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 +1,66 @@
+import numpy as np
+from prml.linear.logistic_regression import LogisticRegression
+
+
+class BayesianLogisticRegression(LogisticRegression):
+    """
+    Logistic regression model
+
+    w ~ Gaussian(0, alpha^(-1)I)
+    y = sigmoid(X @ w)
+    t ~ Bernoulli(t|y)
+    """
+
+    def __init__(self, alpha:float=1.):
+        self.alpha = alpha
+
+    def fit(self, X:np.ndarray, t:np.ndarray, max_iter:int=100):
+        """
+        bayesian estimation of logistic regression model
+        using Laplace approximation
+
+        Parameters
+        ----------
+        X : (N, D) np.ndarray
+            training data independent variable
+        t : (N,) np.ndarray
+            training data dependent variable
+            binary 0 or 1
+        max_iter : int, optional
+            maximum number of paramter update iteration (the default is 100)
+        """
+        w = np.zeros(np.size(X, 1))
+        eye = np.eye(np.size(X, 1))
+        self.w_mean = np.copy(w)
+        self.w_precision = self.alpha * eye
+        for _ in range(max_iter):
+            w_prev = np.copy(w)
+            y = self._sigmoid(X @ w)
+            grad = X.T @ (y - t) + self.w_precision @ (w - self.w_mean)
+            hessian = (X.T * y * (1 - y)) @ X + self.w_precision
+            try:
+                w -= np.linalg.solve(hessian, grad)
+            except np.linalg.LinAlgError:
+                break
+            if np.allclose(w, w_prev):
+                break
+        self.w_mean = w
+        self.w_precision = hessian
+
+    def proba(self, X:np.ndarray):
+        """
+        compute probability of input belonging class 1
+
+        Parameters
+        ----------
+        X : (N, D) np.ndarray
+            training data independent variable
+
+        Returns
+        -------
+        (N,) np.ndarray
+            probability of positive
+        """
+        mu_a = X @ self.w_mean
+        var_a = np.sum(np.linalg.solve(self.w_precision, X.T).T * X, axis=1)
+        return self._sigmoid(mu_a / np.sqrt(1 + np.pi * var_a / 8))