n",
        "plt.show()\n",
        "YpredLine = [ Fx2(model, X) for X in zip([1]*(rangeValue[1]-rangeValue[0]+1), range(rangeValue[0], rangeValue[1]), [0]*(rangeValue[1]-rangeValue[0]+1)) ]\n",
        "plt.plot(dataX1pos, dataX2pos, \"g+\")\n",
        "plt.plot(dataX1neg, dataX2neg, \"ro\")\n",
        "plt.plot(range(rangeValue[0], rangeValue[1]), YpredLine, \"g\")\n",
        "plt.show()\n",
        "print(iteration, model)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 863
        },
        "id": "FQCl6dKRepuB",
        "outputId": "1f3b051b-37ae-4554-a255-22c49db5a8dc"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0 (0.001, 0.001, 0.001)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "iteration = 0\n",
        "totalIterations = 100\n",
        "printIterations = 10\n",
        "for _ in range(totalIterations):\n",
        "  yPredicted = [sigmoid(F(model, x)) for x in X]\n",
        "  if iteration % printIterations  == 0:\n",
        "    YpredLine = [ Fx2(model, X) for X in zip([1]*(rangeValue[1]-rangeValue[0]+1), range(rangeValue[0], rangeValue[1]), [0]*(rangeValue[1]-rangeValue[0]+1)) ]\n",
        "    plt.plot(dataX1pos, dataX2pos, \"g+\")\n",
        "    plt.plot(dataX1neg, dataX2neg, \"ro\")\n",
        "    plt.plot(range(rangeValue[0], rangeValue[1]), YpredLine, \"g\")\n",
        "    plt.show()\n",
        "    print(iteration, model)\n",
        "  Error = sum([(r-y)**2.0 for r,y in zip(Y, yPredicted)])\n",
        "  if (iteration+1)%1000==0:\n",
        "    print(\"Iteration: \", iteration, \"Error=\", Error, model)\n",
        "    #plt.plot(dataX1, yPredicted, \"r+\")\n",
        "    #plt.plot(dataX1, Y, \"g+\")\n",
        "    #plt.show()\n",
        "  deltaX0 = 1/len(Y)*sum( [(-2*(r-y)*sigmoid(F(model, x))*(1-sigmoid(F(model, x)))*x[0]) for r,y,x in zip(Y, yPredicted, X)] )\n",
        "  deltaX1 = 1/len(Y)*sum( [(-2*(r-y)*sigmoid(F(model, x))*(1-sigmoid(F(model, x)))*x[1]) for r,y,x in zip(Y, yPredicted, X)] )\n",
        "  deltaX2 = 1/len(Y)*sum( [(-2*(r-y)*sigmoid(F(model, x))*(1-sigmoid(F(model, x)))*x[2]) for r,y,x in zip(Y, yPredicted, X)] )\n",
        "\n",
        "  model = [model[0]-alpha1*deltaX0, model[1]-alpha1*deltaX1, model[2]-alpha1*deltaX2]\n",
        "  iteration += 1"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "0pvKQRC1fjS8",
        "outputId": "fb6806e2-5b62-4b8b-f1ec-91bdeaf442c2"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0 (0.001, 0.001, 0.001)\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "10 [0.03719158389993168, 0.33858927562721547, 0.07036368358678491]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "20 [0.029914403688717985, 0.3793162229334939, 0.019248111736648265]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "30 [0.019524011778922813, 0.40239201707780475, -0.04195409941470878]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "40 [0.007641963959389207, 0.42250003806934117, -0.11012778372286583]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "50 [-0.005139394433525741, 0.44463107808987656, -0.18402587497150932]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "60 [-0.01850877771952353, 0.4705611398308249, -0.26267678119785925]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "70 [-0.03227362801826262, 0.5005732166937356, -0.3451479596756229]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "80 [-0.04628459841835359, 0.5343180400957924, -0.43046321523168807]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "90 [-0.0604088462387872, 0.5712029325870476, -0.517612531583876]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "iteration = 0\n",
