AnswersAndDemos/Class weights and threshold in Logistic Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Do class-weights and threshold perform the same role in Logistic Regression?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## I. Abstract:\n",
    "\n",
    "As explained in the question 'Class weights and threshold limit', threshold limit determines the rate of false negativity and false positivity. We guess the excessive false negativity rate as compared to the false positivity rate on using 0.5 as the threshold is due to the imbalance in the dataset - too low $y=1$ samples as compared to $y=0$ samples. It seems logical because $y=0$ samples have greater influence over the classifier as compared to $y=1$ samples. As a result error rates in $y=0$ class is lower compared to $y=1$ class. First, we will put this assumption to test.\n",
    "\n",
    "If the assumption turns out valid, we will check if manipulating class-weights achieves the same end as manipulating threshold limit.\n",
    "\n",
    "Hence there will be two parts to this study, namely -\n",
    "<ul>\n",
    "    <li>Does false negativity rate depend on dataset imbalance?</li>\n",
    "    <li>If above answer is yes, do threshold limit and class-weights achieve the same end?</li>\n",
    "</ul>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## II. Preparing the simulated training data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We first decide the characteristics of the training dataset.\n",
    "\n",
    "<b>Characteristics of training data:</b>\n",
    "<ol>\n",
    "    <li>There will be one feature, credit balance- a number between 0-20,000- and a response- the default status. 1 denotes default=yes and 0 denotes default=no. The training set size will be $n$</li>\n",
    "    <li>We will take a probability distribution $P(y=1|x)$ such that people with higher credit balance have a higher chance of default.</li>\n",
    "    <li>In the traning set $\\frac {\\text{entries with y=1}} {n} = defaultProportion$.</li>\n",
    "    </ol>\n",
    "    \n",
    "We will define a function <b><i>generateTrainingSet(n, defaultProportion, defaultProbabilityDist, xDist, \\*args, \\*\\*kwargs)</i></b> that will generate the training set with given size and proportion of $y=1$ samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn import metrics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For higher credit balance we want a higher probability of default. We use the logistic function, $\\frac {e^{{\\beta}_0 + {\\beta}_1x}} {1+e^{{\\beta}_0 + {\\beta}_1x}}$, with parameters ${\\beta}_0$ and ${\\beta}_1$ chosen to meet our requirements.\n",
    "\n",
    "Below, is the plot of the logistic function thus derived, that returns the probability of default given any credit balance $x$ between 0 and 20000."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "defaultProbabilityDist = lambda x: np.exp(-9.952+0.0006319*x)/(1+np.exp(-9.952+0.0006319*x)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = np.linspace(0,20000,10000)\n",
    "Y = [defaultProbabilityDist(x) for x in X]\n",
    "plt.plot(X,Y)\n",
    "plt.xlabel('Credit balance')\n",
    "plt.ylabel('Probability of default')\n",
    "plt.title('Probability of default for given credit balance');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below is the function to generate the training set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generateTrainingSet(n, defaultProportion, defaultProbabilityDist, xDist, *args, **kwargs):\n",
    "    trainingSet = pd.DataFrame(columns=['Balance','Default'])\n",
    "    defaultSize = np.around(n*defaultProportion)\n",
    "    while len(trainingSet.loc[trainingSet['Default']==0.0]) < n-defaultSize:\n",
    "        x = xDist(*args, **kwargs)\n",
    "        p = defaultProbabilityDist(x)\n",
    "        y = np.random.choice([0,1],p=[(1-p),p])\n",
    "        if y==0:\n",
    "            trainingSet.loc[len(trainingSet)] = [x,y]\n",
    "        if (y==1) and (len(trainingSet.loc[trainingSet['Default']==1.0]) < defaultSize):\n",
    "            trainingSet.loc[len(trainingSet)] = [x,y]\n",
    "\n",
    "    while len(trainingSet) < n:\n",
    "        x = x = xDist(*args, **kwargs)\n",
    "        p = defaultProbabilityDist(x)\n",
    "        y = np.random.choice([0,1],p=[(1-p),p])\n",
    "        if y==1:\n",
    "            trainingSet.loc[len(trainingSet)] = [x,y]\n",
    "            \n",
    "    return trainingSet"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "trainingSet = generateTrainingSet(1000,0.1,defaultProbabilityDist,np.random.uniform,low=0.0,high=20000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Balance</th>\n",
       "      <th>Default</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>9444.112802</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5378.944966</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>15778.867748</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2907.466604</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>15043.977947</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Balance  Default\n",
