chore: import upstream snapshot with attribution

2026-07-13 13:30:25 +08:00
commit f19b2512d7
562 changed files with 38082 additions and 0 deletions
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+import numpy as np
+from prml.linear.regression import Regression
+
+
+class VariationalLinearRegression(Regression):
+    """
+    variational bayesian estimation of linear regression model
+    p(w,alpha|X,t)
+    ~ q(w)q(alpha)
+    = N(w|w_mean, w_var)Gamma(alpha|a,b)
+
+    Attributes
+    ----------
+    a : float
+        a parameter of variational posterior gamma distribution
+    b : float
+        another parameter of variational posterior gamma distribution
+    w_mean : (n_features,) ndarray
+        mean of variational posterior gaussian distribution
+    w_var : (n_features, n_feautures) ndarray
+        variance of variational posterior gaussian distribution
+    n_iter : int
+        number of iterations performed
+    """
+
+    def __init__(self, beta:float=1., a0:float=1., b0:float=1.):
+        """
+        construct variational linear regressor
+        Parameters
+        ----------
+        beta : float
+            precision of observation noise
+        a0 : float
+            a parameter of prior gamma distribution
+            Gamma(alpha|a0,b0)
+        b0 : float
+            another parameter of prior gamma distribution
+            Gamma(alpha|a0,b0)
+        """
+        self.beta = beta
+        self.a0 = a0
+        self.b0 = b0
+
+    def fit(self, X:np.ndarray, t:np.ndarray, iter_max:int=100):
+        """
+        variational bayesian estimation of parameter
+
+        Parameters
+        ----------
+        X : (N, D) np.ndarray
+            training independent variable
+        t : (N,) np.ndarray
+            training dependent variable
+        iter_max : int, optional
+            maximum number of iteration (the default is 100)
+        """
+        D = np.size(X, 1)
+        self.a = self.a0 + 0.5 * D
+        self.b = self.b0
+        I = np.eye(D)
+        for _ in range(iter_max):
+            param = self.b
+            self.w_var = np.linalg.inv(self.a * I / self.b + self.beta * X.T @ X)
+            self.w_mean = self.beta * self.w_var @ X.T @ t
+            self.b = self.b0 + 0.5 * (np.sum(self.w_mean ** 2) + np.trace(self.w_var))
+            if np.allclose(self.b, param):
+                break
+
+    def predict(self, X:np.ndarray, return_std:bool=False):
+        """
+        make prediction of input
+
+        Parameters
+        ----------
+        X : (N, D) np.ndarray
+            independent variable
+        return_std : bool, optional
+            return standard deviation of predictive distribution if True
+            (the default is False)
+
+        Returns
+        -------
+        y : (N,) np.ndarray
+            mean of predictive distribution
+        y_std : (N,) np.ndarray
+            standard deviation of predictive distribution
+        """
+        y = X @ self.w_mean
+        if return_std:
+            y_var = 1 / self.beta + np.sum(X @ self.w_var * X, axis=1)
+            y_std = np.sqrt(y_var)
+            return y, y_std
+        return y