Notebooks/Spark-Example-20b-Imbalanced-Classes.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistic regression with Class weighting implementation\n",
    "Date: 10/01/2022"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import findspark\n",
    "findspark.init()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from __future__ import print_function\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from sklearn.datasets import make_blobs\n",
    "from matplotlib import pyplot\n",
    "from pandas import DataFrame\n",
    "import matplotlib.cm as cm\n",
    "from pyspark import SparkContext\n",
    "from pyspark.sql import SparkSession\n",
    "sc = SparkContext(\"local\")\n",
    "spark = SparkSession.builder.getOrCreate()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate Data with make_blobs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[99000, 1000]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_feature = 2 # the number of features\n",
    "n_components = 2 # the number of clusters\n",
    "\n",
    "max_iter = 4 # max iterations \n",
    "n=100000 # the number of total samples\n",
    "\n",
    "ratio_positive = 0.01 # The classes ratio. We are crating a very imbalanced dataset.\n",
    "n_samples = [int(n*(1-ratio_positive)), int(n*ratio_positive)]\n",
    "n_components = [1,1]\n",
    "n_samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# generate isotropic Gaussian blobs (data from mixture Gaussian distributions)\n",
    "X, y = make_blobs(n_samples=n_samples, # the number of total samples\n",
    "                  centers=None, # the number of clusters\n",
    "                  n_features=n_feature, # the number of features\n",
    "                  cluster_std = 1.5, # the std of each cluster\n",
    "                  random_state=2) # 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# scatter plot, data points annotated by different colors\n",
    "df = DataFrame(dict(x=X[:,0], y=X[:,1], label=y))\n",
    "cluster_name = set(y)\n",
    "colors = dict(zip(cluster_name, cm.rainbow(np.linspace(0, 1, len(cluster_name)))))\n",
    "fig, ax = pyplot.subplots()\n",
    "grouped = df.groupby('label')\n",
    "for key, group in grouped:\n",
    "    group.plot(ax=ax, kind='scatter', x='x', y='y', label=key, color=colors[key].reshape(1,-1))\n",
    "pyplot.title('Original 2D Data from {} Clusters'.format(n_components))\n",
    "pyplot.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Class Weights Calculation\n",
    "In machine learning, it is often important to consider class imbalances when training a model. Class imbalance occurs when the number of samples in different classes of the target variable varies significantly. This can lead to biased model performance, as the model may prioritize the majority class and overlook the minority class. To address this issue, one approach is to assign weights to each class based on their sample sizes.\n",
    "\n",
    "## Class Weights Calculation\n",
    "To calculate the weights of the classes, we can use the following formula:\n",
    "\n",
    "$$w_j = \\frac{n_{\\text{samples}}}{n_{\\text{classes}} \\times n_{\\text{samples}_j}}$$\n",
    "\n",
    "Where:\n",
    "- $w_j$ is the weight for each class, with 'j' representing the class.\n",
    "- $n_{\\text{samples}}$ is the total number of samples or rows in the dataset.\n",
    "- $n_{\\text{classes}}$ is the total number of unique classes in the target.\n",
    "- $n_{\\text{samples}_j}$ is the total number of rows of the respective class.\n",
    "\n",
    "The intuition behind this formula is to assign higher weights to classes with fewer samples, thus giving them more importance during model training.\n",
    "\n",
    "## Example\n",
    "Let's consider a dataset with the following information:\n",
    "- Total number of samples ($n_{\\text{samples}}$): 1000\n",
    "- Total number of classes ($n_{\\text{classes}}$): 5\n",
    "- Number of samples for each class ($n_{\\text{samples}_j}$):\n",
    "    - Class A: 200\n",
    "    - Class B: 300\n",
    "    - Class C: 150\n",
    "    - Class D: 100\n",
