有序逻辑回归函数python代码

下面是一个用Python编写的有序逻辑回归函数的示例代码：

import numpy as np
from scipy.optimize import minimize

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

def ordinal_logistic_regression(X, y):
    n_samples, n_features = X.shape
    n_classes = len(np.unique(y))
    
    # Initialize parameters
    theta = np.zeros((n_features, n_classes - 1))
    
    # Define cost function
    def cost_function(theta, X, y):
        m = len(y)
        probabilities = sigmoid(X @ theta)
        loss = np.zeros_like(probabilities)
        
        for i in range(n_classes - 1):
            loss[:, i] = np.where(y == i + 1, -np.log(probabilities[:, i]), 0)
        
        cost = np.sum(loss) / m
        return cost
    
    # Define gradient function
    def gradient(theta, X, y):
        m = len(y)
        probabilities = sigmoid(X @ theta)
        gradients = np.zeros_like(theta)
        
        for i in range(n_classes - 1):
            gradients[:, i] = np.sum((probabilities[:, i] - (y == i + 1))[:, None] * X, axis=0) / m
        
        return gradients.flatten()
    
    # Minimize the cost function
    result = minimize(cost_function, theta, args=(X, y), method='BFGS', jac=gradient)
    optimal_theta = result.x
    
    return optimal_theta

# Example usage:
X = np.array([[1, 2], [2, 3], [3, 4], [4, 5]])
y = np.array([1, 2, 3, 3])

theta = ordinal_logistic_regression(X, y)
print("Optimal Theta:")
print(theta)

这个代码使用了NumPy库来进行数值计算，并使用了SciPy库中的minimize函数进行优化。sigmoid函数用于计算逻辑回归的预测概率。`ordinal_logistic_regression`函数实现了