       "0   9444.112802      0.0\n",
       "1   5378.944966      0.0\n",
       "2  15778.867748      0.0\n",
       "3   2907.466604      0.0\n",
       "4  15043.977947      1.0"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trainingSet.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The below figure shows that people with <b>Default status = Yes</b> have, on the average, a higher credit balance. Besides, in the training set, <b>Default status = Yes</b> is only 10% the entire training set. Hence the imbalance we wanted to create is present as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.boxplot([trainingSet.loc[trainingSet['Default']==1.0]['Balance'], trainingSet.loc[trainingSet['Default']==0.0]['Balance']],\n",
    "           labels=['Yes','No'])\n",
    "plt.xlabel('Default status')\n",
    "plt.ylabel('Credit balance');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "900"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(trainingSet.loc[trainingSet['Default']==0.0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "100"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(trainingSet.loc[trainingSet['Default']==1.0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## III. Finding the false negativity rate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Applying Logistic Regression to predict the default status."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "clf = LogisticRegression().fit(trainingSet[['Balance']],trainingSet['Default'])\n",
    "trainingSet['Default prediction'] = clf.predict(trainingSet[['Balance']])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 1.])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clf.classes_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Balance</th>\n",
       "      <th>Default</th>\n",
       "      <th>Default prediction</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>9444.112802</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5378.944966</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>15778.867748</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2907.466604</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>15043.977947</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>995</th>\n",
       "      <td>6773.634351</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>996</th>\n",
       "      <td>15844.504623</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>997</th>\n",
       "      <td>14617.847761</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>998</th>\n",
       "      <td>17502.691883</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>999</th>\n",
       "      <td>3113.535301</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1000 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          Balance  Default  Default prediction\n",
       "0     9444.112802      0.0                 0.0\n",
       "1     5378.944966      0.0                 0.0\n",
       "2    15778.867748      0.0                 0.0\n",
       "3     2907.466604      0.0                 0.0\n",
       "4    15043.977947      1.0                 0.0\n",
       "..            ...      ...                 ...\n",
       "995   6773.634351      0.0                 0.0\n",
       "996  15844.504623      0.0                 0.0\n",
       "997  14617.847761      0.0                 0.0\n",
       "998  17502.691883      0.0                 1.0\n",
       "999   3113.535301      0.0                 0.0\n",
       "\n",
       "[1000 rows x 3 columns]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trainingSet"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Producing the confusion matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Predicted 0</th>\n",
       "      <th>Predicted 1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>True 0</th>\n",
       "      <td>0.977778</td>\n",
       "      <td>0.022222</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>True 1</th>\n",
       "      <td>0.440000</td>\n",
       "      <td>0.560000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Predicted 0  Predicted 1\n",
       "True 0     0.977778     0.022222\n",
       "True 1     0.440000     0.560000"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "confuMatrix = metrics.confusion_matrix(trainingSet['Default'], trainingSet['Default prediction'],normalize='true')\n",
    "confusionMatrix = pd.DataFrame(data=confuMatrix, columns=['Predicted 0','Predicted 1'], index=['True 0', 'True 1'])\n",
    "confusionMatrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overall error rate: 0.064\n"
     ]
    }
   ],
   "source": [
    "confuMatrix = metrics.confusion_matrix(trainingSet['Default'], trainingSet['Default prediction'],normalize='all')\n",
    "print('Overall error rate:', confuMatrix[0,1] + confuMatrix[1,0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hence the false negative and true positive rate are 44% and 56% respectively. The false positive rate is 2.22% and overall error rate is 6.4%. We will now study the false negative rate, false positive rate and overall error rate as function of training dataset imbalance (default=yes proportion in training set)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## IV. Error rates vs imbalance in training dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "def errorRateVsImbalance(numOfPoints,propRange):\n",
