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 +1,88 @@
+import numpy as np
+from prml.linear.logistic_regression import LogisticRegression
+
+
+class VariationalLogisticRegression(LogisticRegression):
+
+    def __init__(self, alpha:float=None, a0:float=1., b0:float=1.):
+        """
+        construct variational logistic regressor
+
+        Parameters
+        ----------
+        alpha : float
+            precision parameter of the prior
+            if None, this is also the subject to estimate
+        a0 : float
+            a parameter of hyper prior Gamma dist.
+            Gamma(alpha|a0,b0)
+            if alpha is not None, this argument will be ignored
+        b0 : float
+            another parameter of hyper prior Gamma dist.
+            Gamma(alpha|a0,b0)
+            if alpha is not None, this argument will be ignored
+        """
+        if alpha is not None:
+            self.__alpha = alpha
+        else:
+            self.a0 = a0
+            self.b0 = b0
+
+    def fit(self, X:np.ndarray, t:np.ndarray, iter_max:int=1000):
+        """
+        variational bayesian estimation of the 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 1000)
+        """
+        N, D = X.shape
+        if hasattr(self, "a0"):
+            self.a = self.a0 + 0.5 * D
+        xi = np.random.uniform(-1, 1, size=N)
+        I = np.eye(D)
+        param = np.copy(xi)
+        for _ in range(iter_max):
+            lambda_ = np.tanh(xi) * 0.25 / xi
+            self.w_var = np.linalg.inv(I / self.alpha + 2 * (lambda_ * X.T) @ X)
+            self.w_mean = self.w_var @ np.sum(X.T * (t - 0.5), axis=1)
+            xi = np.sqrt(np.sum(X @ (self.w_var + self.w_mean * self.w_mean[:, None]) * X, axis=-1))
+            if np.allclose(xi, param):
+                break
+            else:
+                param = np.copy(xi)
+
+    @property
+    def alpha(self):
+        if hasattr(self, "__alpha"):
+            return self.__alpha
+        else:
+            try:
+                self.b = self.b0 + 0.5 * (np.sum(self.w_mean ** 2) + np.trace(self.w_var))
+            except AttributeError:
+                self.b = self.b0
+            return self.a / self.b
+
+    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(X @ self.w_var * X, axis=1)
+        y = self._sigmoid(mu_a / np.sqrt(1 + np.pi * var_a / 8))
+        return y