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 +1,83 @@
+import numpy as np
+from prml.linear.classifier import Classifier
+from prml.preprocess.label_transformer import LabelTransformer
+
+
+class SoftmaxRegression(Classifier):
+    """
+    Softmax regression model
+    aka
+    multinomial logistic regression,
+    multiclass logistic regression,
+    maximum entropy classifier.
+
+    y = softmax(X @ W)
+    t ~ Categorical(t|y)
+    """
+
+    @staticmethod
+    def _softmax(a):
+        a_max = np.max(a, axis=-1, keepdims=True)
+        exp_a = np.exp(a - a_max)
+        return exp_a / np.sum(exp_a, axis=-1, keepdims=True)
+
+    def fit(self, X:np.ndarray, t:np.ndarray, max_iter:int=100, learning_rate:float=0.1):
+        """
+        maximum likelihood estimation of the parameter
+
+        Parameters
+        ----------
+        X : (N, D) np.ndarray
+            training independent variable
+        t : (N,) or (N, K) np.ndarray
+            training dependent variable
+            in class index or one-of-k encoding
+        max_iter : int, optional
+            maximum number of iteration (the default is 100)
+        learning_rate : float, optional
+            learning rate of gradient descent (the default is 0.1)
+        """
+        if t.ndim == 1:
+            t = LabelTransformer().encode(t)
+        self.n_classes = np.size(t, 1)
+        W = np.zeros((np.size(X, 1), self.n_classes))
+        for _ in range(max_iter):
+            W_prev = np.copy(W)
+            y = self._softmax(X @ W)
+            grad = X.T @ (y - t)
+            W -= learning_rate * grad
+            if np.allclose(W, W_prev):
+                break
+        self.W = W
+
+    def proba(self, X:np.ndarray):
+        """
+        compute probability of input belonging each class
+
+        Parameters
+        ----------
+        X : (N, D) np.ndarray
+            independent variable
+
+        Returns
+        -------
+        (N, K) np.ndarray
+            probability of each class
+        """
+        return self._softmax(X @ self.W)
+
+    def classify(self, X:np.ndarray):
+        """
+        classify input data
+
+        Parameters
+        ----------
+        X : (N, D) np.ndarray
+            independent variable to be classified
+
+        Returns
+        -------
+        (N,) np.ndarray
+            class index for each input
+        """
+        return np.argmax(self.proba(X), axis=-1)