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@perellonieto
Created November 30, 2023 16:09
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{
"cells": [
{
"cell_type": "markdown",
"id": "b2b71428-74e5-48da-ba77-6649938167a4",
"metadata": {},
"source": [
"# Fitting probability scores with a linear model\n",
"\n",
"This is a toy example showing the difference between fitting binary labels or true posterior probabilities.\n",
"The example uses a synthetic dataset formed by two Gaussian distributions (one per class) where we know the true posterior probabilities and from which we can sample labels.\n",
"\n",
"Then some classification and regression models are trained and evaluated using Mean Absolute Error against the true posterior probabilities."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "7138a172-8f9c-4ee1-a636-e7248996d34a",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import sklearn\n",
"from sklearn.datasets import make_blobs"
]
},
{
"cell_type": "markdown",
"id": "55885625-6040-4b91-a192-9fb2a8b0f298",
"metadata": {},
"source": [
"## Dataset"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "687fba04-3bca-4dd3-973d-15612e28ddd6",
"metadata": {},
"outputs": [],
"source": [
"from scipy.stats import norm\n",
"\n",
"class TwoGaussians(object):\n",
" def __init__(self, locations=[-1, 1], scales=[1, 1], priors=[0.2, 0.8]):\n",
" self.locations = locations\n",
" self.scales = scales\n",
" self.priors = priors\n",
"\n",
" def sample(self, n_samples=100):\n",
" n_samples_positive = np.random.binomial(n_samples, self.priors[0], 1)[0]\n",
" samples_per_class = [n_samples_positive, n_samples - n_samples_positive]\n",
" samples = []\n",
" for i, (loc, scale, size) in enumerate(zip(self.locations, self.scales, samples_per_class)):\n",
" samples.append(norm.rvs(loc=loc, scale=scale, size=size))\n",
" X = np.hstack(samples).reshape(-1, 1)\n",
" Y = np.hstack([np.zeros(samples_per_class[0]), np.ones(samples_per_class[1])])\n",
" X, Y = sklearn.utils.shuffle(X, Y)\n",
" return X, Y\n",
"\n",
" def likelihoods(self, X):\n",
" pdfs = [norm.pdf(X.T, loc=loc, scale=scale) for loc, scale in zip(self.locations, self.scales)]\n",
" P = np.vstack(pdfs).T\n",
" return P\n",
"\n",
" def posteriors(self, X):\n",
" pdfs = self.likelihoods(X)\n",
" for i, prior in enumerate(self.priors):\n",
" pdfs[:,i] *= prior\n",
" Z = pdfs.sum(axis=1)\n",
" P = pdfs/Z[:,None]\n",
" return P"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "bf8f7b01-4687-4966-ae8e-cd0107fb656c",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fd054ddaca0>"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"data_generator = TwoGaussians(locations=[0, 5], scales=[3, 3], priors=[0.3, 0.7])\n",
"X, Y = data_generator.sample(100)\n",
"\n",
"fig = plt.figure()\n",
"plt.scatter(X, Y, marker='|', s=100, label='samples')\n",
"for i in range(2):\n",
" plt.scatter(X[:], data_generator.likelihoods(X)[:, i], marker='.',\n",
" alpha=0.5, label=f'$P(X|Y={i})$')\n",
"plt.legend()\n",
"\n",
"fig = plt.figure()\n",
"plt.scatter(X, Y, marker='|', s=100, label='samples')\n",
"true_posteriors = data_generator.posteriors(X)\n",
"for i in range(2):\n",
" plt.scatter(X, true_posteriors[:,i], marker='.',\n",
" alpha=0.5, label=f'$P(Y={i}|X)$')\n",
"plt.legend()"
]
},
{
"cell_type": "markdown",
"id": "d7c31495-20bc-4b35-a31a-2bf662556973",
"metadata": {},
"source": [
"## Models"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "d73b5022-8d32-4066-94d7-1c754be59b36",
"metadata": {},
"outputs": [],
"source": [
"from sklearn.linear_model import LogisticRegression\n",
"from sklearn.linear_model import LinearRegression\n",
"\n",
"class MyLogisticRegression(LogisticRegression):\n",
" def fit(self, X, Y, S, *args, **kwargs):\n",
" return super().fit(X, Y, *args, **kwargs)\n",
"\n",
"class MyLinearRegression(LinearRegression):\n",
" def fit(self, X, Y, S, *args, **kwargs):\n",
