wehub-resource-sync
94 lines
2.8 KiB
Python
Executable File
94 lines
2.8 KiB
Python
Executable File
import numpy as np
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from prml.linear.regression import Regression
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class VariationalLinearRegression(Regression):
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"""
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variational bayesian estimation of linear regression model
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p(w,alpha|X,t)
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~ q(w)q(alpha)
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= N(w|w_mean, w_var)Gamma(alpha|a,b)
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Attributes
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----------
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a : float
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a parameter of variational posterior gamma distribution
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b : float
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another parameter of variational posterior gamma distribution
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w_mean : (n_features,) ndarray
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mean of variational posterior gaussian distribution
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w_var : (n_features, n_feautures) ndarray
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variance of variational posterior gaussian distribution
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n_iter : int
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number of iterations performed
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"""
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def __init__(self, beta:float=1., a0:float=1., b0:float=1.):
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"""
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construct variational linear regressor
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Parameters
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----------
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beta : float
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precision of observation noise
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a0 : float
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a parameter of prior gamma distribution
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Gamma(alpha|a0,b0)
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b0 : float
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another parameter of prior gamma distribution
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Gamma(alpha|a0,b0)
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"""
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self.beta = beta
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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=100):
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"""
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variational bayesian estimation of 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 100)
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"""
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D = np.size(X, 1)
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self.a = self.a0 + 0.5 * D
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self.b = self.b0
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I = np.eye(D)
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for _ in range(iter_max):
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param = self.b
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self.w_var = np.linalg.inv(self.a * I / self.b + self.beta * X.T @ X)
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self.w_mean = self.beta * self.w_var @ X.T @ t
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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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if np.allclose(self.b, param):
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break
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def predict(self, X:np.ndarray, return_std:bool=False):
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"""
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make prediction of input
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Parameters
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----------
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X : (N, D) np.ndarray
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independent variable
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return_std : bool, optional
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return standard deviation of predictive distribution if True
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(the default is False)
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Returns
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-------
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y : (N,) np.ndarray
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mean of predictive distribution
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y_std : (N,) np.ndarray
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standard deviation of predictive distribution
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"""
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y = X @ self.w_mean
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if return_std:
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y_var = 1 / self.beta + np.sum(X @ self.w_var * X, axis=1)
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y_std = np.sqrt(y_var)
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return y, y_std
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return y
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