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{
"cells": [
{
"cell_type": "markdown",
"source": [
"Michel Kiffel<br />\n",
"mkiffel@gmail.com<br />\n",
"This notebook supports [this blog article](https://mkffl.github.io/2022/03/02/Decisions-Part-3.html)"
],
"metadata": {
"id": "KPhuGzHOTnPv"
}
},
{
"cell_type": "markdown",
"metadata": {
"id": "k0iuDR861Vsi"
},
"source": [
"## Objective\n",
"- Visual validation of ML model score calibration\n",
" - Calibration of log-likelihood ratios using logistic regression\n",
" - Validation using known score distributions to calculate the true ratios\n",
" - Visual inspection of calibration fit on a separate dataset of scores\n",
"\n",
"## Logistic regression calibration\n",
"- Estimate \n",
"$$\\text{llr}(x ; \\omega) = \\log \\frac{ p(x \\vert \\omega_1)}{p(x \\vert \\omega_0)}$$\n",
"- Using logistic regression, which by default estimates target class log-odds i.e.\n",
"$$\\text{log-odds}(\\omega; x) = \\log \\frac{ p(\\omega_1 \\vert x)}{p(\\omega_0 \\vert x)}$$\n",
"\n",
"- Conversion from log-odds to llr uses the relation log-odds = llr + effective-prior (ep) hence llr = log-odds - ep\n",
"\n",
"## Score distributions\n",
"- I test two assumptions for the score class-conditional density\n",
" - Gaussian: logistic regression calibration works well as expected\n",
" - Skew-normal: lack of fit\n",
"\n",
"Main source is *Tutorial on logistic-regression calibration and fusion: Converting a score to a likelihood ratio* by GS Morrison\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "do-mtxdB1Vss"
},
"outputs": [],
"source": [
"# Stats\n",
"import numpy as np\n",
"import seaborn as sns\n",
"from scipy.special import logit, expit\n",
"from scipy.stats import norm as f_norm, skewnorm\n",
"\n",
"# Off the shelf stats models\n",
"from sklearn.linear_model import LogisticRegression as lr\n",
"\n",
"import pandas as pd\n",
"import matplotlib.pyplot as plt\n",
"from IPython.display import Image\n",
"from IPython.core.display import HTML"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "Zm67U0vf1Vs9"
},
"outputs": [],
"source": [
"# Utils\n",
"def reshape_to_1d(array):\n",
" \"\"\" Reshape [] to [[]], a requirement from sklearn. \"\"\"\n",
" return np.reshape(array,(-1, 1))\n",
"\n",
"def get_logistic_estimates(clf):\n",
" \"\"\" Find the logistic reg parameter estimates \"\"\"\n",
" return clf.intercept_[0], clf.coef_[0][0]\n",
"\n",
"def get_effective_prior(tarN, nontarN):\n",
" return logit(tarN/(tarN+nontarN))\n",
"\n",
"def logistic_logodds(x, β_0, β_1):\n",
" return β_0 + β_1*x\n",
"\n",
"def log_likelihood_ratio_density(tar_density, nontar_density):\n",
" def func(x):\n",
" return np.log(tar_density(x)/nontar_density(x))\n",
" \n",
" return func\n",
"\n",
"# Data\n",
"def generate_data(nontar_rv, tar_rv, nontarN, tarN):\n",
" \"\"\" Simulate the scores from two classes\n",
" \n",
" Args:\n",
" nontar_rv (scipy.continuous_dist): rv for w0 class\n",
" tar_rv (scipy.continuous_dist): rv for w1 class\n",