" S_logit = np.log(S/(1 - S))\n",
" return super().fit(X, S_logit, *args, **kwargs)\n",
" \n",
" def predict_proba(self, X, *args, **kwargs):\n",
" S = super().predict(X)\n",
" P = 1/(1 + np.exp(-S))\n",
" return P\n",
"\n",
"from sklearn.neural_network import MLPClassifier\n",
"\n",
"class MyMLPClassifier(MLPClassifier):\n",
" def __init__(self, **kwargs):\n",
" return super().__init__(activation='logistic', hidden_layer_sizes=100, **kwargs)\n",
" \n",
" def fit(self, X, Y, S, *args, **kwargs):\n",
" return super().fit(X, Y, *args, **kwargs)\n",
"\n",
" def __str__(self):\n",
" return f\"{__class__.__name__}() Layer sizes: {[l.shape for l in self.coefs_]}\"\n",
"\n",
"\n",
"from sklearn.neural_network import MLPRegressor\n",
"\n",
"class MyMLPRegressor(MLPRegressor):\n",
" def __init__(self, **kwargs):\n",
" return super().__init__(activation='logistic', hidden_layer_sizes=100, **kwargs)\n",
" \n",
" def fit(self, X, Y, S, *args, **kwargs):\n",
" return super().fit(X, S, *args, **kwargs)\n",
"\n",
" def predict_proba(self, X, *args, **kwargs):\n",
" return super().predict(X, *args, **kwargs)\n",
"\n",
" def __str__(self):\n",
" return f\"{__class__.__name__}() Layer sizes: {[l.shape for l in self.coefs_]}\"\n",
"\n",
"class MyMLPRegressorLogit(MyMLPRegressor):\n",
" def fit(self, X, Y, S, *args, **kwargs):\n",
" S_logit = np.log(S/(1 - S))\n",
" return super().fit(X, Y, S_logit, *args, **kwargs)\n",
"\n",
" def predict_proba(self, X, *args, **kwargs):\n",
" S = super().predict(X)\n",
" P = 1/(1 + np.exp(-S))\n",
" return P\n",
"\n",
"models_dict = {'lr': MyLogisticRegression,\n",
" 'lr-logit': MyLinearRegression,\n",
" 'mlp': MyMLPClassifier,\n",
" 'mlp-reg': MyMLPRegressor,\n",
" 'mlp-logit': MyMLPRegressorLogit}"
]
},
{
"cell_type": "markdown",
"id": "63f8c9dd-9cbe-4fff-b9b0-5eed3b71539f",
"metadata": {},
"source": [
"## Training and evaluation of the models"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "e6132a99-b605-4dc8-b218-f1bfe40e37de",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"MyLogisticRegression()\n",
"MyLinearRegression()\n",
"MyMLPClassifier() Layer sizes: [(1, 100), (100, 1)]\n",
"MyMLPRegressor() Layer sizes: [(1, 100), (100, 2)]\n",
"MyMLPRegressor() Layer sizes: [(1, 100), (100, 2)]\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/mp15688/git/logistic_probabilities/venv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (200) reached and the optimization hasn't converged yet.\n",
" warnings.warn(\n",
"/home/mp15688/git/logistic_probabilities/venv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (200) reached and the optimization hasn't converged yet.\n",
" warnings.warn(\n"
]
},
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fd02adab5e0>"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"\n",
"clf_dict = {}\n",
"mae_dict = {}\n",
"\n",
"fig = plt.figure()\n",
"plt.grid(True)\n",
"plt.scatter(X, Y, marker='|', s=100, label='samples')\n",
"plt.scatter(X, true_posteriors[:,1], marker='x',\n",
" alpha=0.9, label=f'true $P(Y={i}|X)$')\n",
"for model_name, model_class in models_dict.items():\n",
" clf_dict[model_name] = model_class()\n",
"\n",
" clf_dict[model_name].fit(X, Y, true_posteriors)\n",
"\n",
" print(clf_dict[model_name])\n",
"\n",
" predicted_proba = clf_dict[model_name].predict_proba(X)[:,1]\n",
" mae_dict[model_name] = np.mean(np.abs(predicted_proba - true_posteriors[:,1]))\n",
" plt.scatter(X, predicted_proba, marker='.', alpha=0.5,\n",
" label=f'{model_name} $f(s_1;x) (MAE = {mae_dict[model_name]:0.2f})$')\n",
"plt.legend()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "a22ccec2-074b-4211-8d2d-b738246c71b3",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"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": "3.9.5"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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