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