" \"\"\"\n",
" w0_sample = nontar_rv.rvs(nontarN)\n",
"\n",
" w1_sample = tar_rv.rvs(tarN)\n",
"\n",
" X = np.concatenate([w0_sample, w1_sample])\n",
"\n",
" y = [0 for d in w0_sample] + [1 for d in w1_sample]\n",
" \n",
" return X, y\n",
"\n",
"# Validation\n",
"def logistic_calibration_validation(x, y, test_x, nontarN, tarN, nontar_rv, tar_rv):\n",
" \"\"\" Validate llr from logistic regression using the formula for two gaussians.\n",
"\n",
" Args:\n",
" x (np.array): raw scores\n",
" y (np.array): labels w0 or w1\n",
" test_x (np.array): validation dataset to visually inspect the calibrated scores\n",
" nontar_rv (scipy.continuous_dist): rv for w0\n",
" tar_rv (scipy.continuous_dist): rv for w1\n",
" \"\"\" \n",
" # True llr\n",
" llr_density = log_likelihood_ratio_density(tar_rv.pdf, nontar_rv.pdf)\n",
" \n",
" llr_true = [llr_density(x) for x in test_x]\n",
" \n",
" # Estimated llr\n",
" x_1d = reshape_to_1d(x)\n",
" \n",
" clf = lr(random_state=0).fit(x_1d, y)\n",
" \n",
" β_0, β_1 = get_logistic_estimates(clf)\n",
" \n",
" lo_preds = [logistic_logodds(x, β_0, β_1) for x in test_x]\n",
" \n",
" effective_prior = get_effective_prior(tarN, nontarN)\n",
" \n",
" llr_preds = [(lo - effective_prior) for lo in lo_preds]\n",
" \n",
" return llr_true, llr_preds\n",
"\n",
"\n",
"def plot_true_and_predicted_llr(test_x, llr_true, llr_preds, title):\n",
" (\n",
" sns.lineplot(\n",
" 'x', \n",
" 'value', \n",
" hue='variable', \n",
" data=(\n",
" pd.DataFrame({\n",
" \"x\": test_x, \n",
" \"llr_true\": llr_true, \n",
" \"llr_preds\": llr_preds})\n",
" .melt(\"x\")\n",
" )\n",
" )\n",
" .set_title(title)\n",
" )\n",
"\n",
"# main\n",
"def run(nontar_rv, tar_rv, nontarN, tarN, title):\n",
" X, y = generate_data(nontar_rv, tar_rv, nontarN, tarN)\n",
" \n",
" sns.distplot(X[:nontarN])\n",
" sns.distplot(X[nontarN:])\n",
" plt.title(\"Class-conditional score distributions\")\n",
" plt.show()\n",
"\n",
" # Validation sample scores\n",
" test_x = np.linspace(-1, 1, 15) #np.linspace(-3, 3, 40)\n",
"\n",
" llr_true, llr_preds = logistic_calibration_validation(X, y, test_x, nontarN, tarN, nontar_rv, tar_rv)\n",
" \n",
" plot_true_and_predicted_llr(test_x, llr_true, llr_preds, title)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "6fB-NYZj1VtF",
"outputId": "fb3c2a39-24ad-494f-8802-aee06ef3b26b"
},
"outputs": [
{
"data": {
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d9X7sNuEHN69j1K34+qPHAhhhEDTsM7ob5kwzZ8tMpS+CxFw48dfA7lezBJ3QtaArr+mivX+Eb79zFXHRc+i6BxRnJvD565bwwqlWnjvREqAIA2xkAFqOGq1pW4CHeojNmInxzHPGcTTNh07oWlCNuj28XNHKwvR4rlqWHZB9fmzrIpbmJPKtx44zNOIOyD4D6tzrRg29cFNw9r/yRnANGUld03zohK4F1d6znfQOu7huZQ4SoJV3HHYbd924msbuIX7+cmVA9hlQ9fsgeYHxEwwLL4X4TD2trnYBndC1oBl1e3jldBulWQmUZCUGdN+bSzJ4x7p87nuten6dIO1vgZ66uQ8kmorNbpRdTj8Lo/PouWum0wldC5ojDT0MOF1cGaBSy3hffOsyPB74wbOng7L/WWk8AIjRvTBYyu83ujCODsCz3zSu+/5oEUsndC0olFLsrm4nOymGkswZzP89A4Xp8XxsazEPH2zg+LmeoBxjRpSCxoOQuRRiL1hSN7AyFhtJvfVEcI+jhRWd0LWgqOsc5Fz3MFtKMwJWO5/Ip69aTEqcg+8/UxG0Y/it8SAMtsOCILbOx9gdkLnESOjhMnJWCzqd0LWg2F3dQazDxvrC1KAeJyXOwR3bSnm5oo39NZ1BPda0jj5kdFPMXRua42WvhKFOo26vaeiErgXBoNPF8cZeLi5KIyZqbv3O/fGRLcVkJcXw/acrzJvnxeOGY49A9ipjdsVQGFtouvVkaI6nzXs6oWsBd/RcD26lJpwWNxjiou189urF7Kvp5LUzJq1NXrsTBloh/6LQHTMuDZLydB1dO08ndC3gXq/rJjsphryUmU3ANRe3bCwiPyWW/37hjDmt9ON/AUd84If6Tyd7BXRWwehwaI+rzUt6CTotoDr6ndR1DvLWVbkXnAx9YG9d0I4bHWXjjitL+eZfj7O7uoNLSzODdqwLuF1w8jFY+tbAzHs+E9mrjPVG2yuM6XW1iKZb6FpAHarvRoB1BSkhP/Z7ywrJTorhv184E9oD1+6EgTZY+a7QHhcgrRiiYnXZRQN0C10LIKUUhxt6KM5MCMqiztO18G/dXMSntpVy1+MnKK/ppKw4PeAxTOiEt9yy5C1w5P9Cc8wxNrsx53rrSaP7YhC7iGrzn26hawFT2dpPe7+TNQtC3zofc+umItLiHdz3anVoDuh2wQlvuSU6PjTHHC97JTh7obfRnONr84ZuoWsB8/SxZgBW5gV5lOQkxlrw6wvTeO5EC//9/Bkyk2LO33/r5qLAH7R2pzGYaNVNgd+3v7JXGJetJyClwLw4NNPpFroWME8fb6YwLY7kOIepcVxSko7dJuyoDEEXxuOPGuWWxdcF/1iTiUmClEJdR9d0QtcCo75zkOPnelmVb165ZUxSrIOLilI5WNdFv9MVvAO5XXDyb7D0evPKLWOyV0JXrV70IsLphK4FxDPHjXLLqnxzyi3jbS3NxOVRHAjmdAC1O7zlFhN6t4yXvRxQRvdFLWLphK4FxLMnWliWk0RGYsz0G4dAdnIsJVkJ7K3pxBOsgUZjg4nMLLeMSSkyphxo0wk9kumTotqc9QyNcqC2i09dUWJ2KG9yyaIMHthXR0VzHyvykv3q9ug3j9tbbjGxd4svm92YtrftlO6+GMF0C12bsx1n2nF7FFctD85CFrO1Ii+Z5Ngo9lR3BH7n9fuMcsuKdwR+37OVuRyGe4ykrkUkndC1OXupopWUOAcXBXmq3Jmy24SNi9I509pPR78zsDuveAJsjvlRbhmTtcy4rHrR3Dg00+iErs2Jx6N45XQbVyzNIso+//6cNhSlIcDBuu7A7VQpOPUELLo8+CsTzUR8OiRkQ+ULZkeimWT+fQK1sHKiqZe2PidXLcsyO5QJpcZHszg7kdfrugJ3crStAjqrYdnbArO/QMpabgx20rMvRiSd0LU5eelUKyJwxdL5mdABLl6YRvfQKNVtAeqjXfGEcTlfE7prGOp2mR2JZgKd0LU5efVMG2sWpJA5T7orTmRlXjKxDhsH67oCs8NTTxoLWaQsCMz+Aimj1JjCV5ddIpJO6NqsDThdvF7XzdbFIZx7fBYcdhvrClI51tjD8Kh7bjvra4bGclh2Q2CCC7SoGCi6BKpeMjsSzQQ6oWuztu9sJy6PYmsoF5OYpfWFqbg8ipNNvXPbUcVTxuXyeVhuGVN6NbQeh94msyPRQsyvhC4i14tIhYhUisiXJ9nmShE5JCLHReSVwIapzUc7K9uJjrJRVhyatUPnojA9ntQ4B0caeua2o4onIXXhGws0z0el1xiX1bqVHmmmHSkqInbgHuA6oAHYLyKPKaVO+GyTCvwMuF4pVSci82uEiRYwvqMtHz/SREFaHI8cnP/zcNtEWFOQws7KdgZHXMRHz2KQtLMfql+BjR+f3yMxc1a/0X1x/a1mR6OFkD8t9E1ApVKqWik1AjwI3Dhum1uBR5RSdQBKqdbAhqnNN/1OF829wyzOSjQ7FL+tLUjFo+D4uVmWXapeALdzfvZu8WWzQelVRgvd4zE7Gi2E/EnoC4B6n+sN3tt8LQXSRORlETkgIh+eaEci8kkRKReR8ra2ttlFrM0L1W39AJSGUULPT4klIyGaww2zHGR06kmIS4OiLYENLBhKr4HBDmg+bHYkWgj5871zou+W40doRAEbgGuAOGC3iOxRSp1+04OUug+4D6CsrCxIU+BpoVDV1k+sw8aCtDizQ/GbeMsur1S00e90kRgzg7KLxw1nnoX0Unj998ELMlBKrzIuK18wulhqEcGfFnoDUOhzvQA4N8E2TyulBpRS7cCrwLrAhKjNR5Wt/SzKTMQ2n2vJE1iVn4ICTs20t8u512Goc36fDPWVmA25a3T3xQjjT0LfDywRkUUiEg3cAjw2bpu/ApeLSJSIxAObgZOBDVWbLzoHRugaHGVxVoLZocxYfkosqXEOTsw0oZ95DpA3JsAKB6XXQP0ecPaZHYkWItMmdKWUC7gTeAYjST+klDouIneIyB3ebU4CTwNHgH3AL5VSx4IXtmamqjCsn48REVbkJ1PZ2o/TNYNBRpXPw4INEB1G/8RKrwaPC86+ZnYkWoj41Q9dKfWkUmqpUqpUKXW397Z7lVL3+mzzfaXUSqXUaqXUj4IVsGa+ytZ+kmKjyEqav8P9p7IqLxmXR3G6pd+/Bwx0QOMBWDKPpsr1R9ElxopKejrdiKFHimoz4lGK6rZ+FmclImFWPx+zMCOB+Gg7J875Ocio+iVAweJrgxpXwEXFQPFlRndLLSLohK7NSEvvMAMj7rAst4yx24QVuclUtPTh9vjR2erMcxCXHp69RUqvMab67TxrdiRaCOg1RbUZqWr11s+zwzehAyzLTeJAXRd1nYMsypyiLq6UUbIovcpYtzMclN//xu/D3j73L90NC7cav5d9LPQxaSGhW+jajFS1DZCZGENKnMPsUOZkcXYiNoHTLdP0AGk9CQOtUHJVaAILtIRsYzBUq15nNBLoFrrmt1G3h7PtA1xUNL/WDp2NWIedhRkJVDT38dZVuW/c4du6Bah+2bgcaLvwvnAgYix6ce51Y3BUuHzL0GZFt9A1vx2q72bE7