    "    - Class E: 250\n",
    "\n",
    "Using the formula, we can calculate the weights for each class:\n",
    "\n",
    "$$w_{\\text{Class A}} = \\frac{1000}{5 \\times 200} = 1$$\n",
    "$$w_{\\text{Class B}} = \\frac{1000}{5 \\times 300} = 0.333$$\n",
    "$$w_{\\text{Class C}} = \\frac{1000}{5 \\times 150} = 1.333$$\n",
    "$$w_{\\text{Class D}} = \\frac{1000}{5 \\times 100} = 2$$\n",
    "$$w_{\\text{Class E}} = \\frac{1000}{5 \\times 250} = 0.8$$\n",
    "\n",
    "## Conclusion\n",
    "Calculating class weights is a useful technique to handle class imbalances in machine learning. By assigning higher weights to classes with fewer samples, we ensure that the model gives equal importance to each class during training. This helps in improving the model's performance on minority classes and overall predictive accuracy."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Class Weights Calculation for Binary Classification\n",
    "In binary classification, class imbalance refers to a situation where the number of samples in one class significantly exceeds the number of samples in the other class. This can lead to biased model performance, as the model may struggle to properly learn and classify the minority class. To address this issue, assigning appropriate weights to the classes can help balance the impact of each class during model training.\n",
    "\n",
    "## Class Weights Calculation\n",
    "To calculate the weights of the classes, we can use the following formula:\n",
    "\n",
    "$$w_j = \\frac{n_{\\text{samples}}}{n_{\\text{classes}} \\times n_{\\text{samples}_j}}$$\n",
    "\n",
    "Where:\n",
    "- $w_j$ is the weight for each class, with 'j' representing the class.\n",
    "- $n_{\\text{samples}}$ is the total number of samples or rows in the dataset.\n",
    "- $n_{\\text{classes}}$ is the total number of unique classes in the target.\n",
    "- $n_{\\text{samples}_j}$ is the total number of rows of the respective class.\n",
    "\n",
    "The intuition behind this formula is to assign higher weights to classes with fewer samples, thus giving them more importance during model training.\n",
    "\n",
    "## Example\n",
    "Let's consider a binary classification dataset with the following information:\n",
    "- Total number of samples $n_{\\text{samples}}= 1000$\n",
    "- Number of unique classes $n_{\\text{classes}} = 2$\n",
    "- Number of samples in the negative class $n_{\\text{samples}_0}= 800$\n",
    "- Number of samples in the positive class $n_{\\text{samples}_1}= 200$\n",
    "\n",
    "Using the formula, we can calculate the class weights:\n",
    "\n",
    "$$w_0 = \\frac{1000}{2*800} = 0.625$$\n",
    "$$w_1 = \\frac{1000}{2*200} = 2.5$$\n",
    "\n",
    "In this case, we assign a higher weight of 2.5 to the positive class (class 1) and a lower weight of 0.625 to the negative class (class 0). This ensures that the model gives equal importance to both classes during training, thus improving its performance on the minority class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5050505050505051 50.0\n"
     ]
    }
   ],
   "source": [
    "w0 = n/(2*n_samples[0])\n",
    "w1 = n/(2*n_samples[1])\n",
    "print(w0,w1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Prepare the data in RDD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(0, array([-3.02457665, -9.92809418,  1.        ]))]\n"
     ]
    }
   ],
   "source": [
    "# read X, y into rdd\n",
    "rdd_X = sc.parallelize(X)\n",
    "rdd_y = sc.parallelize(y)\n",
    "\n",
    "# split data into train and test\n",
    "# Add: map(lambda x: (x[0],np.append(x[1],1)))\n",
    "traindata, testdata = rdd_y.zip(rdd_X).randomSplit([0.8, 0.2], seed=12345)\n",
    "traindata.cache()\n",
    "\n",
    "traindata1 = traindata.map(lambda x: (x[0],np.append(x[1],1)))\n",
    "traindata1.cache()\n",
    "train_size = traindata1.count()\n",
    "print(traindata1.take(1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### The standard Logistic Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The standard version of the code\n",