        "totalIterations = 20000\n",
        "printIterations = 1000\n",
        "for _ in range(totalIterations):\n",
        "  yPredicted = [sigmoid(F(model, x)) for x in X]\n",
        "  Error = sum([(r-y)**2.0 for r,y in zip(Y, yPredicted)])\n",
        "  if iteration%printIterations==0:\n",
        "    print(\"Iteration: \", iteration, \"Error=\", Error, model)\n",
        "    #plt.plot(dataX1, yPredicted, \"r+\")\n",
        "    #plt.plot(dataX1, Y, \"g+\")\n",
        "    #plt.show()\n",
        "  deltaX0 = 1/len(Y)*sum( [(-2*(r-y)*sigmoid(F(model, x))*(1-sigmoid(F(model, x)))*x[0]) for r,y,x in zip(Y, yPredicted, X)] )\n",
        "  deltaX1 = 1/len(Y)*sum( [(-2*(r-y)*sigmoid(F(model, x))*(1-sigmoid(F(model, x)))*x[1]) for r,y,x in zip(Y, yPredicted, X)] )\n",
        "  deltaX2 = 1/len(Y)*sum( [(-2*(r-y)*sigmoid(F(model, x))*(1-sigmoid(F(model, x)))*x[2]) for r,y,x in zip(Y, yPredicted, X)] )\n",
        "\n",
        "  model = [model[0]-alpha1*deltaX0, model[1]-alpha1*deltaX1, model[2]-alpha1*deltaX2]\n",
        "  iteration += 1"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kfCMP6OEju_7",
        "outputId": "5c948841-2006-4c66-9db8-cd4817d71bd8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteration:  0 Error= 87.82913950000415 [-0.07452880484648727, 0.6105479898490707, -0.6056162234294623]\n",
            "Iteration:  1000 Error= 56.91390454757567 [-0.7127834309883042, 2.5436355075081667, -3.9517633713830533]\n",
            "Iteration:  2000 Error= 54.58094621640255 [-0.9824495975364035, 3.176529756801453, -4.97016700892917]\n",
            "Iteration:  3000 Error= 53.669568512396914 [-1.1743558301591552, 3.577039472485061, -5.606000330876993]\n",
            "Iteration:  4000 Error= 53.16691204711841 [-1.3290638665964698, 3.87554150446739, -6.075463112286811]\n",
            "Iteration:  5000 Error= 52.842529142486825 [-1.4611929763155678, 4.115666123072972, -6.4502890994940705]\n",
            "Iteration:  6000 Error= 52.61328822820388 [-1.5778649239225424, 4.317625115927819, -6.763541242992173]\n",
            "Iteration:  7000 Error= 52.441369683073916 [-1.6831493087389082, 4.492523865319226, -7.03331555552532]\n",
            "Iteration:  8000 Error= 52.306918112719195 [-1.779617829215342, 4.647154547065553, -7.270643417533447]\n",
            "Iteration:  9000 Error= 52.19843461477117 [-1.8690129151037262, 4.785990720479784, -7.4827693269627895]\n",
            "Iteration:  10000 Error= 52.1087646056229 [-1.9525772151803837, 4.912143611810118, -7.674718291608297]\n",
            "Iteration:  11000 Error= 52.0332055964812 [-2.031232487970548, 5.02786920900812, -7.8501251188289505]\n",
            "Iteration:  12000 Error= 51.968529880943834 [-2.105684087527304, 5.134858336390987, -8.011707844480233]\n",
            "Iteration:  13000 Error= 51.91244276923736 [-2.176485582297717, 5.234412716402873, -8.161554553358368]\n",
            "Iteration:  14000 Error= 51.86326473192246 [-2.2440806021327036, 5.3275570497652875, -8.30130565485165]\n",
            "Iteration:  15000 Error= 51.819736017848925 [-2.308830986073344, 5.415113220896581, -8.432274368300837]\n",
            "Iteration:  16000 Error= 51.7808917813422 [-2.3710363274405095, 5.497751070054729, -8.555529034254942]\n",
            "Iteration:  17000 Error= 51.74597958602398 [-2.4309479177685374, 5.576024117725662, -8.671950946003907]\n",