Qnr+rmvZTlJNPcO0z04MvlG7achIcto5YarsVWMumvNjkQLMp3QNb/trGxHCM/+5xNZlpsEMHn3RY8bOiohc2kIowqCjCWAQJsuu1idTuia33ZVdpCfGkdctDW+tmcnxZAa76Bisjp6dy24R8I/oUfHQ9pCndAjgE7oml8GnC4O1nVZpnUOxqjRZTlJVLX243JPMM1sWwUg3hZumMtcBt31MBKghbK1eUkndM0v+2qM5eYWh3l3xfGW5SQx4vZwtmOCRNd+GlIKjRZuuMteDijjOWmWpRO65pdd3uXmFmZYILn5KMlKJMomnG4eV3Zxj0B3HWQuNiewQEspAkecLrtYnE7oml92VnawoSgNh91afzLRUTZKshIurKN31YByQ7pFErrNDhlLjYSu9FIEVmWtT6cWFB39Tk409XLZkkyzQwmKpTlJtPePUNPuU3bpqAQE0ktMiyvgspbDcI/33IBmRTqha9PaXd0BwKWlGSZHEhzLcozuiy9X+CyF21EFKQXgiDUpqiAYm8tdT9ZlWTqha9PaWdlBUkwUaxakmB1KUGQkxpCZGMOLFd51bt2jRpfFjFJzAwu0+HRjKgA9na5l6YSuTWtnZTuXlGYQZbH6ua+lOYnsre5g2I1xMtTjsk793FfWcqjZCaPDZkeiBYF1P6FaQNR3DlLXOchWi5ZbxizNScLp8rC3Ldqa9fMxWcvANQR1u8yORAsCndC1Ke2qagdg62JrnhAdsygzgZgoG680R0NnFSTnWaP/+XgZi8Hm0GUXi9IJXZvSjsoOspNiLDegaDyH3cbmkgx2NtuMxSCsWG4BYxWjokugUid0K9IJXZuUUordVe1sXZwZtsvNzcS2pVkkDNSBZ9R6J0R9Lb4GWo9DX7PZkWgBphO6NqmKlj7a+0cs211xvCuXZXGJ7aRxJd3CCb30GuNSl10sRyd0bVI7zkRG/XxMSWYC2xwnOGfPhxgLl5hyVhtzvFfq/uhWoxO6NqldVR2UZCaQnxpndighIR436+U0r46uYGSCyRctw2aD0quh+iXwWPmJRh6d0LUJjbo97K3u4NLFkVFuAaDpMDHKyQ7XSg52hPeaqdMqvRoGO6D5sNmRaAGkE7o2oSMN3QyMuNlaGhnlFgBqdwJQrpbzcnO0ycEEWenVxqWuo1uKXiRae5MH9tYB8OKpVgRo7Bo6f5vl1e6EhCyKkxJ4pVn48hoLLwaRmA25a4zui5f/o9nRaAGiW+jahKrb+slLiSU+JjL+54tyQ+1uyFjMtpwRTvY4aBmy+Mej9Gqo3wPOSZbg08JOZHxatRkZdXuo6xzkkpLIqZ+n9p4GZw+kl7ItcYTvHoNXW6K5udiCc56U329cukeNOWue/5bR82VM2cdMCUubO4s3QbTZqOscxOVRlGYlmB1KyGR3lhu/ZJSyIsVFVqzbmAbAytJKwB4NrXoVI6vQCV27QHVbPzaB4owISuhd5ZC6EOLSEIFtOSO81hKN28qL+9ijjLld2vWCF1ahE7p2gaq2ARakxhHjsJsdSmgoD9mdB6D4svM3bcsdoWfUxuFOi1cls5bBQJvRhVELezqha2/iHHXT0DVIaZaFR0qOk9JfScxoDyzcev62y7JHsKF4pTnGxMhCIGu5cakXj7YEizc/tJmq6RjEo6AkghJ6jrd+/tfuReS27z5/e2lCIk/U2bg0vpPNi9LNCi+4ErIhLs1YZ9TnH5oWnnQLXXuT6rZ+7DZhYYYF5wKfRHZnOQOxuQzELXjT7euS+6kaiKXPZeGPiYjRSm8/DR632dFoc2Thv1RtNqra+ylKj8dh4eXm3kQpsjsP0JpeZiQ3H+tTBlAIR3otfnI4cxm4ho11VLWwFiGfWs0f3YMjNHUPUxJB3RVT+quIHemkJX3TBfeVxg+TFOXi9R6Ll58ylwKi6+gWoBO6dt7es50ooDTT4gnMR07nPgBaMjZecJ9NYH3yAId6EqzdfTE6HlKLdEK3AJ3QtfN2V3XgsAsF6ZExXS5Adkc5A7F5F9TPx2xI6afPHcWhDov3H8haDt31MGLh+WsigE7o2nm7qtopzkggyhYhfxbKQ3bnfqN1PskSe2uTB7CjeKHJ4t0Xs5cDyjg5qoUtvz65InK9iFSISKWIfHmK7TaKiFtE3hO4ELVQaOtzcrqlP6K6K6b0VxI72k1L+oXlljEJUR6WJQ7yotX7o6cUQVSs0X1RC1vTfo8UETtwD3Ad0ADsF5HHlFInJtjuu8AzwQhUC67d1cZIQavP31Ja96fzv+d07AUgdrjtTbePd3HqAP/bkEDjoI0F8RZd4cdmN3q7tJ0CpSb9xqLNb/600DcBlUqpaqXUCPAgcOME230WeBhoDWB8WojsrmonKTaKvJTIqZ8nD9Qy7EhlJDp1yu02pPQD8KLVyy5Zy2C4W7fSw5g/CX0BUO9zvcF723kisgC4Cbh3qh2JyCdFpFxEytva2mYaqxZEu6o62LwoA7stQlpmSpE0WEtvQvG0m+bFjFCc6OLFJovPvjg2DYBexShs+ZPQJ/qEj3hkl0EAACAASURBVO/E9SPgS0qpKYeaKaXuU0qVKaXKsrKy/I1RC7LG7iFqOwa5tDRy5j+Pd7bgcA/Rl7Bw2m1F4KrcEXa2RjPoCkFwZolPN6YCqHrB7Ei0WfInoTcAhT7XC4Bz47YpAx4UkRrgPcDPRORdAYlQC7rdVUb9PJIWhE4eqAGgN77Yr+2vyXMy4hF2tVq8lZ69As6+Bs5+syPRZsGfhL4fWCIii0QkGrgFeMx3A6XUIqVUsVKqGPgz8Gml1F8CHq0WFLuq2klPiGZpdpLZoYRM0kAtw440RqJT/Np+U9YoCVEe63dfzFkNbidUv2R2JNosTJvQlVIu4E6M3isngYeUUsdF5A4RuSPYAWrBpZRid1UHW0oysEVM/dxD8oB/9fMx0Ta4ImeEl5qjUVYeNZpeArGpUPGU2ZFos+DX8Del1JPAk+Num/AEqFLqo3MPSwuVmo5BmnqG2RJJ9