    "def LogisticRegression_optimized(traindata=traindata,\n",
    "                       max_iteration = max_iter,\n",
    "                       learningRate = 0.01,\n",
    "                       regularization = 0.01,\n",
    "                       mini_batch_size = 512,\n",
    "                       tolerance = 10e-8,\n",
    "                       beta = 0.9,\n",
    "                       beta2 = 0.999,\n",
    "                       optimizer = 'SGD',  #optimizer: 'Momentum' / 'Adam' / 'Nesterov' / 'Adagrad' / 'RMSprop' / 'SGD' \n",
    "                       train_size=1\n",
    "                      ):\n",
    "\n",
    "    # initialization\n",
    "    prev_cost = 0\n",
    "    L_cost = []\n",
    "    prev_validation = 0\n",
    "    \n",
    "    parameter_size = len(traindata.take(1)[0][1])\n",
    "\n",
    "    np.random.seed(0)\n",
    "    parameter_vector = np.random.normal(0, 0.1, parameter_size)\n",
    "    momentum = np.zeros(parameter_size)\n",
    "    prev_mom = np.zeros(parameter_size)\n",
    "    second_mom = np.array(parameter_size)\n",
    "    gti = np.zeros(parameter_size)\n",
    "    epsilon = 10e-8\n",
    "    \n",
    "    for i in range(max_iteration):\n",
    "\n",
    "        bc_weights = parameter_vector\n",
    "        min_batch = traindata.sample(False, mini_batch_size / train_size, 1 + i)\n",
    "\n",
    "        res = min_batch.treeAggregate((np.zeros(parameter_size), 0, 0),\\\n",
    "              lambda x, y:(x[0]\\\n",
    "                          + (y[1]) * (-y[0] + (1/(np.exp(-np.dot(y[1], bc_weights))+1))),\\\n",
    "                          x[1] \\\n",
    "                          + y[0] * (-(np.dot(y[1], bc_weights))) \\\n",
    "                          + np.log(1 + np.exp(np.dot(y[1],bc_weights))),\\\n",
    "                          x[2] + 1),\n",
    "              lambda x, y:(x[0] + y[0], x[1] + y[1], x[2] + y[2]))        \n",
    "\n",
    "        # Optimise\n",
    "        gradients = res[0]\n",
    "        sum_cost = res[1]\n",
    "        num_samples = res[2]\n",
    "        cost =  sum_cost/num_samples + regularization * (np.square(parameter_vector).sum())\n",
    "\n",
    "        # calculate gradients\n",
    "        gradient_derivative = (1.0 / num_samples) * gradients + 2 * regularization * parameter_vector\n",
    "        \n",
    "        if optimizer == 'SGD':\n",
    "            parameter_vector = parameter_vector - learningRate * gradient_derivative\n",
    "\n",
    "        if optimizer =='Momentum':\n",
    "            momentum = beta * momentum + learningRate * gradient_derivative\n",
    "            parameter_vector = parameter_vector - momentum\n",
    "            \n",
    "        if optimizer == 'Nesterov':\n",
    "            parameter_temp = parameter_vector - beta * prev_mom\n",
    "            parameter_vector = parameter_temp - learningRate * gradient_derivative\n",
    "            prev_mom = momentum\n",
    "            momentum = beta * momentum + learningRate * gradient_derivative\n",
    "            \n",
    "        if optimizer == 'Adam':\n",
    "            momentum = beta * momentum + (1 - beta) * gradient_derivative\n",
    "            second_mom = beta2 * second_mom + (1 - beta2) * (gradient_derivative**2)\n",
    "            momentum_ = momentum / (1 - beta**(i + 1))\n",
    "            second_mom_ = second_mom / (1 - beta2**(i + 1))\n",
    "            parameter_vector = parameter_vector - learningRate * momentum_ / (np.sqrt(second_mom_) + epsilon)\n",
    "\n",
    "        if optimizer == 'Adagrad':\n",
    "            gti += gradient_derivative**2\n",
    "            adj_grad = gradient_derivative / (np.sqrt(gti)  + epsilon)\n",
    "            parameter_vector = parameter_vector - learningRate  * adj_grad\n",
    "        \n",
    "        if optimizer == 'RMSprop':\n",
    "            sq_grad = gradient_derivative**2\n",
    "            exp_grad = beta * gti / (i + 1) + (1 - beta) * sq_grad\n",
    "            parameter_vector = parameter_vector - learningRate / np.sqrt(exp_grad + epsilon) * gradient_derivative\n",
