wehub-resource-sync
89 lines
2.7 KiB
Python
Executable File
89 lines
2.7 KiB
Python
Executable File
import numpy as np
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from prml.linear.logistic_regression import LogisticRegression
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class VariationalLogisticRegression(LogisticRegression):
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def __init__(self, alpha:float=None, a0:float=1., b0:float=1.):
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"""
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construct variational logistic regressor
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Parameters
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----------
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alpha : float
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precision parameter of the prior
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if None, this is also the subject to estimate
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a0 : float
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a parameter of hyper prior Gamma dist.
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Gamma(alpha|a0,b0)
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if alpha is not None, this argument will be ignored
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b0 : float
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another parameter of hyper prior Gamma dist.
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Gamma(alpha|a0,b0)
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if alpha is not None, this argument will be ignored
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"""
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if alpha is not None:
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self.__alpha = alpha
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else:
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self.a0 = a0
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self.b0 = b0
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def fit(self, X:np.ndarray, t:np.ndarray, iter_max:int=1000):
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"""
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variational bayesian estimation of the parameter
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Parameters
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----------
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X : (N, D) np.ndarray
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training independent variable
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t : (N,) np.ndarray
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training dependent variable
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iter_max : int, optional
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maximum number of iteration (the default is 1000)
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"""
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N, D = X.shape
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if hasattr(self, "a0"):
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self.a = self.a0 + 0.5 * D
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xi = np.random.uniform(-1, 1, size=N)
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I = np.eye(D)
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param = np.copy(xi)
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for _ in range(iter_max):
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lambda_ = np.tanh(xi) * 0.25 / xi
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self.w_var = np.linalg.inv(I / self.alpha + 2 * (lambda_ * X.T) @ X)
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self.w_mean = self.w_var @ np.sum(X.T * (t - 0.5), axis=1)
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xi = np.sqrt(np.sum(X @ (self.w_var + self.w_mean * self.w_mean[:, None]) * X, axis=-1))
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if np.allclose(xi, param):
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break
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else:
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param = np.copy(xi)
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@property
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def alpha(self):
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if hasattr(self, "__alpha"):
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return self.__alpha
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else:
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try:
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self.b = self.b0 + 0.5 * (np.sum(self.w_mean ** 2) + np.trace(self.w_var))
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except AttributeError:
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self.b = self.b0
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return self.a / self.b
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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(X @ self.w_var * X, axis=1)
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y = self._sigmoid(mu_a / np.sqrt(1 + np.pi * var_a / 8))
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return y
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