sigmoidal回归与scipy,numpy,python等

import numpy as np
from scipy.optimize import minimize

# 定义sigmoid函数
def sigmoid(x):
    return 1 / (1 + np.exp(-x))

# 定义损失函数
def loss(theta, X, y):
    m = len(y)
    h = sigmoid(X.dot(theta))
    J = -1/m * (np.log(h).T.dot(y) + np.log(1-h).T.dot(1-y))
    return J

# 定义梯度函数
def gradient(theta, X, y):
    m = len(y)
    h = sigmoid(X.dot(theta))
    grad = 1/m * X.T.dot(h-y)
    return grad

# 使用scipy的minimize函数进行参数优化
def train(X, y):
    m, n = X.shape
    X = np.concatenate((np.ones((m, 1)), X), axis=1)
    initial_theta = np.zeros(n+1)
    result = minimize(loss, initial_theta, args=(X, y), jac=gradient)
    return result.x

# 使用训练好的参数进行预测
def predict(X, theta):
    m = X.shape[0]
    X = np.concatenate((np.ones((m, 1)), X), axis=1)
    prob = sigmoid(X.dot(theta))
    return (prob >= 0.5).astype(int)

# 示例数据
X = np.array([[1, 2], [3, 4], [5, 6]])
y = np.array([0, 0, 1])

# 训练模型
theta = train(X, y)

# 预测新样本
new_X = np.array([[7, 8], [9, 10]])
predictions = predict(new_X, theta)
print(predictions)