    "            gti += sq_grad\n",
    "            \n",
    "            \n",
    "        print(\"Iteration No.\", i, \" Cost=\", cost, \"graients=\",gradients)\n",
    "        \n",
    "        # Stop if the cost is not descreasing\n",
    "        if abs(cost - prev_cost) < tolerance:\n",
    "            print(\"cost - prev_cost: \" + str(cost - prev_cost))\n",
    "            break\n",
    "        prev_cost = cost\n",
    "        L_cost.append(cost)\n",
    "        \n",
    "    return parameter_vector, L_cost"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Weighted Logistic Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def LogisticRegression_weighted(traindata=traindata,\n",
    "                       max_iteration = max_iter,\n",
    "                       learningRate = 0.01,\n",
    "                       regularization = 0.01,\n",
    "                       mini_batch_size = 512,\n",
    "                       tolerance = 10e-8,\n",
    "                       beta = 0.9,\n",
    "                       beta2 = 0.999,\n",
    "                       optimizer = 'SGD',  #optimizer: 'Momentum' / 'Adam' / 'Nesterov' / 'Adagrad' / 'RMSprop' / 'SGD' \n",
    "                       train_size=1\n",
    "                      ):\n",
    "\n",
    "    # initialization\n",
    "    prev_cost = 0\n",
    "    L_cost = []\n",
    "    prev_validation = 0\n",
    "    \n",
    "    parameter_size = len(traindata.take(1)[0][1])\n",
    "    np.random.seed(0)\n",
    "    parameter_vector = np.random.normal(0, 0.1, parameter_size)\n",
    "    momentum = np.zeros(parameter_size)\n",
    "    prev_mom = np.zeros(parameter_size)\n",
    "    second_mom = np.array(parameter_size)\n",
    "    gti = np.zeros(parameter_size)\n",
    "    epsilon = 10e-8\n",
    "    \n",
    "    for i in range(max_iteration):\n",
    "\n",
    "        bc_weights = parameter_vector\n",
    "        min_batch = traindata.sample(False, mini_batch_size / train_size, 1 + i)\n",
    "  \n",
    "        # treeAggregate(vector of gradients, total_cost, number_of_samples)\n",
    "        # Calcualtion of positive class. Only the samples labeled as 1 are filtered and then  processed\n",
    "        res1 = min_batch.filter(lambda x: x[0]==1).treeAggregate(\n",
    "              (np.zeros(parameter_size), 0, 0),\n",
    "              lambda x, y:(x[0]+\\\n",
    "                          (y[1])*(-y[0]+(1/(np.exp(-np.dot(y[1], bc_weights))+1))),\\\n",
    "                          x[1]+\\\n",
    "                          y[0]*(-(np.dot(y[1], bc_weights)))+np.log(1 + np.exp(np.dot(y[1],bc_weights))),\\\n",
    "                          x[2] + 1),\n",
    "              lambda x, y:(x[0] + y[0], x[1] + y[1], x[2] + y[2])\n",
    "              )        \n",
    "        # Calcualtion of negative class. Only the samples labeled as 0 are filtered and then processed\n",
    "        res0 = min_batch.filter(lambda x: x[0]==0).treeAggregate(\n",
    "              (np.zeros(parameter_size), 0, 0),\n",
    "              lambda x, y:(x[0]+\\\n",
    "                          (y[1])*(-y[0]+(1/(np.exp(-np.dot(y[1], bc_weights))+1))),\\\n",
    "                          x[1]+\\\n",
    "                          y[0]*(-(np.dot(y[1], bc_weights)))+np.log(1 + np.exp(np.dot(y[1],bc_weights))),\\\n",
    "                          x[2] + 1),\n",
    "              lambda x, y:(x[0] + y[0], x[1] + y[1], x[2] + y[2])\n",
    "              )        \n",
    "        \n",
    "        # The total gradients are a weighted sum\n",
    "        gradients = w0*res0[0]+w1*res1[0]\n",
    "        sum_cost = w0*res0[1]+w1*res1[1]\n",
    "        num_samples = res0[2]+res1[2]\n",
    "        \n",
    "        cost =  sum_cost/num_samples + regularization * (np.square(parameter_vector).sum())\n",
    "\n",
    "        # calculate gradients\n",
    "        gradient_derivative = (1.0 / num_samples) * gradients + 2 * regularization * parameter_vector\n",
    "        \n",
    "        if optimizer == 'SGD':\n",
    "            parameter_vector = parameter_vector - learningRate * gradient_derivative\n",