            "Iteration:  18000 Error= 51.71440332890651 [-2.48877892941919, 5.6503953141248004, -8.78227597532652]\n",
            "Iteration:  19000 Error= 51.68568416661116 [-2.5447120039717706, 5.72125599242118, -8.887125170542024]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "model = [-2.539199432207093, 5.714317984749782, -8.876870949270439]\n",
        "YpredLine = [ Fx2(model, X) for X in zip([1]*(rangeValue[1]-rangeValue[0]+1), range(rangeValue[0], rangeValue[1]), [0]*(rangeValue[1]-rangeValue[0]+1)) ]\n",
        "plt.plot(dataX1pos, dataX2pos, \"g+\")\n",
        "plt.plot(dataX1neg, dataX2neg, \"ro\")\n",
        "plt.plot(range(rangeValue[0], rangeValue[1]), YpredLine, \"g\")\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hnMOvik-kgQq",
        "outputId": "f9ca86e9-c1f5-4b8d-f32e-22729906b02f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Multi Dimensional Linear Case"
      ],
      "metadata": {
        "id": "oMoA33Ipi0Kw"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "eps = 0\n",
        "coef = (1, 2, 3)\n",
        "w = (0, 0, 0)\n",
        "Noise = lambda eps: np.random.random()*eps - (eps/2)\n",
        "\n",
        "\n",
        "Fa = lambda w, x: w[0] + w[1]*x[0] + w[2]*x[1]\n",
        "X = [(-7, -3), (-2, 3), (1, 8), (3, 2), (7, -5)]\n",
        "Y = [round(Fa(coef, x) + Noise(eps),2) for x in X]\n",
        "print (Y)\n",
        "\n",
        "X1 = [x1 for (x1, x2) in X]\n",
        "plt.plot(X1,Y,'.')\n",
        "Hxs = [Fa(coef, x) for x in X]\n",
        "\n",
        "plt.plot(X1, Y, '.')\n",
        "plt.plot(X1, Hxs, '-', color=\"green\")\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1ELaZmg2izqK",
        "outputId": "228cca4e-bdd6-467a-e647-acb988b2241c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[-22.0, 6.0, 27.0, 13.0, 0.0]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "SquaredErrorA = lambda X, Y, w : sum([(y-Fa(w, x))**2 for x,y in zip(X,Y)])"
      ],
      "metadata": {
        "id": "9S-1xpc-k_vG"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "ws= [(0,0,0), (0,1,0), (1,0,1), (1,1,1), (1,2,3)]\n",
        "for model in ws:\n",
        "  print (model, SquaredErrorA(X, Y, model))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4VlhLL6pkvHD",
        "outputId": "023bca2c-6468-4765-9b68-3ce88f95cbbf"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(0, 0, 0) 1418.0\n",
            "(0, 1, 0) 1114.0\n",
            "(1, 0, 1) 844.0\n",
            "(1, 1, 1) 532.0\n",
            "(1, 2, 3) 0.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## Average Gradients\n",
        "w = [0,0,0]\n",
        "data = [(x,y) for x, y in zip(X,Y)]\n",
        "print(data)\n",
        "Gradients = np.array([ ((y-Fa(w,x)), (y-Fa(w,x))*x[0], (y-Fa(w,x))*x[1]   ) for (x, y) in data ])\n",
        "print(Gradients)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fVLqbnU6lp2Z",
        "outputId": "01548d47-6976-477e-9363-529e8bc16e5e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[((-7, -3), -22.0), ((-2, 3), 6.0), ((1, 8), 27.0), ((3, 2), 13.0), ((7, -5), 0.0)]\n",
            "[[-22. 154.  66.]\n",
            " [  6. -12.  18.]\n",
            " [ 27.  27. 216.]\n",
            " [ 13.  39.  26.]\n",
            " [  0.   0.  -0.]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "GradientBatch = np.array([0.0, 0.0, 0.0])\n",
        "for g in Gradients:\n",
        "  GradientBatch += g\n",
        "GradientBatch = GradientBatch/len(Gradients)\n",
        "print (GradientBatch)\n",
