wehub-resource-sync
88 lines
2.7 KiB
Python
Executable File
88 lines
2.7 KiB
Python
Executable File
import numpy as np
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from prml.linear.regression import Regression
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class BayesianRegression(Regression):
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"""
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Bayesian regression model
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w ~ N(w|0, alpha^(-1)I)
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y = X @ w
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t ~ N(t|X @ w, beta^(-1))
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"""
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def __init__(self, alpha:float=1., beta:float=1.):
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self.alpha = alpha
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self.beta = beta
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self.w_mean = None
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self.w_precision = None
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def _is_prior_defined(self) -> bool:
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return self.w_mean is not None and self.w_precision is not None
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def _get_prior(self, ndim:int) -> tuple:
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if self._is_prior_defined():
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return self.w_mean, self.w_precision
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else:
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return np.zeros(ndim), self.alpha * np.eye(ndim)
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def fit(self, X:np.ndarray, t:np.ndarray):
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"""
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bayesian update of parameters given training dataset
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Parameters
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----------
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X : (N, n_features) 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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"""
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mean_prev, precision_prev = self._get_prior(np.size(X, 1))
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w_precision = precision_prev + self.beta * X.T @ X
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w_mean = np.linalg.solve(
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w_precision,
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precision_prev @ mean_prev + self.beta * X.T @ t
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)
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self.w_mean = w_mean
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self.w_precision = w_precision
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self.w_cov = np.linalg.inv(self.w_precision)
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def predict(self, X:np.ndarray, return_std:bool=False, sample_size:int=None):
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"""
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return mean (and standard deviation) of predictive distribution
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Parameters
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----------
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X : (N, n_features) np.ndarray
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independent variable
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return_std : bool, optional
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flag to return standard deviation (the default is False)
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sample_size : int, optional
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number of samples to draw from the predictive distribution
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(the default is None, no sampling from the distribution)
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Returns
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-------
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y : (N,) np.ndarray
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mean of the predictive distribution
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y_std : (N,) np.ndarray
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standard deviation of the predictive distribution
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y_sample : (N, sample_size) np.ndarray
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samples from the predictive distribution
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"""
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if sample_size is not None:
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w_sample = np.random.multivariate_normal(
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self.w_mean, self.w_cov, size=sample_size
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)
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y_sample = X @ w_sample.T
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return y_sample
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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_cov * 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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