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 +1,59 @@
+import numpy as np
+from prml.dimreduction.pca import PCA
+
+
+class BayesianPCA(PCA):
+
+    def fit(self, X, iter_max=100, initial="random"):
+        """
+        empirical bayes estimation of pca parameters
+
+        Parameters
+        ----------
+        X : (sample_size, n_features) ndarray
+            input data
+        iter_max : int
+            maximum number of em steps
+
+        Returns
+        -------
+        mean : (n_features,) ndarray
+            sample mean fo the input data
+        W : (n_features, n_components) ndarray
+            projection matrix
+        var : float
+            variance of observation noise
+        """
+        initial_list = ["random", "eigen"]
+        self.mean = np.mean(X, axis=0)
+        self.I = np.eye(self.n_components)
+        if initial not in initial_list:
+            print("availabel initializations are {}".format(initial_list))
+        if initial == "random":
+            self.W = np.eye(np.size(X, 1), self.n_components)
+            self.var = 1.
+        elif initial == "eigen":
+            self.eigen(X)
+        self.alpha = len(self.mean) / np.sum(self.W ** 2, axis=0).clip(min=1e-10)
+        for i in range(iter_max):
+            W = np.copy(self.W)
+            stats = self._expectation(X - self.mean)
+            self._maximization(X - self.mean, *stats)
+            self.alpha = len(self.mean) / np.sum(self.W ** 2, axis=0).clip(min=1e-10)
+            if np.allclose(W, self.W):
+                break
+        self.n_iter = i + 1
+
+    def _maximization(self, X, Ez, Ezz):
+        self.W = X.T @ Ez @ np.linalg.inv(np.sum(Ezz, axis=0) + self.var * np.diag(self.alpha))
+        self.var = np.mean(
+            np.mean(X ** 2, axis=-1)
+            - 2 * np.mean(Ez @ self.W.T * X, axis=-1)
+            + np.trace((Ezz @ self.W.T @ self.W).T) / len(self.mean))
+
+    def maximize(self, D, Ez, Ezz):
+        self.W = D.T.dot(Ez).dot(np.linalg.inv(np.sum(Ezz, axis=0) + self.var * np.diag(self.alpha)))
+        self.var = np.mean(
+            np.mean(D ** 2, axis=-1)
+            - 2 * np.mean(Ez.dot(self.W.T) * D, axis=-1)
+            + np.trace(Ezz.dot(self.W.T).dot(self.W).T) / self.ndim)