待阅读https://www.cnblogs.com/Determined22/p/6362951.html
import numpy as np
from prml.linear.classifier import Classifier
class LogisticRegression(Classifier):
"""
Logistic regression model
y = sigmoid(X @ w)
t ~ Bernoulli(t|y)
"""
@staticmethod
def _sigmoid(a):
return np.tanh(a * 0.5) * 0.5 + 0.5
def fit(self, X:np.ndarray, t:np.ndarray, max_iter:int=100):
"""
maximum likelihood estimation of logistic regression model
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))
for _ in range(max_iter):
w_prev = np.copy(w)
y = self._sigmoid(X @ w)
grad = X.T @ (y - t)
hessian = (X.T * y * (1 - y)) @ X
try:
w -= np.linalg.solve(hessian, grad)
except np.linalg.LinAlgError:
break
if np.allclose(w, w_prev):
break
self.w = w
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
"""
return self._sigmoid(X @ self.w)
def classify(self, X:np.ndarray, threshold:float=0.5):
"""
classify input data
Parameters
----------
X : (N, D) np.ndarray
independent variable to be classified
threshold : float, optional
threshold of binary classification (default is 0.5)
Returns
-------
(N,) np.ndarray
binary class for each input
"""
return (self.proba(X) > threshold).astype(np.int)
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)#t是N*K的，K表示类别数
W = np.zeros((np.size(X, 1)),self.n_classes)
for _ in range(max_iter):
for i in range(np.size(t,0)):
W_prev = np.copy(W)
y = self._softmax(X[i] @ W)
grad = X[i].T @ (y - t[i])
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)