        "for g in GradientBatch:\n",
        "  print (f\"{g=}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "w72fUWdnoGlN",
        "outputId": "06c9f4f5-67e3-43cd-9e8c-9741662c1eef"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[ 4.8 41.6 65.2]\n",
            "g=4.8\n",
            "g=41.6\n",
            "g=65.2\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "learningRate = 0.1\n",
        "wNew = np.add(w, GradientBatch*learningRate)\n",
        "print (wNew)\n",
        "print (w)\n",
        "print (SquaredErrorA(X, Y, (0,0,0)))\n",
        "print (w, SquaredErrorA(X, Y, w))\n",
        "for (l, model) in [(learningRate, np.add(w, GradientBatch*learningRate)) for learningRate in (0.01, 0.1, 1.0)]:\n",
        "  print (l, model, SquaredErrorA(X, Y, model))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vFn152UXoOn7",
        "outputId": "f236999c-f0b2-4083-fd09-1fa2b27e5171"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[0.48 4.16 6.52]\n",
            "[0, 0, 0]\n",
            "1418.0\n",
            "[0, 0, 0] 1418.0\n",
            "0.01 [0.048 0.416 0.652] 881.2543840000001\n",
            "0.1 [0.48 4.16 6.52] 1785.1984000000007\n",
            "1.0 [ 4.8 41.6 65.2] 578555.44\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Algorithm Test\n",
        "learningRate = 0.01\n",
        "w = [0,0,0]\n",
        "data = [(x,y) for x, y in zip(X, Y)]\n",
        "Iterations = 0\n",
        "print (f\"{Iterations=}, {w=}  {SquaredErrorA(X, Y, w)=}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "uY0iNUYMpU1p",
        "outputId": "45e01537-dc8a-4350-9e40-a51b113adbe4"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iterations=0, w=[0, 0, 0]  SquaredErrorA(X, Y, w)=1418.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "Iterations = Iterations + 1\n",
        "GradientBatch = np.array([0.0, 0.0, 0.0])\n",
        "Gradients = np.array([ ((y-Fa(w,x)), (y-Fa(w,x))*x[0], (y-Fa(w,x))*x[1]   ) for (x, y) in data ])\n",
        "for g in Gradients:\n",
        "  GradientBatch += g\n",
        "GradientBatch = GradientBatch/len(Gradients)\n",
        "print (GradientBatch)\n",
        "w = np.add(w, GradientBatch*learningRate)\n",
        "print (f\"{Iterations=}, {w=}  {SquaredErrorA(X, Y, w)=}\")\n",
        "#print ( {SquaredError(X, Y, w)=})"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "yATNWsTDplc4",
        "outputId": "3edd2519-d270-47e3-b887-8702648b9e89"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[ 4.8 41.6 65.2]\n",
            "Iterations=1, w=array([0.048, 0.416, 0.652])  SquaredErrorA(X, Y, w)=881.2543840000001\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Quiz 1"
      ],
      "metadata": {
        "id": "R8BCz45LwkFs"
      }
    },
    {
      "cell_type": "markdown",
      "source": [],
      "metadata": {
        "id": "_7g5yAjxxxCZ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "Y = [-13, -3, 3, 7, 15]\n",
        "y2 = [y**2 for y in Y ]\n",
        "y2Sum = sum(y2)\n",
        "print (f\"{y2=}, {y2Sum=}, {y2Sum/len(y2)=}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tx-0YLzrwmdW",
        "outputId": "6ca0f654-3aa5-4432-a3d6-e7d79b28b5c8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "y2=[169, 9, 9, 49, 225], y2Sum=461, y2Sum/len(y2)=92.2\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "trainingData = [((1, -7), -13), ((1, -2), -3), ((1, 1), 3), ((1, 3), 7), ((1, 7), 15)]\n",
        "y2 = [(y-x[1])**2 for (x,y) in trainingData ]\n",
