Python 逻辑回归成本变化变为常数

经过几次梯度下降迭代后，成本函数变化变为常数，这是它不应该执行的最明确的方式：

梯度下降函数的初始结果似乎是正确的，成本函数和假设函数的结果也是正确的，所以我认为问题不在这里。对不起，如果问题太不明确，我自己也不能再缩小范围了。如果你能解释一下我的程序出了什么问题，我将不胜感激

以下是我正在使用的数据的外观：

34.62365962451697,78.0246928153624,0

30.28671076822607,43.89499752400101,0

35.84740876993872,72.90219802708364,0

60.18259938620976,86.30855209546826,1

79.0327360507101,75.3443764369103,1

45.08327747668339,56.3163717815305,0

这是代码：

import numpy as np
from matplotlib import pyplot as plt


data = np.genfromtxt("ex2data1.txt", delimiter=",")

X = data[:,0:-1]
X = np.array(X)
m = len(X)
ones = np.ones((m,1))
X = np.hstack((ones,X))

Y = data[:,-1]
Y = np.array(Y)
Y = Y.reshape((m,1))

Cost_History = [[],[]]

def Sigmoid(z):
    G = float(1/float(1+np.exp(-1.0*z)))
    return G

def Hypothesis(theta, x):
    z = np.dot(x,theta)
    return Sigmoid(z)

def Cost_Function(X, Y, theta, m):
    sumOfErrors = 0
    for i in range(m):
        xi = X[i]
        yi = Y[i]
        hi = Hypothesis(theta, xi)
        sumOfErrors += yi*np.log(hi) + (1-yi)*np.log(1-hi)
    const = -(1/m)
    J = const * sumOfErrors
    return J

def Cost_Function_Derivative(X, Y, theta, feature, alpha, m):
    sumErrors = 0
    for i in range(m):
        xi = X[i]
        yi = Y[i]
        hi = Hypothesis(theta, xi)
        error = (hi - yi)*xi[feature]
        sumErrors += error
    constant = float(alpha)/float(m)
    J = constant * sumErrors
    return J

def Gradient_Descent(X, Y, theta, alpha, m):
    new_theta = np.zeros((len(theta),1))
    for feature in range(len(theta)):
        CFDerivative = Cost_Function_Derivative(X, Y, theta, feature, alpha, m)
        new_theta[feature] = theta[feature] - CFDerivative
    return new_theta


def Logistic_Regression(X,Y,alpha, theta, iterations, m):
    for iter in range(iterations):
        theta = Gradient_Descent(X, Y, theta, alpha, m)
        cost = Cost_Function(X, Y, theta, m)
        Cost_History[0].append(cost)
        Cost_History[1].append(iter)
        if iter % 100 == 0:
            print(theta, cost, iter)
    return theta

alpha = 0.001
iterations = 1500

theta = np.zeros((len(X[0]),1))
theta = Logistic_Regression(X, Y, alpha, theta, iterations, m)
print(theta)
test = np.array((1,85,45))
print(Hypothesis(theta, test))

wrong = 0
for i in range(m):
    xi = X[i]
    yi = Y[i]
    hi = Hypothesis(theta, xi)
    if yi != round(hi):
        wrong+=1
print(wrong/m)

plt.plot(Cost_History[1], Cost_History[0], "b")
plt.show()

---

从给定的图中可以明显看出，成本实际上仍在下降。快速搜索可以发现，您的数据当前可以是，通过将代码运行500000次迭代，我得到的结果如下，看起来与您预期的一样：

在大约20000000步之后，

theta

的值变为

[-25.15510086,0.20618186,0.20142117]

。为了确保这是我们所期望的，我们可以将该值与使用较大值

C

获得的参数进行比较：

from sklearn.linear_model import LogisticRegression
model = LogisticRegression(C=1e10, tol=1e-6).fit(X, Y.ravel())
model.coef_[0] + np.array([model.intercept_[0], 0, 0])
# array([-25.16127356,   0.20623123,   0.20147112])

或者同样的事情发生在：

当然，运行这么多步骤的算法肯定需要一段时间。在实践中，您通常会使用二阶优化例程或随机梯度下降，但事实证明，您的大多数代码都可以使用向量化操作（如矩阵乘法）来表达，这将增加足够的性能，使其相对较快地收敛。特别是，您的方法可以按如下方式重写，唯一的区别是

Y

无需再进行重塑：

def hypothesis(theta, X):
    return 1/(1+np.exp(-np.dot(X, theta)))

def cost_function(X, Y, theta):
    h = hypothesis(theta, X)
    return -np.mean(Y*np.log(h) + (1-Y)*np.log(1-h))

def gradient_descent(X, Y, theta, alpha):
    h = hypothesis(theta, X)
    return theta - alpha*np.dot(X.T, h - Y)/len(X)

def logistic_regression(X, Y, alpha, theta, iterations):
    for iter in range(iterations):
        theta = gradient_descent(X, Y, theta, alpha)     
        if iter % 100000 == 0:
            cost = cost_function(X, Y, theta)
            cost_history[0].append(cost)
            cost_history[1].append(iter)
            print(theta, cost, iter)
    return theta

def hypothesis(theta, X):
    return 1/(1+np.exp(-np.dot(X, theta)))

def cost_function(X, Y, theta):
    h = hypothesis(theta, X)
    return -np.mean(Y*np.log(h) + (1-Y)*np.log(1-h))

def gradient_descent(X, Y, theta, alpha):
    h = hypothesis(theta, X)
    return theta - alpha*np.dot(X.T, h - Y)/len(X)

def logistic_regression(X, Y, alpha, theta, iterations):
    for iter in range(iterations):
        theta = gradient_descent(X, Y, theta, alpha)     
        if iter % 100000 == 0:
            cost = cost_function(X, Y, theta)
            cost_history[0].append(cost)
            cost_history[1].append(iter)
            print(theta, cost, iter)
    return theta