[英]How to vectorize Logistic Regression?
我正在嘗試使用針對Coursera ML類的python實現正則化邏輯回歸,但是在向量化方面存在很多麻煩。 使用此存儲庫:
我嘗試了許多不同的方法,但從未獲得正確的漸變或為此付出代價,這是我目前的實現方式:
h = utils.sigmoid( np.dot(X, theta) )
J = (-1/m) * ( y.T.dot( np.log(h) ) + (1 - y.T).dot( np.log( 1 - h ) ) ) + ( lambda_/(2*m) ) * np.sum( np.square(theta[1:]) )
grad = ((1/m) * (h - y).T.dot( X )).T + grad_theta_reg
結果如下:
Cost : 0.693147
預期
cost: 2.534819
漸變色:
[-0.100000, -0.030000, -0.080000, -0.130000]
預期的漸變:
[0.146561, -0.548558, 0.724722, 1.398003]
知道發生了什么事的人的任何幫助將不勝感激。
下面是Logistic回歸的矢量化版本的有效代碼段。 您可以在這里查看更多內容https://github.com/hzitoun/coursera_machine_learning_matlab_python
主要
theta_t = np.array([[-2], [-1], [1], [2]])
data = np.arange(1, 16).reshape(3, 5).T
X_t = np.c_[np.ones((5,1)), data/10]
y_t = (np.array([[1], [0], [1], [0], [1]]) >= 0.5) * 1
lambda_t = 3
J, grad = lrCostFunction(theta_t, X_t, y_t, lambda_t), lrGradient(theta_t, X_t, y_t, lambda_t, flattenResult=False)
print('\nCost: f\n', J)
print('Expected cost: 2.534819\n')
print('Gradients:\n')
print(' f \n', grad)
print('Expected gradients:\n')
print(' 0.146561\n -0.548558\n 0.724722\n 1.398003\n')
lrCostFunction
from sigmoid import sigmoid
import numpy as np
def lrCostFunction(theta, X, y, reg_lambda):
"""LRCOSTFUNCTION Compute cost and gradient for logistic regression with
regularization
J = LRCOSTFUNCTION(theta, X, y, lambda) computes the cost of using
theta as the parameter for regularized logistic regression and the
gradient of the cost w.r.t. to the parameters.
"""
m, n = X.shape #number of training examples
theta = theta.reshape((n,1))
prediction = sigmoid(X.dot(theta))
cost_y_1 = (1 - y) * np.log(1 - prediction)
cost_y_0 = -1 * y * np.log(prediction)
J = (1.0/m) * np.sum(cost_y_0 - cost_y_1) + (reg_lambda/(2.0 * m)) * np.sum(np.power(theta[1:], 2))
return J
漸變
from sigmoid import sigmoid
import numpy as np
def lrGradient(theta, X,y, reg_lambda, flattenResult=True):
m,n = X.shape
theta = theta.reshape((n,1))
prediction = sigmoid(np.dot(X, theta))
errors = np.subtract(prediction, y)
grad = (1.0/m) * np.dot(X.T, errors)
grad_with_regul = grad[1:] + (reg_lambda/m) * theta[1:]
firstRow = grad[0, :].reshape((1,1))
grad = np.r_[firstRow, grad_with_regul]
if flattenResult:
return grad.flatten()
return grad
希望能有所幫助!
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