        "y2Sum = sum(y2)\n",
        "print (f\"{y2=}, {y2Sum=}, {y2Sum/len(y2)=}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ldEfCDc1xz-4",
        "outputId": "854c3b4c-62a2-4ed9-f396-47f3e1208071"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "y2=[36, 1, 4, 16, 64], y2Sum=121, y2Sum/len(y2)=24.2\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "trainingData = [((1, -7), -13), ((1, -2), -3), ((1, 1), 3), ((1, 3), 7), ((1, 7), 15)]\n",
        "y2 = [(y-x[0])**2 for (x,y) in trainingData ]\n",
        "y2Sum = sum(y2)\n",
        "print (f\"{y2=}, {y2Sum=}, {y2Sum/len(y2)=}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AR4bshsa0oKj",
        "outputId": "a89a95d8-9f2c-48a1-812b-765a3e0274b5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "y2=[196, 16, 4, 36, 196], y2Sum=448, y2Sum/len(y2)=89.6\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "trainingData = [((1, -7), -13), ((1, -2), -3), ((1, 1), 3), ((1, 3), 7), ((1, 7), 15)]\n",
        "y2 = [(y-(x[0]+x[1]))**2 for (x,y) in trainingData ]\n",
        "y2Sum = sum(y2)\n",
        "print (f\"{y2=}, {y2Sum=}, {y2Sum/len(y2)=}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "htPTUNjw1Oec",
        "outputId": "bd7e099c-db64-4097-f555-f9e9db8ff0a2"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "y2=[49, 4, 1, 9, 49], y2Sum=112, y2Sum/len(y2)=22.4\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "learningRate = 0.01\n",
        "w=(0,0)\n",
        "trainingData = [((1, -7), -13), ((1, -2), -3), ((1, 1), 3), ((1, 3), 7), ((1, 7), 15)]\n",
        "gradW0 = [ (y-(w[0]*x[0]+w[1]*x[1])) for (x,y) in trainingData ]\n",
        "gradW1 = [((y-(w[0]*x[0]+w[1]*x[1]))*x[1]) for (x,y) in trainingData ]\n",
        "gradW0sum = sum(gradW0)\n",
        "gradW1sum = sum(gradW1)\n",
        "print (f\"{gradW1=}\")\n",
        "print (f\"{gradW0sum=}, {gradW0sum/len(trainingData)=}, {gradW0sum/len(trainingData)*learningRate=}\")\n",
        "print (f\"{gradW1sum=}, {gradW1sum/len(trainingData)=}, {gradW1sum/len(trainingData)*learningRate=}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mP1hwyo_1y2t",
        "outputId": "988eccc7-e3c7-406e-c920-72670d6f9c1e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "gradW1=[91, 6, 3, 21, 105]\n",
            "gradW0sum=9, gradW0sum/len(trainingData)=1.8, gradW0sum/len(trainingData)*learningRate=0.018000000000000002\n",
            "gradW1sum=226, gradW1sum/len(trainingData)=45.2, gradW1sum/len(trainingData)*learningRate=0.452\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "learningRate = 0.001\n",
        "w=(0.0018,0.0452)\n",
        "trainingData = [((1, -7), -13), ((1, -2), -3), ((1, 1), 3), ((1, 3), 7), ((1, 7), 15)]\n",
        "Errors = [ (y-(w[0]*x[0]+w[1]*x[1]))**2 for (x,y) in trainingData ]\n",
        "print( F\"{sum(Errors)=}, {Errors=}\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "I-sknacG7b0A",
        "outputId": "f9d82bc2-005d-4cfc-94af-a2935995ef4e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "sum(Errors)=440.76636212, Errors=[160.91937316, 8.47624996, 8.720208999999999, 47.09527875999999, 215.55525124000002]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "learningRate = 0.01\n",
        "w=(0.018,0.452)\n",
        "trainingData = [((1, -7), -13), ((1, -2), -3), ((1, 1), 3), ((1, 3), 7), ((1, 7), 15)]\n",
        "Errors = [ (y-(w[0]*x[0]+w[1]*x[1]))**2 for (x,y) in trainingData ]\n",
        "print( F\"{sum(Errors)=}, {Errors=}\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "z03u8Jq68OvK",