    "    proportions = np.linspace(propRange[0], propRange[1], numOfPoints)\n",
    "    falseNegRates, falsePosRates, overallErrorRates = [],[],[]\n",
    "    for prop in proportions:\n",
    "        trainingSet = generateTrainingSet(1000,prop,defaultProbabilityDist,np.random.uniform,low=0.0,high=20000)\n",
    "        clf = LogisticRegression().fit(trainingSet[['Balance']],trainingSet['Default'])\n",
    "        trainingSet['Default prediction'] = clf.predict(trainingSet[['Balance']])\n",
    "        confuMatrix = metrics.confusion_matrix(trainingSet['Default'], trainingSet['Default prediction'],normalize='true')\n",
    "        falseNegRates.append(confuMatrix[1,0])\n",
    "        falsePosRates.append(confuMatrix[0,1])\n",
    "        confuMatrix = metrics.confusion_matrix(trainingSet['Default'], trainingSet['Default prediction'],normalize='all')\n",
    "        overallErrorRates.append(confuMatrix[0,1] + confuMatrix[1,0])\n",
    "    return falseNegRates, falsePosRates, overallErrorRates, proportions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "falseNegRates, falsePosRates, overallErrorRates, proportions = errorRateVsImbalance(100,(0.01,0.5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10,7))\n",
    "plt.plot(proportions,falseNegRates,'.g',label='False Neg.')\n",
    "plt.plot(proportions,falsePosRates,'.r',label='False Pos')\n",
    "plt.plot(proportions,overallErrorRates,'.b',label='Overall error')\n",
    "fig.suptitle('Errors vs positive proportion')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### IV a. Why does the overall error rate increase with increasing balance?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As training dataset goes from imbalance (lower $y=1$ entries) to balance, the false negative rate will decrease. This is logical as model will be more ***learned*** in the $y=1$ domain. So will the false positive rate increase as the model will get comparatively less scope to learn $y=0$ domain. \n",
    "\n",
    "However, why is it so that the overall error rate, which denotes the models overall ***learned-ness***, increases. It could have equally stayed the same or decreased.\n",
    "\n",
    "To answer this question we will take a closer look at the original and predicted decision boundaries, i.e., $x$ values for which $P(y=1|x)=0.5$. The original decision boundary is governed by the distribution used to simulate the training dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [],
   "source": [
    "orgDecisionBoundary = -(-9.952/0.0006319)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {},
   "outputs": [],
   "source": [
    "def decisionBoundaries(proportions,orgDecisionBoundary):\n",
    "    for prop in proportions:\n",
    "        trainingSet = generateTrainingSet(1000,prop,defaultProbabilityDist,np.random.uniform,low=0.0,high=20000)\n",
    "        trainingSet['Original Prob'] = [defaultProbabilityDist(x) for x in trainingSet['Balance']]\n",
    "        \n",
    "        clf = LogisticRegression().fit(trainingSet[['Balance']],trainingSet['Default'])\n",
    "        predDecisionBoundary = -(clf.intercept_[0]/clf.coef_[0,0])\n",
    "        \n",
    "        orgDefaultSetX = trainingSet.loc[trainingSet['Default']==1.0]['Balance']\n",
    "        orgDefaultSetY = trainingSet.loc[trainingSet['Default']==1.0]['Original Prob']\n",
    "        \n",
    "        orgNonDefaultSetX = trainingSet.loc[trainingSet['Default']==0.0]['Balance']\n",
    "        orgNonDefaultSetY = trainingSet.loc[trainingSet['Default']==0.0]['Original Prob']\n",
    "        \n",
    "        strOrg = f'Org boundary={np.around(orgDecisionBoundary,2)}'\n",
    "        strPred = f'Pred boundary={np.around(predDecisionBoundary,2)}'\n",
    "        \n",
    "        fig, (ax1,ax2) = plt.subplots(1,2, figsize=(14,5))\n",
    "        \n",
    "        ax1.plot(orgDefaultSetX, orgDefaultSetY,'.g',label='Default')\n",
    "        #ax1.plot(orgNonDefaultSetX, orgNonDefaultSetY,'.r', label='Non-default')\n",
    "        ax1.axvline(orgDecisionBoundary,c='k',ls='--',label=strOrg)\n",
    "        ax1.axvline(predDecisionBoundary,c='b',ls='--',label=strPred)\n",
    "        #ax1.axhline(0.5,c='b',ls='--',label='0.5 Prob.')\n",
    "        ax1.set_xlabel('Balance')\n",
    "        ax1.set_ylabel('Default probability')\n",
    "        ax1.set_title('Original data default cases')\n",
    "        ax1.legend()\n",
    "\n",
    "        #ax2.plot(orgDefaultSetX, orgDefaultSetY,'.g',label='Default')\n",
    "        ax2.plot(orgNonDefaultSetX, orgNonDefaultSetY,'.r', label='Non-default')\n",
    "        ax2.axvline(orgDecisionBoundary,c='k',ls='--',label=strOrg)\n",
    "        ax2.axvline(predDecisionBoundary,c='b',ls='--',label=strPred)\n",
    "        #ax2.axhline(0.5,c='b',ls='--',label='0.5 Prob.')\n",
