wehub-resource-sync
67 lines
1.9 KiB
Python
Executable File
67 lines
1.9 KiB
Python
Executable File
import numpy as np
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from prml.linear.logistic_regression import LogisticRegression
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class BayesianLogisticRegression(LogisticRegression):
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"""
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Logistic regression model
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w ~ Gaussian(0, alpha^(-1)I)
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y = sigmoid(X @ w)
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t ~ Bernoulli(t|y)
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"""
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def __init__(self, alpha:float=1.):
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self.alpha = alpha
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def fit(self, X:np.ndarray, t:np.ndarray, max_iter:int=100):
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"""
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bayesian estimation of logistic regression model
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using Laplace approximation
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Parameters
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----------
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X : (N, D) np.ndarray
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training data independent variable
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t : (N,) np.ndarray
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training data dependent variable
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binary 0 or 1
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max_iter : int, optional
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maximum number of paramter update iteration (the default is 100)
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"""
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w = np.zeros(np.size(X, 1))
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eye = np.eye(np.size(X, 1))
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self.w_mean = np.copy(w)
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self.w_precision = self.alpha * eye
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for _ in range(max_iter):
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w_prev = np.copy(w)
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y = self._sigmoid(X @ w)
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grad = X.T @ (y - t) + self.w_precision @ (w - self.w_mean)
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hessian = (X.T * y * (1 - y)) @ X + self.w_precision
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try:
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w -= np.linalg.solve(hessian, grad)
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except np.linalg.LinAlgError:
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break
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if np.allclose(w, w_prev):
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break
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self.w_mean = w
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self.w_precision = hessian
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def proba(self, X:np.ndarray):
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"""
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compute probability of input belonging class 1
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Parameters
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----------
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X : (N, D) np.ndarray
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training data independent variable
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Returns
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-------
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(N,) np.ndarray
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probability of positive
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"""
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mu_a = X @ self.w_mean
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var_a = np.sum(np.linalg.solve(self.w_precision, X.T).T * X, axis=1)
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return self._sigmoid(mu_a / np.sqrt(1 + np.pi * var_a / 8))
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