        "outputId": "50c594a9-d8ba-48b9-e3b5-115fd10159e2"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "sum(Errors)=279.28821199999993, Errors=[97.10131599999998, 4.468996, 6.400899999999999, 31.651875999999994, 139.665124]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "learningRate = 0.01\n",
        "w=(0.18,4.52)\n",
        "trainingData = [((1, -7), -13), ((1, -2), -3), ((1, 1), 3), ((1, 3), 7), ((1, 7), 15)]\n",
        "Errors = [ (y-(w[0]*x[0]+w[1]*x[1]))**2 for (x,y) in trainingData ]\n",
        "print( F\"{sum(Errors)=}, {Errors=}\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gqUo58rj8dfy",
        "outputId": "23fa0ad8-dfef-4a1a-e1a4-108332d097ee"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "sum(Errors)=706.3411999999998, Errors=[340.7715999999999, 34.33959999999999, 2.8899999999999975, 45.42759999999998, 282.9123999999999]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "learningRate = 0.01\n",
        "Activation = lambda z: 1/(1+math.exp(-z))\n",
        "w=(1,1)\n",
        "print (Activation(0))\n",
        "trainingData = [((1, -7), 0),  ((1, -2), 0), ((1, 1), 1),  ((1, 3), 1),  ((1, 7), 1)]\n",
        "Errors = [ (y-Activation(w[0]*x[0]+w[1]*x[1]))**2 for (x,y) in trainingData ]\n",
        "print( F\"{sum(Errors)=}, {sum(Errors)/len(Errors)=}, {Errors=}, \")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XzXvPY0n8uIE",
        "outputId": "b62c0b9f-dc00-4687-fb45-fb3235e01f48"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.5\n",
            "sum(Errors)=0.0868685548209095, sum(Errors)/len(Errors)=0.017373710964181898, Errors=[6.1138652747265155e-06, 0.07232948812851325, 0.01420933661861107, 0.00032350374880044124, 1.124597100038127e-07], \n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "w=(1,1)\n",
        "x=(1,-7)\n",
        "Activation(w[0]*x[0]+w[1]*x[1])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BME1F1il-DLQ",
        "outputId": "51353a03-60e9-4eac-98da-da6fb02a33c7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.0024726231566347743"
            ]
          },
          "metadata": {},
          "execution_count": 141
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Quiz 1"
      ],
      "metadata": {
        "id": "kHpPHXYi8YRN"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "Range = lambda x, p: (round(x-(10**-p)/2,p+1), round(x,p+1), round(x+(10**-p)/2,p+1))\n",
        "Fq = lambda w, x: w[0]*x[0] + w[1]*x[1]\n",
        "SEq = lambda X, Y, w : sum([(y-Fq(w, x))**2 for x,y in zip(X,Y)])\n",
        "Agr = lambda X, Y, w : np.sum([ np.array([(y-Fq(w, x))*x[0], (y-Fq(w, x))*x[1] ])  for x,y in zip(X,Y)], axis=0) / len(Y)\n",
        "Agr2 = lambda X, Y, w : np.sum([ np.array([2*(y-Fq(w, x))*x[0], 2*(y-Fq(w, x))*x[1] ])  for x,y in zip(X,Y)], axis=0) / len(Y)\n",
        "#trainingData = [((1, -7), -13), ((1, -2), -3), ((1, 1), 3), ((1, 3), 7), ((1, 7), 15)]\n",
        "trainingData = ((1, -10), -19), ((1, -3), -5), ((1, 0), 1), ((1, 3), 7), ((1, 10), 21)\n",
        "X = [x for x,y in trainingData]\n",
        "Y = [y for x,y in trainingData]\n",
        "\n",
        "print (F\"{SEq(X, Y, (1,2))=}\")\n",
        "\n",
        "w1=(0,0)\n",
        "w2=(0,1)\n",
        "w3=(1,0)\n",
        "w4=(1,1)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "EEXjb6el8ZpL",
        "outputId": "ce3677f7-8b5e-4e73-b2ef-59a9c7bf9920"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "SEq(X, Y, (1,2))=0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "p=1\n",
