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
@@ -0,0 +1,87 @@
+import numpy as np
+from prml.linear.regression import Regression
+
+
+class BayesianRegression(Regression):
+    """
+    Bayesian regression model
+
+    w ~ N(w|0, alpha^(-1)I)
+    y = X @ w
+    t ~ N(t|X @ w, beta^(-1))
+    """
+
+    def __init__(self, alpha:float=1., beta:float=1.):
+        self.alpha = alpha
+        self.beta = beta
+        self.w_mean = None
+        self.w_precision = None
+
+    def _is_prior_defined(self) -> bool:
+        return self.w_mean is not None and self.w_precision is not None
+
+    def _get_prior(self, ndim:int) -> tuple:
+        if self._is_prior_defined():
+            return self.w_mean, self.w_precision
+        else:
+            return np.zeros(ndim), self.alpha * np.eye(ndim)
+
+    def fit(self, X:np.ndarray, t:np.ndarray):
+        """
+        bayesian update of parameters given training dataset
+
+        Parameters
+        ----------
+        X : (N, n_features) np.ndarray
+            training data independent variable
+        t : (N,) np.ndarray
+            training data dependent variable
+        """
+
+        mean_prev, precision_prev = self._get_prior(np.size(X, 1))
+
+        w_precision = precision_prev + self.beta * X.T @ X
+        w_mean = np.linalg.solve(
+            w_precision,
+            precision_prev @ mean_prev + self.beta * X.T @ t
+        )
+        self.w_mean = w_mean
+        self.w_precision = w_precision
+        self.w_cov = np.linalg.inv(self.w_precision)
+
+    def predict(self, X:np.ndarray, return_std:bool=False, sample_size:int=None):
+        """
+        return mean (and standard deviation) of predictive distribution
+
+        Parameters
+        ----------
+        X : (N, n_features) np.ndarray
+            independent variable
+        return_std : bool, optional
+            flag to return standard deviation (the default is False)
+        sample_size : int, optional
+            number of samples to draw from the predictive distribution
+            (the default is None, no sampling from the distribution)
+
+        Returns
+        -------
+        y : (N,) np.ndarray
+            mean of the predictive distribution
+        y_std : (N,) np.ndarray
+            standard deviation of the predictive distribution
+        y_sample : (N, sample_size) np.ndarray
+            samples from the predictive distribution
+        """
+
+        if sample_size is not None:
+            w_sample = np.random.multivariate_normal(
+                self.w_mean, self.w_cov, size=sample_size
+            )
+            y_sample = X @ w_sample.T
+            return y_sample
+        y = X @ self.w_mean
+        if return_std:
+            y_var = 1 / self.beta + np.sum(X @ self.w_cov * X, axis=1)
+            y_std = np.sqrt(y_var)
+            return y, y_std
+        return y