    "\n",
    "        if optimizer =='Momentum':\n",
    "            momentum = beta * momentum + learningRate * gradient_derivative\n",
    "            parameter_vector = parameter_vector - momentum\n",
    "            \n",
    "        if optimizer == 'Nesterov':\n",
    "            parameter_temp = parameter_vector - beta * prev_mom\n",
    "            parameter_vector = parameter_temp - learningRate * gradient_derivative\n",
    "            prev_mom = momentum\n",
    "            momentum = beta * momentum + learningRate * gradient_derivative\n",
    "            \n",
    "        if optimizer == 'Adam':\n",
    "            momentum = beta * momentum + (1 - beta) * gradient_derivative\n",
    "            second_mom = beta2 * second_mom + (1 - beta2) * (gradient_derivative**2)\n",
    "            momentum_ = momentum / (1 - beta**(i + 1))\n",
    "            second_mom_ = second_mom / (1 - beta2**(i + 1))\n",
    "            parameter_vector = parameter_vector - learningRate * momentum_ / (np.sqrt(second_mom_) + epsilon)\n",
    "\n",
    "        if optimizer == 'Adagrad':\n",
    "            gti += gradient_derivative**2\n",
    "            adj_grad = gradient_derivative / (np.sqrt(gti)  + epsilon)\n",
    "            parameter_vector = parameter_vector - learningRate  * adj_grad\n",
    "        \n",
    "        if optimizer == 'RMSprop':\n",
    "            sq_grad = gradient_derivative**2\n",
    "            exp_grad = beta * gti / (i + 1) + (1 - beta) * sq_grad\n",
    "            parameter_vector = parameter_vector - learningRate / np.sqrt(exp_grad + epsilon) * gradient_derivative\n",
    "            gti += sq_grad\n",
    "            \n",
    "            \n",
    "        print(\"Iteration No.\", i, \" Cost=\", cost, \"graients=\",gradients)\n",
    "        \n",
    "        # Stop if the cost is not descreasing\n",
    "        if abs(cost - prev_cost) < tolerance:\n",
    "            print(\"cost - prev_cost: \" + str(cost - prev_cost))\n",
    "            break\n",
    "        prev_cost = cost\n",
    "        L_cost.append(cost)\n",
    "        \n",
    "    return parameter_vector, L_cost"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Train using Weigthed model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration No. 0  Cost= 0.5444083217357665 graients= [ -31201.59377083 -117068.91882609   -3103.65624296]\n",
      "Iteration No. 1  Cost= 0.4903000740836418 graients= [-26670.57565798 -90785.56125139  -5579.53988256]\n",
      "Iteration No. 2  Cost= 0.47316261944109544 graients= [-25199.74948646 -83279.25844109  -6186.47073437]\n",
      "Iteration No. 3  Cost= 0.458922953896996 graients= [-23948.90916534 -76578.67131719  -6755.83510642]\n",
      "Iteration No. 4  Cost= 0.44639976063122333 graients= [-22833.78798316 -70595.31815954  -7261.70058317]\n",
      "Iteration No. 5  Cost= 0.43516072456262644 graients= [-21822.04911898 -65209.53226919  -7710.39871798]\n",
      "Iteration No. 6  Cost= 0.4249638157556091 graients= [-20895.60438347 -60339.88898409  -8108.26305416]\n",
      "Iteration No. 7  Cost= 0.4156445950662801 graients= [-20042.09910987 -55924.76916227  -8460.73634796]\n",
      "Iteration No. 8  Cost= 0.4070794046261979 graients= [-19252.13025463 -51913.96679909  -8772.53640517]\n",
      "Iteration No. 9  Cost= 0.3991698751566547 graients= [-18518.1036417  -48264.82736493  -9047.81333482]\n",
      "Iteration No. 10  Cost= 0.3918351529926094 graients= [-17833.67907242 -44940.2695112   -9290.25347807]\n",
      "Iteration No. 11  Cost= 0.38500743909867613 graients= [-17193.46119103 -41907.64649059  -9503.14950241]\n",
      "Iteration No. 12  Cost= 0.37862914387738317 graients= [-16592.80590201 -39138.01206862  -9689.45137864]\n",
      "Iteration No. 13  Cost= 0.37265091822119245 graients= [-16027.68690717 -36605.59699394  -9851.80634438]\n",
      "Iteration No. 14  Cost= 0.367030204978235 graients= [-15494.59662241 -34287.40457966  -9992.59208183]\n",
      "Iteration No. 15  Cost= 0.36173012476276256 graients= [-14990.46860507 -32162.8801078  -10113.94531282]\n",