        "Wseq = SEq(X, Y, w1)\n",
        "print (f\"{w1=}: {Wseq=} / {Range(Wseq, p)=}\")\n",
        "\n",
        "Wseq = SEq(X, Y, w2)\n",
        "print (f\"{w2=}: {Wseq=} / {Range(Wseq, p)=}\")\n",
        "\n",
        "Wseq = SEq(X, Y, w3)\n",
        "print (f\"{w3=}: {Wseq=} / {Range(Wseq, p)=}\")\n",
        "\n",
        "Wseq = SEq(X, Y, w4)\n",
        "print (f\"{w4=}: {Wseq=} / {Range(Wseq, p)=}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "a5gioGBC8sQe",
        "outputId": "a4cfba54-5e11-46d8-df80-7f3a427b8aba"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "w1=(0, 0): Wseq=877 / Range(Wseq, p)=(876.95, 877, 877.05)\n",
            "w2=(0, 1): Wseq=223 / Range(Wseq, p)=(222.95, 223, 223.05)\n",
            "w3=(1, 0): Wseq=872 / Range(Wseq, p)=(871.95, 872, 872.05)\n",
            "w4=(1, 1): Wseq=218 / Range(Wseq, p)=(217.95, 218, 218.05)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "LR =0.01\n",
        "g = Agr(X, Y, w1)\n",
        "p=3\n",
        "print(f\"{round(g[0]*LR,3)=} / {Range(g[0]*LR,p)=}\")\n",
        "print(f\"{round(g[1]*LR,3)=} / {Range(g[1]*LR,p)=}\")\n",
        "print(\"W/ 2\")\n",
        "g = Agr2(X, Y, w1)\n",
        "print(f\"{round(g[0]*LR,3)=} / {Range(g[0]*LR,p)=}\")\n",
        "print(f\"{round(g[1]*LR,3)=} / {Range(g[1]*LR,p)=}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Drg0pxqB-9LB",
        "outputId": "eba96424-0b3e-4a94-ea89-d839b078bfc5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "round(g[0]*LR,3)=0.01 / Range(g[0]*LR,p)=(0.0095, 0.01, 0.0105)\n",
            "round(g[1]*LR,3)=0.872 / Range(g[1]*LR,p)=(0.8715, 0.872, 0.8725)\n",
            "W/ 2\n",
            "round(g[0]*LR,3)=0.02 / Range(g[0]*LR,p)=(0.0195, 0.02, 0.0205)\n",
            "round(g[1]*LR,3)=1.744 / Range(g[1]*LR,p)=(1.7435, 1.744, 1.7445)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "LR =0.1\n",
        "g = Agr(X, Y, w1)\n",
        "p=2\n",
        "print(f\"{round(g[0]*LR,3)=} / {Range(g[0]*LR,p)=}\")\n",
        "print(f\"{round(g[1]*LR,3)=} / {Range(g[1]*LR,p)=}\")\n",
        "print(\"W/ 2\")\n",
        "g = Agr2(X, Y, w1)\n",
        "print(f\"{round(g[0]*LR,3)=} / {Range(g[0]*LR,p)=}\")\n",
        "print(f\"{round(g[1]*LR,3)=} / {Range(g[1]*LR,p)=}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0D75O9zqFSzE",
        "outputId": "488816c6-225a-4ff7-90e5-832577bb8610"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "round(g[0]*LR,3)=0.1 / Range(g[0]*LR,p)=(0.095, 0.1, 0.105)\n",
            "round(g[1]*LR,3)=8.72 / Range(g[1]*LR,p)=(8.715, 8.72, 8.725)\n",
            "W/ 2\n",
            "round(g[0]*LR,3)=0.2 / Range(g[0]*LR,p)=(0.195, 0.2, 0.205)\n",
            "round(g[1]*LR,3)=17.44 / Range(g[1]*LR,p)=(17.435, 17.44, 17.445)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "LR =0.001\n",
        "g = Agr(X, Y, w1)\n",
        "p=4\n",
        "print(f\"{round(g[0]*LR,3)=} / {Range(g[0]*LR,p)=}\")\n",
        "print(f\"{round(g[1]*LR,3)=} / {Range(g[1]*LR,p)=}\")\n",
        "print(\"W/ 2\")\n",
        "g = Agr2(X, Y, w1)\n",
        "print(f\"{round(g[0]*LR,3)=} / {Range(g[0]*LR,p)=}\")\n",
        "print(f\"{round(g[1]*LR,3)=} / {Range(g[1]*LR,p)=}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8eTI4fn0FYOy",
        "outputId": "ca1e1716-23d3-49aa-d25a-c0f1024115df"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "round(g[0]*LR,3)=0.001 / Range(g[0]*LR,p)=(0.00095, 0.001, 0.00105)\n",
            "round(g[1]*LR,3)=0.087 / Range(g[1]*LR,p)=(0.08715, 0.0872, 0.08725)\n",