fPhFqI8w/T6UT/3dVXeCE81xnKiJ4pVqRYtptvssOQtcPppY/ZFW4QscmIRETIkUJvMrqp2gIg6ITpWP++bQQsd4KpcJ4D1e7ss226sYFS/z+xItBmy+AQV2ngP7K170/UH99WTHBvF7qoO9lR3mhRVaCUP1DAcnc6II9nvx+w9a7w2i+MT+WuNnU2xb36tLLUAxuJrwOaAiidh4Razo9FmQLfQI5hSiuo2Y7i/RMjIQPG4SR6soSehZFaPvzjVWPSiZ9TCpYjYFGN9VV1HDzs6oUewlj4nAyNuyw/395U0VIfdM0pPYumsHn9RSj8K4ZDVF71Y9jboOAPtZ8yORJsBndAjWHWb0dc4sibkqsaDbUY9XHwtinOS5hjlQLfFX7Nl241L3UoPKzqhR7CqtgHSE6JJi7f4ST4fKf1V9McX4LbPrj+5CFycMsCR3gRcFp2nC4DUQshdY9TRtbChE3qE8ijF2fZ+SjItXjrwEePsIGG4edblljEXp/Qz5LFzot/iC2kvexvU74WBdrMj0fykE3qEOtc9xPCoJ6LKLXntuwHmnNBXJw3gEA8Hrb7W6LLtoDxw5lmzI9H8pBN6hKpuM5Yai6QFofPadzFqj2MgNndO+4m1K9YkD3KgO9Hao0bz1kNSHpx6wuxIND/phB6hqtv7yUqKITnWYXYoISHKTV7ba/QkLgaZ+5/9hpQ+WkeiaRi28PkHEVjxDqh8Xk/WFSZ0Qo9ALo+HmvbBiOqumNF9hNjRbrqSlgZkfxenGN9wyq3e22XVTeAaNqYC0OY9ndAjUGPXECNuDyWZFk9GPha0voxHouZcPx+THu2iJH7I+nX0wksgMReOP2p2JJofdEKPQFVt/QhEVA+XBa2v0pq+Abc9NmD73JDSz5mBOGuPGrXZYNW74Mxz4OwzOxptGjqhR6CqtgFyU2KJj4mMqXwSBhtI7a+kMeuKgO53Q6oxatTyrfRVNxlzpFfosst8pxN6hBlxeajrHKQ0grorLmh9BYDG7CsDut/iOCcZjlEOWD2hF2yCpHw49rDZkWjT0Ak9wtR0DOD2KBZnWzwJ+ShofYmehEX0JxQFdL8ixmRdR3oTGJ5yNd0wZ7PBmndD5XN6kNE8pxN6hKls7cduE4ozIqN+HjPSRXZnOfW51wZl/xtS+nF6bOy2+lqj624FjwuO/tnsSLQp6IQeYara+lmYHk90VGS89QtaXsKm3NTnBCehr0oaJMbm4XmrL3qRsxLy1sHhB8yORJtCZHyqNQDa+pw09QxHVLmlqOU5+uMW0JW8Iij7j7Yp1iYP8GJTjLVHjYLRSm86DC0nzI5Em4RO6BFkbLm5SEnojtFectr3GOWWIC7gUZbST9OQnePdFu81tOY9YIvSrfR5zOJ/gZqvHWfaiXPYyU+NMzuUkFjQ+gp25QpauWXMRSn9CIrnm6JZnWaBxaPL75/8vqzlcOC3kFo8+QLSZR8LSlja9HQLPUIopdhR2U5JVgK2CFlubmHTMwzGZNOeujaox0lxuLk4Y5QXmmY3x3pYKdgIzl5oP212JNoEdEKPENXtAxFVP48Z6SKvfSc1+W8LyGRc07kmb4SjXQ6ahyz+kcpeBY54aNhndiTaBCz+16eN2XHGqJ8vyU4yOZLQKGp6BptyUZP/9pAc79o8JwAvWL23iz0K8i+G5mMwOmR2NNo4OqFHiB2V7RSmx5GeYPGE41V87gm6ExfTHaDZFaezJNlNUYKbF85FQNmlcBN4RuHcIbMj0cbRCT0CuNwe9lR1cNniLLNDCYmEwXqyug9Rk39DUHu3+BKBa/Kc7GiNZtAC50WnlFJozMBYv8fsSLRxdEKPAIcbeuhzurh8SabZoYRE8TljYeOa/BtCetzr8p2MeIQdVh81KgJFW6C7FnoazI5G86G7LUaAHWfaEYEtJRk8dazZ7HCCqrT2IZbWPkhvfBF5bTtCeuyNmaMkOTw8fy6Gt+SPhPTYIVe4EU49DrU7Ye37zI5G89It9AjwyulW1i5IIS0C6ufxw03EjbTTnhLcrooTcdjgytwRXmyKxmP1UaOOeFhwMTQegNFhs6PRvHRCt7j2fiev13dz9fIcs0MJicyeo3jETmdKcIb6T+faPCftTjuHOyPgy+/CreAegcb9ZkeieemEbnEvV7ShFFyzItvsUIJOlJuMnuN0Jy7BbTdnNOyVuSPYRfF8JAwySi0yTpDW7sT6E9mEB53QLe7FUy3kJMewKj/Z7FCCLqdjL9GuftpT15gWQ0q0YmPmKM9HQvdFMFrpfc3QWW12JBo6oVvaiMvDq6fbuXp5DhIBw/0XNf4Nly2G7sQlpsbxlnwnFb1RVPdZeK3RMfkXQVSs0UrXTKcTuoXtO9tJv9PFNcutX25xjPZS2PwcHSlrUDZz69fXLzBGjT7VGAGt9KgYY36XpsN6Eel5QCd0C3v+ZAsxUTa2LrZ+//OFTU8T5XHSlrbe7FDIj/ewPn2UpyMhoYNRdlFuqN9rdiQRTyd0i/J4FE8ebeLKZVnERVv/q39pw6N0JS1lIDbP7FAA2L7AydEuB/UDEfARS8qFjCVQswM8Vl5cdf6LgL+2yFRe20Vrn5Mb1uabHUrQpfSdJqPnGNUFN4VsqP90ti8w+mY/Eymt9EXbYLjbKL1optEJ3aKeOHKOmChbRNTPSxsexS1RIR/qP5WiRA8rU0cjo44Oxpqj8Zlw9mXdhdFEOqFbkNujePJYM1ctyyYhxtoDXGyeUYobH6cx5yqc0Wlmh/Mm2xc4OdARbf050sGYc37RNuiug3o9V7pZ/PpLE5HrRaRCRCpF5MsT3P8BETni/dklIusCH6rmr/01nbT1Oblh7fyoJwfTgtaXiR3tpqrgJrNDucB2b2+XiCm7FG4CRxzsucfsSCLWtM03EbED9wDXAQ3AfhF5TCnlu/T3WWCbUqpLRLYD9wGbgxGwNr2/HmokzmHnaguWW0rr/vSm68tqH2AkKon4wXMX3BdKe892Tnh7QWwi/1dp4yOLQxyQGaJioHALnPwbdNVC2kKzI4o4/rTQNwGVSqlqpdQI8CBwo+8GSqldSqku79U9QEFgw9T8NeB08dihc9ywNs/y5Zbo0V5S+qtoS10XkmXmZmNzWh8n++PpcM6Pk7VBt+hyQGDffWZHEpH8+RQsAOp9rjd4b5vMx4GnJrpDRD4pIuUiUt7W1uZ/lJrfnjjaxMCIm/dtLDQ7lKDL7D6MoGhLNb/v+WQ2pfahEJ6NlLJLXBqsvBEO/k4PNDKBPwl9oqbFhKexReQqjIT+pYnuV0rdp5QqU0qVZWVFxuo5ofbQ/npKshIoWzi/ThAGnPKQ3XWQnoRinDHpZkczqYVxTnJjRniiIdbsUEJny2fA2QsHf292JBHHn4TeAPg29wqAc+M3EpG1wC+BG5VSHYEJT5uJytY+ymu7uGVjoeXnbkntryRmtIfWtDKzQ5mSCGxN72VXq4OWSOjtAlBQBkWXwu6fgstpdjQRxZ8i635giYgsAhqBW4BbfTcQkSLgEeBDSqnTAY9S88tvd9VitwlKwQN768wOJ6iyOw8wEpVAV9Iys0OZ1mXpvTzclMnf6mO4femQ2eGExhX/BP/7d3DoASj7mNnRRIxpmwxKKRdwJ/AMcBJ4SCl1XETuEJE7vJt9E8gAfiYih0SkPGgRaxNq73fyUHk9FxWmkhTrMDucoIoe6Sa1/wxtqRehbPN/WoP82BHWpY3ySF0ElV1Kr4b8i2HHD8E9anY0EcOv74BKqSeVUkuVUqVKqbu9t92rlLrX+/vtSqk0pdR678/8/h5sQb/dVcOI28PlS6x/biK763UAWtMuNjkS/72raJgT3Q4qeub/P6CAEIFtXzQGGh01rztppImQop61DThd/G53LW9ZmUNWkrV7U4hyk9X9Ot2JSxiJTjU7HL+9vXAYuygejaRW+tLrIWcNvPYDPWlXiOiEbgG/3nGWnqFR7thWanYoQZfad5poVz+t6RvMDmVGsmIVV+aO8OeaWEY9ZkcTIiJGLb2jEk78xexoIoJO6GGupXeYn79SxfbVuVxUZPGuikBOZzlORzLdieE39PL9i4Zod9p5oSna7FBCZ8U7IXMZvPqf4ImU/2Tm0Qk9zP3nMxW43Iovb19udihBlzRQS8rAWaN2Pk9Hhk7lytwRcuPc/LHanAWsTWGzweX/CK0noOIJs6OxvPD7VGjnHarv5s8HG/jo1mIWZiSYHU7QLal7EA822lIvMjuUWYmywXuLh3m1JZqGSFj4Yszqd0PGYnjxbl1LD7II+quylqERN1946BB5ybHceXX4lR9myjHaR2n9o3SmrGLUkWR2OLP23mKjH/qDZyOolW6Pgqu/AW0n4fCDZkdjaTqhh6nvPn2K6rYBvn/zOpIt3u8coLThERzuAZoywnsSz4IED9fmj/CH6jiGI6mxuvJGo1/6S/8Oo8NmR2NZOqGHoedOtPCbXTV89NLiiFgAWjwultY+QEvaBgbjwn9JvduXDNI1YuOR2gjqwigC130behtg771mR2NZ1p5f1YIqW/v4/P8dYs2ClIg4EQpQ0PICiUPnOLjii8Q4J553PJxsyhxlTdoovzoTzy2LhrFZbdqd8vsnvy97ldHjZd37ISkndDFFCJ3Q56HJ5mEZdLr4+StVxDps/M+HNhDriIBRh0qxuuoX9CQU05h9JSX1j5gd0ZyJGK30z+1L4aWmaK7JHzE7pNBZ+S549XvwwrfhXT8zOxrL0Qk9TDhdbn67u4aeoVEe/OQl5KdGxkm1Ba2vkNZXwe61d6MkfP+BjV/RKFNBVnQ8/3EohoThZi4pmb9TAAdUYhZc8vew67+h7ONQEF4DxOY7XUMPAy6Phwf21tHQNcQtG4soK46QD79SrKq6j/64BdTkbTc7moCKErgpr53KwThe77V+l9M3ueKfITEXHv8cuF1mR2MpOqHPcx6lePhAA2da+7npogWszE82O6SQyWvfSWbPUY6XfBxls15Pnm0ZPWRHj/DQuSzUhEvGWFRsMmz/LjQfhb0/NzsaS9EJfR5TSvHE0SYON/Tw1pU5kdMyx5iEa33Fj+iPW8DZBTdO/4AwFCXw7rwOzg7G8nSkLFE3ZuWNsHS70Y2xq9bsaCxDJ/R57JXTbeyu6mBraQZXLLX+tLi+ihsfJ62vgsNLP4fHbt25Ty7P6KEwdpi7jyRGVr90EbjhP40pHB67U8/zEiA6oc9T+2s6efZEC+sLU9m+Js/yS8r5sruHWXvmJ3SkrKY2761mhxNUdoGPFrbSMGjnF6fjzQ4ntFIK4K13w9lXYf8vzY7GEnQvl3nodEsffz3UyNKcRN59cQG2ccnc6svLraz6JQnDLexe+x9hOQnXTK1OHmT7gmHuOZXATUXDFCREUGv14o/AycfhuW8aqxxlWn8ai2Cy/qclzJw418sD++rISY7l/RuLsFtu1MnUVp/+KauqfkFbylqSBmoorfvTm36s6qtr+7Gh+MqB5Mg6QSoC7/wJOGLh4dv0otJzpBP6PNLSO8zHf7uf2CgbH95STEwkDBzyIcpNybm/4bbHUpf7FrPDCanCBA9fWTvAa63R/PFsBE0JAJCcBzfeA02H4flvmx1NWNMJfZ4YcLq47Tf76R0a5SOXFpMSZ71uetNZVXkfiUPnqM19K66oCKsnAx8oGWJr9gh3H0mkpj+y/pmz/AbY9CnYcw+c0vOmz5auoc8Dbo/iH/74OiebevnVRzbS1BN5s9Hltu1iTeXPaU9ZQ0fKarPDMYVN4HtlvdzwfDp37E7m0au6iLPiJ3SyuV4yFkNKITx6B3ziRchcEtq4LEC30OeBux4/wQunWvn2jau5anm22eGEXMJgPZce/hI9iaWczb/BqKtGqAXxHn60qZeKnii+/npSZNXT7Q4ou824fPAD4OwzO6KwoxO6yX75WjW/2VXDJy5fxIcuWWh2OCEXN9TMNfs+geDhtYt+iMdm3T7n/royd4R/WDHIw7Vx/OJ0ZMzZc15cGrznfmNh6T/fpqcGmCGd