有序逻辑回归函数python代码
时间: 2023-11-12 11:56:37 浏览: 106
下面是一个用Python编写的有序逻辑回归函数的示例代码:
```python
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
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