      "Iteration No. 16  Cost= 0.35671859131719363 graients= [-14512.61459454 -30213.6305259  -10217.78698748]\n",
      "Iteration No. 17  Cost= 0.35196759324505505 graients= [-14058.67219932 -28423.1815164  -10305.84472643]\n",
      "Iteration No. 18  Cost= 0.34745260155761887 graients= [-13626.56077588 -26776.7643374  -10379.67291904]\n",
      "Iteration No. 19  Cost= 0.34315207548696447 graients= [-13214.4438657  -25261.12756319 -10440.67075258]\n"
     ]
    }
   ],
   "source": [
    "# Call to the original function\n",
    "parameter_vector_sgd_w, L_cost_sgd_w = LogisticRegression_weighted(traindata=traindata1,\n",
    "                       max_iteration = 20,\n",
    "                       learningRate = 0.01,\n",
    "                       regularization = 0,\n",
    "                       mini_batch_size = 50000,\n",
    "                       tolerance = 10e-8,\n",
    "                       optimizer = 'RMSprop',\n",
    "                      )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Train using standard model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration No. 0  Cost= 0.4809999126603584 graients= [ -19635.7718688  -176091.62976705   18486.64656711]\n",
      "Iteration No. 1  Cost= 0.3608912571083019 graients= [ -14401.41099418 -138338.96298425   14561.84234888]\n",
      "Iteration No. 2  Cost= 0.32655948948720975 graients= [ -12700.29326845 -125957.97317614   13261.24054832]\n",
      "Iteration No. 3  Cost= 0.29797067152299817 graients= [ -11473.34608183 -115875.31060548   12226.55135998]\n",
      "Iteration No. 4  Cost= 0.27427632764295345 graients= [ -10394.28316154 -107801.70613718   11385.85587071]\n",
      "Iteration No. 5  Cost= 0.25268935402130677 graients= [ -9410.10241405 -99173.74821336  10474.29403372]\n",
      "Iteration No. 6  Cost= 0.234055554199937 graients= [ -8601.84222552 -92208.07006886   9732.31826197]\n",
      "Iteration No. 7  Cost= 0.21702175932167103 graients= [ -7817.22688513 -85851.94203895   9075.23689723]\n",
      "Iteration No. 8  Cost= 0.20187165938629142 graients= [ -7188.01646083 -80719.36757137   8533.58847835]\n",
      "Iteration No. 9  Cost= 0.1884348549042304 graients= [ -6587.57284423 -75447.61192472   7971.55094869]\n",
      "Iteration No. 10  Cost= 0.17705970348384098 graients= [ -6013.51933626 -70259.20263765   7420.52372909]\n",
      "Iteration No. 11  Cost= 0.16637678142869994 graients= [ -5560.85303579 -66163.78104411   6981.87816234]\n",
      "Iteration No. 12  Cost= 0.1563064063799434 graients= [ -5161.76894399 -62121.04215017   6555.79301937]\n",
      "Iteration No. 13  Cost= 0.14746528418844457 graients= [ -4841.60937698 -58679.22412718   6189.95004222]\n",
      "Iteration No. 14  Cost= 0.13919230008545466 graients= [ -4483.86816426 -55447.08266647   5854.39429427]\n",
      "Iteration No. 15  Cost= 0.13200982631132613 graients= [ -4161.19470864 -52237.6016903    5508.17400586]\n",
      "Iteration No. 16  Cost= 0.12529010244673763 graients= [ -3882.59135087 -49732.12543863   5245.65102279]\n",
      "Iteration No. 17  Cost= 0.11976133346313982 graients= [ -3626.83027587 -47120.67461924   4955.5825984 ]\n",
      "Iteration No. 18  Cost= 0.11313997938041889 graients= [ -3462.34668958 -44355.08022405   4667.23719661]\n",
      "Iteration No. 19  Cost= 0.10839024255076746 graients= [ -3204.68233038 -42525.97422037   4459.69343422]\n"
     ]
    }
   ],
   "source": [
    "# Call of the optimzed function wiht the same parameters\n",
    "parameter_vector_sgd, L_cost_sgd = LogisticRegression_optimized(traindata=traindata1,\n",
    "                       max_iteration = 20,\n",
    "                       learningRate = 0.01,\n",
    "                       regularization = 0,\n",
    "                       mini_batch_size = 50000,\n",
    "                       tolerance = 10e-8,\n",
    "                       optimizer = 'RMSprop',\n",
    "                       train_size = train_size\n",
    "                      )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Prepare test dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0, array([ -0.9911372 , -10.01991492,   1.        ])),\n",