0E306OsN/NsTJ9m+OpevbF9hdjghFzfcwtX7P0HMSDcvlf0PfYmLzA5p3vjcygFuKBjm348m8URDhI0iLdlmDDo68yw8/SUi62vK3FixQhcWXjrVyj//6QiXlmbwo1vWY4uw7olpPcfZduAfcLj6ebnsZ3SmRmbdfDI2gR9s7KV5yMbn9yWTGNXDttwImma37DboPGvMypiYC9v+2eyIwoJO6Cb4jydP8uudZ8lOjuHaFTk8fKDR7JBCR3lYUvcQF536Ac7oNJ675Hd0Jy8zOyrTjZ9ed8ynC7q5a7CI23cm88XFDaxNHrxgm82LLDrHz7Xfhv5WeOnfIDoetnzG7IjmPZ3QQ+xkUy+/211LcqyDj166KDIWqfBK7qtiw8nvkNexh6bMS9m99m6GY6y/hN5cJEZ5+NrSeu46Xcj3Kgv40uIG1kyQ1C3FtxdMwUZjcelnvgp1e6H0Kij7mHmxzXO6hh5CB+u6eN//7MZhF27buojEmMj4fxo/1MzmI9/gbTv+jszuo+xb9Q1eKrtXJ3M/JUe5+cbSevJiR/heZQHHeiOoj77NDhd9CPLWw8m/wsm/6Zr6FCIjo8wDL1W08pk/HCQrKYb3bigkLcGavTl8h+dHuQbJb99BTud+AFoyNrFr/fdwRqeZFV7YSo5y840l9fzr6UK+U1nAZxedY3Nav9lhhYYtCi7+MByNh6oX4KEPG8vXxSSZHdm8o1voQaaU4r5Xq7jtN/spzkjgT5/aYtlkPsbmGSG/7TXWnfkJuR176UhZzeHFd1KX+xadzOcg2eHmm8vqWRQ/zH9VL+Cp1gh6LcUGa26GFe+EU4/DL66BpiNmRzXv6BZ6ELX3O/nyw0d4/mQrN6zJ4/s3ryU+2rovuXhcZHeWs6DtVaJd/XQmLaMh+yqGYiNvsFSwJEe5+frSen5yNp/f1OfQMRLFxmI3EdFJSsSYkXHj7fDIJ+AXV8FlX4DLvwCOCOuvPwnrZhcTKaX4y6FG7n7iJL3DLr759pV8bGuxpec0z+x6nY3H7yatr4Le+CLOFN5Mf3yh2WFZUoxN8YWSRu6vz+FvLRl49g7z/bJe4iPl01yyDT69B57+Crz6PTj0AFzzDVj9HrBHyoswsch+9kFQXtPJ956pYN/ZTtYVpPCH96xjWa51a32xznbWV/wXJY2PMRCbw5mC99CZvCKih++Hgk3gtsIWsqJH+WNDFpW96dy7pYdFSRGy7FF8Ovzd/8BFH4Bnvw6PfspYzm7LZ+CiD0J0hC287SXKpDPGZWVlqry83JRjz9VEC0zUdgzwwqlWKlv7SYiJ4roVOZQVp12wOEW4O3/SU3nI6dxPQevL2NQozRlbaMy6XA/dN4EzLpd/2JfMiBu+dVE/Ny8ctvb/0/HdFj0eo66+6yfQsA9iU43ujgsvNaYS8GcfYUREDiilyia6T7fQ58CjFBXNfeysaqe6bYCEmCi2r85l86IMoqOse745aaCWhU1Pk+BsoTuhhNq863UXRBNdkTvCk9d28vl9yXyxPJlnGmP49vq+yFn5yGaDle80fur2GqNLTz0Blc9DzkpYuBWylkfE6lc6oc/C0Iib8tpO9lR30DU4SkqcIyISedxQM6UNj5DZcwynI4XThTfTlbRcl1fmgfx4Dw9s6+b+M3H84Hgi1z2bwe1LBrl96SAp0Rbrtz3Z9LtjFl8L+RdB3R6o2w0txyEu3WixF262dHdHXXLxk8ej2FnVzkPlDTx1tAmXR1GcEc+W0kxW5iVbeqm4KNcgy2r+l5XVv8TuGeFc5laaMrfisUXeIhzz0fih/42DNv79SCJPNMSS5PDwvuJhbi0ZoiRS6uu+PC5oPgq1O40ZHMUOeWvhLf9mtNzDsDEyVclFJ/QpKKU42tjDU8eaeezQORq7h0iJc7AiL5mNxWnkpVi7q1TMSBel9Q+z/OzviB3toj7najqSV+m+5PPMZHO5nOiO4p5T8TzTGINLCStTR7k2b4RNmSOsTXeR7LBYy306/S1GYm/YD6NDkLkMNnwEVt4IKQVmR+c3ndBnYKyc8kpFG08da6axewi7TbhscSY3lxVw7YocHjlo3cm07O5h8tp3UtT0LIUtz59vkR9d/Pd0pK2z9ELN4Wq6ybmePt3Dax0plHcncnogDoXRKk2JcpEdM0p2zAjZ0aOkOlykOdzeSxepDhfRNmW9yb/cIxCdCOW/gsYDxm0FG41BS8tvgPSSed1yn/NJURG5HvgxYAd+qZT6zrj7xXv/24BB4KNKqYNzijoEPB5FfdcgJ5v6OH6uhz3VHRyq72bUrXDYhcuXZPH/rl3CdStzSI23SO8NpYhyDRAz2kP0aC/Rrl4SBs+R0l9JRs9RMrqPYVejOB0pVBXcxJmiW+hJWmx21NocpDncvDO3k3fmdjLotnFmIJbqgVhaR6JpdTo43R/H7pFkPFyYxOLtbvJOK7JjPWTHesiPd1OQ4KYw3kNBgpv8eDex4Ta/nD3a6O540Qeg/Qyc+CucfAye+4bxk5ANhZug6BLIv9hYCi8ha14n+THTttBFxA6cBq4DGoD9wPuVUid8tnkb8FmMhL4Z+LFSavNU+w1UC93jUbiVwu1ReLyXTpeHAaeLvmEX/U4XA07jsrXXybmeIZp7hmnsHqKytZ/BEaOuaBNYsyCFS0ozcI56WJgRT0yUSX+pSiF4EOVBlOv8pc3jRvBg84zicA0Q5RrA4R4gyjXkvRwgyjVItKv/fLKOHn3jJ9bZRpR7GOHC99wjdgZjc6nLvY7mzC20pG9ETVAj1y10a/Io6HXZ6R6Nons0ii6fS1t0HK3DNlqG7DQP2XCpNye2nFgjyRfEeyj0Jvm0aEVKtIdkhyLZ4SHaDtE2hcNmXEbb5mF+HGiH9gpjHvbBduiqeeO+mGTIKIXUhZCYA0k5xmVcmtHnPTrRe+n93R5tTCwmdqN3jc0esCc81xb6JqBSKVXt3dmDwI3ACZ9tbgR+p4z/DntEJFVE8pRSTXOM/QJPHW3icw8eOp/EZyo+2k5eSiz5qXG8t6yQFXlJLMtNZmlO4vlh+RP1Mw+24sbH2XzsXxDlwabmtuyWR+yMRCUz4jB+nI4U+uILiRtuw2WPxWWPxW2P817G4oxKNuriYqOq6OYAPSMtnNgEUh1uUh1uwPmm+3xLLm4FLUM2Ggbs1A/aaRiwUT9gp2HQzoEOB483xOBW/iUuuyhswLuLh/nOhnmwfmhCpvGzcKvRT72vGZqPGSdTOyqh4wy0HIOqF8HZO4sDyBtJ/tLPGqNbA8yfhL4AqPe53oDRCp9umwXAmxK6iHwS+KT3ar+IVMwo2jdkAu2zfCwnZ/tA88zi+XbN8lD/NMvHBdyc3uMwFGnPF7zP+bvAd82O5AK3BWOnPu/xN70/szLp4sP+JPSJ/t2Obxr7sw1KqfuA+/w45tQBiZRP9pXDiiLt+ULkPedIe74Qec85FM/Xn1EwDYDvLEsFwLlZbKNpmqYFkT8JfT+wREQWiUg0cAvw2LhtHgM+LIZLgJ5g1M81TdO0yU1bclFKuUTkTuAZjG6Lv1ZKHReRO7z33ws8idHDpRKj22KwZ76Zc9kmzETa84XIe86R9nwh8p5z0J+vaQOLNE3TtMCy7kxSmqZpEUYndE3TNIsI24QuIt8SkUYROeT9eZvZMYWCiPyTiCgRsfQE5CJyl4gc8b63z4pIvtkxBZuIfF9ETnmf96Mikmp2TMEkIjeLyHER8YiIpbsvisj1IlIhIpUi8uVgHSdsE7rXfyml1nt/njQ7mGATkUKMKRhCP5Q19L6vlFqrlFoPPM4cRmGEkeeA1UqptRjTbXzF5HiC7Rjwd8CrZgcSTN7pU+4BtgMrgfeLyMpgHCvcE3qk+S/gi0wwaMtqlFK+Y6sTiIzn/KxS5+d92IMxnsOylFInlVKzHS0eTs5Pn6KUGgHGpk8JuHBP6Hd6v57+WkQsPUm3iLwTaFRKHTY7llARkbtFpB74AJHRQvd1G/CU2UFoATHZ1CgBN6+XoBOR54HcCe76GvBz4C6MlttdwA8I0gQMoTLN8/0q8JbQRhRcUz1fpdRflVJfA74mIl8B7gT+JaQBBsF0z9m7zdcAF/CHUMYWDP483wjg19QogTCvE7pS6lp/thORX2DUWcPaZM9XRNYAi4DDxtTzFAAHRWSTUqo5hCEGlL/vL/AA8AQWSOjTPWcR+QjwduAaZYFBIjN4j60sZFOjhG3JRUTyfK7ehHGCxZKUUkeVUtlKqWKlVDHGH8jF4ZzMpyMiS3yuvhM4ZVYsoeJdSOZLwDuVUoNmx6MFjD/TpwTEvG6hT+N7IrIe46tLDfApc8PRAuw7IrIM8AC1wB0mxxMKPwVigOe838T2KKUs+7xF5CbgJ0AW8ISIHFJKvdXksAJusulTgnEsPfRf0zTNIsK25KJpmqa9mU7omqZpFqETuqZpmkXohK5pmmYROqFrmqZZhE7omqZpFqETuqZpmkX8fxwv9HcxWQAAAAJJREFU+60j1FqZAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"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": [
"nontarN = 1_000\n",
"tarN = 1_000\n",
"nontar_rv = f_norm(-3, 0.5)\n",
"tar_rv = f_norm(-2, 0.5)\n",
"\n",
"run(nontar_rv, tar_rv, nontarN, tarN, \"Balanced dataset with normally distributed scores\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "s0JIJ_XW1VtG",
"outputId": "1e728a9f-1186-4950-cc8b-680431b25e56"
},
"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"
},
{
"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": [
"tarN = 1_000\n",
"nontarN = int(7*tarN)\n",
"nontar_rv = f_norm(-3, 0.5)\n",
"tar_rv = f_norm(-2, 0.5)\n",
"\n",
"run(nontar_rv, tar_rv, nontarN, tarN, \"Imbalanced dataset with normally distributed scores\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "8i61UylH1VtI",
"outputId": "4dab1a14-2257-4f00-981a-497a840d8a1b"
},
"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"
},
{
"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": [
"tarN = 1_000\n",
"nontarN = 1_000\n",
"nontar_rv = skewnorm(a=4, loc=-0.5, scale=0.5)\n",
"tar_rv = skewnorm(a=-4, loc=0.5, scale=0.5)\n",
"\n",
"run(nontar_rv, tar_rv, nontarN, tarN, \"Balanced dataset with skew-normally distributed scores\")"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.5"
},
"colab": {
"name": "Logistic Calibration.ipynb",
"provenance": [],
"collapsed_sections": []
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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