    "        ax2.set_xlabel('Balance')\n",
    "        ax2.set_ylabel('Default probability')\n",
    "        ax2.set_title('Original data non-default cases')\n",
    "        ax2.legend()\n",
    "\n",
    "        fig.suptitle(f'Default proportion = {prop*100}%')\n",
    "        plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "decisionBoundaries((0.1,0.3,0.5),orgDecisionBoundary)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### About the figures above -\n",
    "\n",
    "The three rows of figures are respectively for the 10, 30 and 50 percent default=yes proportion in the data. The left hand plots show the original data for which default=yes in green. The right hand plots show the original data where default=no in red. In each figure the back vertical line shows the decision boundary governed by the simulating function; it stays the same throughout. The blue vertical line shows the predicted decision boundary."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### First, we go through the 3 left hand plots where only default=yes cases are plotted. \n",
    "\n",
    "<b><i>At the top the default=yes proportion is 10%.</i></b>\n",
    "<ul>\n",
    "    <li>The cases to the left of the original decision boundary are the ones where probability for default is less than 50%; yet a default happens. That's nature's way of throwing in unavoidable random errors.</li> \n",
    "    <li>Had the prediction boundary been exactly the same as the original boundary it would have been an exact learning of nature by the model; best possible scenario. Even then, all data points to the left of the prediction boundary will be predicted as default=no yet originally have default=yes; this is the false negative error. When the prediction boundary is same as original boundary, the only false negative errors are those caused by unavoidable random error.</li> \n",
    "    <li>However, the prediction boundary lies to the right of the original boundary because the training set has low number of default=yes samples. <b>To motivate this point, had there been no default=yes samples the prediction boundary would have been to the extreme right, identifying all samples as default=no.</b></li>\n",
    "    <li>This is the source of the higher than usual false negative rate; the prediction boundary being to the right of original boundary due to low proportion of default=yes or positive cases.</li>\n",
    "    </ul>\n",
    "    \n",
    "<b><i>Below it in the second row, default=yes proportion is 30%.</i></b>\n",
    "<ul>\n",
    "    <li>As the default=yes sample proportion increases the prediction boundary moves left. <b>To motivate this movement, just imagine that all training samples were default=yes. The prediction boundary would have been to the extreme left predicting default=yes for all cases.</b></li>\n",
    "    <li>As the prediction boundary moves to the left the false negative errors decrease. This would try to bring the overall error down.</li>\n",
    "    </ul>\n",
    "    \n",
    "<b><i>At the bottom, where default=yes proportion is 50% -</i></b>\n",
    "<ul>\n",
    "    <li>The prediction boundary moves even more left, further decreasing the false negative errors.</li>\n",
    "    </ul>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Next, we go through the 3 right-hand figures where only default=no cases are plotted \n",
    "\n",
    "<b><i>At the top the default=yes proportion is 10%.</i></b>\n",
    "<ul>\n",
    "    <li>The cases to the right of the original decision boundary are the ones where probability for default is more than 50%; yet a default does not happen. Here this is the unavoidable random error.</li>\n",
    "    <li>The prediction boundary is to the right of the original boundary. Cases to the right of the prediction boundary are the ones where defult=yes or y=1 is predicted yet originally default=no or y=0. These are the false positive errors.</li>\n",
    "    </ul>\n",
    "    \n",
    "<b><i>Below it in the second row, default=yes proportion is 30%.</i></b>\n",
    "<ul>\n",
    "    <li>As the prediction boundary moves to the left the false positive errors increase. This would try to bring the overall error up.</li>\n",
    "    </ul>\n",
    "    \n",
    "<b><i>At the bottom, where default=yes proportion is 50% -</i></b>\n",
    "<ul>\n",
    "    <li>The prediction boundary moves even more left, further increasing the false positive errors.</li>\n",
    "    </ul>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### So in terms of the overall error rate as the default=yes proportion increases-\n",
    "\n",
    "With the prediction boundary moving left, the false negative error goes down. However, the false positive error goes up. But here lies a very tricky point. \n",
    "<ul>\n",
    "    <li>Look at the left hand figures. As the blues line moves left the number of cases to its left which constitute the false negative errors decrease. However, when the default=yes proportion is low the desity of these green points overall is low. Hence even with an appreciable left movement of the blue line, the decrease in the number of points to its left is low.</li>\n",
