留一法交叉验证优化BP神经网络代码

以下是一个基于留一法交叉验证的优化BP神经网络的代码示例：

import numpy as np

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

# 定义BP神经网络模型
class BPNeuralNetwork:
    def __init__(self, layers, lr=0.1, epochs=1000):
        self.layers = layers
        self.lr = lr
        self.epochs = epochs
        self.weights = [np.random.randn(y, x) for x, y in zip(layers[:-1], layers[1:])]
        self.biases = [np.random.randn(y, 1) for y in layers[1:]]
    
    def train(self, X, y):
        # 留一法交叉验证
        n = X.shape[0]
        for i in range(n):
            X_train = np.delete(X, i, axis=0)
            y_train = np.delete(y, i, axis=0)
            X_test = X[i].reshape(1, -1)
            y_test = y[i].reshape(1, -1)
            self._train(X_train, y_train, X_test, y_test)
    
    def _train(self, X_train, y_train, X_test, y_test):
        # 前向传播
        a = X_train.T
        for w, b in zip(self.weights, self.biases):
            z = np.dot(w, a) + b
            a = sigmoid(z)
        # 反向传播
        delta = (a - y_train.T) * a * (1 - a)
        for w, b in zip(self.weights[::-1], self.biases[::-1]):
            dw = np.dot(delta, a.T)
            db = np.sum(delta, axis=1, keepdims=True)
            w -= self.lr * dw
            b -= self.lr * db
            delta = np.dot(w.T, delta) * a * (1 - a)
            a = sigmoid(np.dot(w, a) + b)
        # 测试误差
        a = X_test.T
        for w, b in zip(self.weights, self.biases):
            z = np.dot(w, a) + b
            a = sigmoid(z)
        error = np.sum((a - y_test.T) ** 2)
        print("Test error:", error)
    
    def predict(self, X):
        a = X.T
        for w, b in zip(self.weights, self.biases):
            z = np.dot(w, a) + b
            a = sigmoid(z)
        return a.T

在这个代码示例中，我们定义了一个 `BPNeuralNetwork` 类来实现BP神经网络模型。其中，`train` 方法使用留一法交叉验证来训练模型，并在每个测试集上计算测试误差。`_train` 方法实现一次前向传播和反向传播，并更新网络参数。`predict` 方法用于对新数据进行预测。

在使用时，我们需要将数据集 `X` 和标签 `y` 传入 `BPNeuralNetwork` 类的构造函数中，并指定神经网络的层数、学习率和迭代次数。然后，调用 `train` 方法来训练模型，最后使用 `predict` 方法进行预测。