            "W/ 2\n",
            "round(g[0]*LR,3)=0.002 / Range(g[0]*LR,p)=(0.00195, 0.002, 0.00205)\n",
            "round(g[1]*LR,3)=0.174 / Range(g[1]*LR,p)=(0.17435, 0.1744, 0.17445)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Quiz 1b"
      ],
      "metadata": {
        "id": "am5bHk4iL4WU"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "G = lambda xIn: 1/(1+np.e**(-xIn))\n",
        "SEqg = lambda X, Y, w : sum([(y-G(Fq(w, x)))**2 for x,y in zip(X,Y)])\n",
        "\n",
        "trainingData = [((1, 7),0), ((1, 2),0), ((1, -11),1),  ((1, -33),1),  ((1, -77),1)]\n",
        "X = [x for x,y in trainingData]\n",
        "Y = [y for x,y in trainingData]\n",
        "\n",
        "wg1 = (1,2)"
      ],
      "metadata": {
        "id": "l434D8CzMAuU"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "p=1\n",
        "Wseqg = SEqg(X, Y, wg1)\n",
        "print (f\"{w1=}: {Wseqg=} / {Range(Wseqg, p)=}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8sH-eE5eMqJJ",
        "outputId": "e52d8b4f-8f9d-475c-fd0c-61fd1efcb564"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "w1=(0, 0): Wseqg=4.986658479084053 / Range(Wseqg, p)=(4.94, 4.99, 5.04)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Midterm Notes"
      ],
      "metadata": {
        "id": "6aD4fMf87Jmd"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "F = lambda w, x: w[0]*x[0] + w[1]*x[1]\n",
        "SquaredError = lambda X, Y, w : sum([(y-F(w, x))**2 for x,y in zip(X,Y)])\n",
        "sigmoid = lambda z : 1/(1+math.e**-z)"
      ],
      "metadata": {
        "id": "IzLuF2Ok7MoW"
      },
      "execution_count": 23,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "data = [((1, -10), -19), ((1, -3), -5), ((1, 0), 1), ((1, 3), 7), ((1, 10), 21)]\n",
        "model = (0,0)\n",
        "Y = [y for x,y in data]\n",
        "X = [x for x,y, in data]\n",
        "pred = [F(model, x) for x, y in zip(X, Y)]\n",
        "difs = [y-F(model, x) for x, y in zip(X, Y)]\n",
        "sDifs = [(y-F(model, x))**2 for x, y in zip(X, Y)]\n",
        "print(f\"{X=}, {Y=}, {pred=}\")\n",
        "print(f\"{difs=}, {sDifs=}, {sum(sDifs)=}\")\n",
        "\n",
        "grad_w0 = [y-F(model, x) for x, y in zip(X, Y)]\n",
        "grad_w1 = [(y-F(model, x))*x[1] for x, y in zip(X, Y)]\n",
        "print(f\"{grad_w0=}, {sum(grad_w0)/len(grad_w0)=}\")\n",
        "print(f\"{grad_w1=}, {sum(grad_w1)/len(grad_w1)=}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "z5DgN2GG72TS",
        "outputId": "2e70cc3e-35b5-48cb-bfbb-8f79ae6bf9fa"
      },
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "X=[(1, -10), (1, -3), (1, 0), (1, 3), (1, 10)], Y=[-19, -5, 1, 7, 21], pred=[0, 0, 0, 0, 0]\n",
            "difs=[-19, -5, 1, 7, 21], sDifs=[361, 25, 1, 49, 441], sum(sDifs)=877\n",
            "grad_w0=[-19, -5, 1, 7, 21], sum(grad_w0)/len(grad_w0)=1.0\n",
            "grad_w1=[190, 15, 0, 21, 210], sum(grad_w1)/len(grad_w1)=87.2\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "SquaredError = lambda X, Y, w : sum([(y-sigmoid(F(w, x)))**2 for x,y in zip(X,Y)])\n",
        "X= [(1, 7), (1, 2), (1, -11),  (1, -33),  (1, -77) ]\n",
        "Y = [0, 0, 1, 1, 1]\n",
        "model = (1,2)\n",
        "print(SquaredError(X, Y, model))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "LDSr1r14Aq-I",
        "outputId": "50f31504-7ecd-4173-8cb8-7a84846929fc"
      },
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "4.986658479084053\n"
          ]
        }
      ]
    }
  ]
}