    "    <li>Look at the right hand figures now. As the blue line moves left the number of cases to its right increases i.e., false positive errors increase. However, the density of the red dots overall is more. Hence the same left movement of the blue line might lead to a relatively larger increase in false positive errors.</li>\n",
    "    <li>Hence in increasing default=yes samples from 10 to 30 percent the increase in false positive errors hopefully trump the decrease in false negative errors.</li>\n",
    "    <li>However standing at a more balanced scenario when the density of the green dots has increased, say default=yes being 30%, the left-movement of the blue line might not give stark differences between the decrement of false negatives and increment of false positives. Thus moving from 30 to 50 percent the overall error rate might be relatively more constant.</li>\n",
    "    <li>Check the <i>Errors vs positive proportion</i> figure now. The overall error rate initially rises then gradually stabilizes.</li>\n",
    "    </ul>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<blockquote><b>Hence that concludes the first part of our study - does false negativity rate depend on dataset imbalance? The answer is yes it does.</b></blockquote>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## V. Do threshold limit manipulation and class-weights achieve the same end?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Towards this end, given an imbalanced training set we first draw an ROC curve, which gives the false positive vs true positive rates at various threshold levels. Now different classifiers for different levels of class-weights manually provided are fit to the same data and the false-positive vs true-positive rate is plotted on the same figure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "trainingSet = generateTrainingSet(1000,0.1,defaultProbabilityDist,np.random.uniform,low=0.0,high=20000)\n",
    "clf = LogisticRegression().fit(trainingSet[['Balance']],trainingSet['Default'])\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8,5))\n",
    "metrics.plot_roc_curve(clf,trainingSet[['Balance']],trainingSet['Default'],ax=ax)\n",
    "\n",
    "proportions = np.linspace(0.9,0.5,10)\n",
    "negClassWeights = 1/(proportions*2)\n",
    "posClassWeights = 1/((1-proportions)*2)\n",
    "falsePositives, truePositives = [],[]\n",
    "for prop,negW,posW in zip(proportions,negClassWeights,posClassWeights):\n",
    "    clfWeights = LogisticRegression(class_weight={0:negW,1:posW}).fit(trainingSet[['Balance']],trainingSet['Default'])\n",
    "    confuMatrixWeights = metrics.confusion_matrix(trainingSet['Default'], clfWeights.predict(trainingSet[['Balance']]),normalize='true')\n",
    "    falsePositives.append(confuMatrixWeights[0,1])\n",
    "    truePositives.append(confuMatrixWeights[1,1])\n",
    "    \n",
    "cax = ax.scatter(falsePositives,truePositives,c=posClassWeights,cmap='viridis',label='class weights')\n",
    "\n",
    "clfBalanced = LogisticRegression(class_weight='balanced').fit(trainingSet[['Balance']],trainingSet['Default'])\n",
    "confuMatrixBalanced = metrics.confusion_matrix(trainingSet['Default'], clfBalanced.predict(trainingSet[['Balance']]),normalize='true')\n",
    "ax.plot(confuMatrixBalanced[0,1],confuMatrixBalanced[1,1],'^r',label='balanced class weight')\n",
    "\n",
    "ax.legend()\n",
    "\n",
    "fig.colorbar(cax);    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<blockquote><b><i>The blue curve is the ROC curve. The colourbar denotes the class-weight of positives or default=yes class. The class-weights vary from 5.0 to 1.0 (which is not using class weights at all). The scatter plots all lying on the ROC curve denote that manipulating the class weights is the same as manipulating threshold. The red dot is the performance of the classifier when class-weight='balanced' i.e., a class weight of 5.0 to positive class. We see that without any class weights i.e., class-weight=1.0 the true positive rate is poorest.</i></b></blockquote>\n",
    "\n",
    "\n",
    "## VI. Conclusion\n",
    "\n",
    "\n",
    "So it seems we have two options at our disposal with imbalanced sets.\n",
    "<ol>\n",
    "    <li>balance them via class-weights</li>\n",
    "    <li>choose a suitable threshold</li>\n",
    "    </ol>\n",
    "\n",
    "I have some doubts regarding the first point though. Balancing via class-weights gives extra weightage to the few positive response samples. If those samples are indeed representative of the real world positive response class it's great. However, if those samples are corrupted, say due to incorrect measurements, then putting extra weightage on them can adversly affect the test set performance of the model. The same challenge possiby does not exist for threshold manipulation though. True, that this line of reasoning needs further empirical study, on test set performance, to be established. "
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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