       " (0, array([ 0.74630673, -8.24840199,  1.        ])),\n",
       " (0, array([ -2.16338454, -12.02110725,   1.        ]))]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Test data need to be in the same format as the train data\n",
    "testdata1 = testdata.map(lambda x: (x[0],np.append(x[1],1)))\n",
    "test_num = testdata1.count()\n",
    "testdata1.take(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.27765989  0.14798432 -0.01031385] [0.29367589 0.1472093  0.25948579]\n"
     ]
    }
   ],
   "source": [
    "# Parameter vector size and test sample size must match.\n",
    "print(parameter_vector_sgd, parameter_vector_sgd_w)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Performance od the weighted model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--Contingency matrix--\n",
      " TP:   134  FP:    12\n",
      " FN:    44  TN: 19785\n",
      "----------------------\n",
      "Accuracy = 0.9971964956195244  \n",
      "F1 = 0.8271604938271605\n"
     ]
    }
   ],
   "source": [
    "# Create an RDD wiht the true value and the predicted value (true, predicted)\n",
    "predictions = testdata1.map(lambda x: (x[0], 1 if np.dot(x[1],parameter_vector_sgd_w)>0 else 0))\n",
    "\n",
    "# predictions = (1, 1) (0, 1) ...\n",
    "#               1 , 0, \n",
    "\n",
    "true_positive = predictions.map(lambda x: 1 if (x[0]== 1) and (x[1]==1) else 0).reduce(lambda x,y:x+y)\n",
    "false_positive = predictions.map(lambda x: 1 if (x[0]== 0) and (x[1]==1) else 0).reduce(lambda x,y:x+y)\n",
    "\n",
    "true_negative = predictions.map(lambda x: 1 if (x[0]== 0) and (x[1]==0) else 0).reduce(lambda x,y:x+y)\n",
    "false_negative = predictions.map(lambda x: 1 if (x[0]== 1) and (x[1]==0) else 0).reduce(lambda x,y:x+y)\n",
    "\n",
    "# Print the Contingency matrix\n",
    "print(\"--Contingency matrix--\")\n",
    "print(f\" TP:{true_positive:6}  FP:{false_positive:6}\")\n",
    "print(f\" FN:{false_negative:6}  TN:{true_negative:6}\")\n",
    "print(\"----------------------\")\n",
    "\n",
    "# Calculate the Accuracy and the F1\n",
    "accuracy = (true_positive+true_negative)/(test_num)\n",
    "f1 = true_positive/(true_positive+0.5*(false_positive+false_negative))\n",
    "print(f\"Accuracy = {accuracy}  \\nF1 = {f1}\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Performance of the standard model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--Contingency matrix--\n",
      " TP:    85  FP:     0\n",
      " FN:    93  TN: 19797\n",
      "----------------------\n",
      "Accuracy = 0.9953441802252816  \n",
      "F1 = 0.6463878326996197\n"
     ]
    }
   ],
   "source": [
    "# Create an RDD wiht the true value and the predicted value (true, predicted)\n",
    "predictions = testdata1.map(lambda x: (x[0], 1 if np.dot(x[1],parameter_vector_sgd)>0 else 0))\n",
    "\n",
    "# predictions = (1, 1) (0, 1) ...\n",
    "#               1 , 0, \n",
    "\n",
    "true_positive = predictions.map(lambda x: 1 if (x[0]== 1) and (x[1]==1) else 0).reduce(lambda x,y:x+y)\n",
    "false_positive = predictions.map(lambda x: 1 if (x[0]== 0) and (x[1]==1) else 0).reduce(lambda x,y:x+y)\n",
    "\n",
    "true_negative = predictions.map(lambda x: 1 if (x[0]== 0) and (x[1]==0) else 0).reduce(lambda x,y:x+y)\n",
    "false_negative = predictions.map(lambda x: 1 if (x[0]== 1) and (x[1]==0) else 0).reduce(lambda x,y:x+y)\n",
    "\n",
    "# Print the Contingency matrix\n",
    "print(\"--Contingency matrix--\")\n",
    "print(f\" TP:{true_positive:6}  FP:{false_positive:6}\")\n",
    "print(f\" FN:{false_negative:6}  TN:{true_negative:6}\")\n",
    "print(\"----------------------\")\n",
    "\n",
    "# Calculate the Accuracy and the F1\n",
    "accuracy = (true_positive+true_negative)/(test_num)\n",
    "f1 = true_positive/(true_positive+0.5*(false_positive+false_negative))\n",
    "print(f\"Accuracy = {accuracy}  \\nF1 = {f1}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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