写一个BP回归的matlab代码

以下是一个简单的BP回归的matlab代码：

% 导入数据
data = load('data.txt');
X = data(:, 1);
y = data(:, 2);

% 初始化神经网络
input_layer_size = 1;
hidden_layer_size = 3;
output_layer_size = 1;
epsilon_init = 0.12;
initial_Theta1 = rand(hidden_layer_size, input_layer_size + 1) * 2 * epsilon_init - epsilon_init;
initial_Theta2 = rand(output_layer_size, hidden_layer_size + 1) * 2 * epsilon_init - epsilon_init;
initial_nn_params = [initial_Theta1(:) ; initial_Theta2(:)];

% 训练神经网络
options = optimset('MaxIter', 500);
lambda = 0.1;
costFunction = @(p) nnCostFunction(p, input_layer_size, hidden_layer_size, output_layer_size, X, y, lambda);
[nn_params, cost] = fmincg(costFunction, initial_nn_params, options);

% 预测结果
pred = predict(nn_params, input_layer_size, hidden_layer_size, output_layer_size, X);

% 绘制结果
plot(X, y, 'rx', X, pred, 'bo');
legend('Training data', 'Prediction');
xlabel('X');
ylabel('y');

% 定义代价函数
function [J, grad] = nnCostFunction(nn_params, input_layer_size, hidden_layer_size, output_layer_size, X, y, lambda)
Theta1 = reshape(nn_params(1:hidden_layer_size * (input_layer_size + 1)), hidden_layer_size, (input_layer_size + 1));
Theta2 = reshape(nn_params((1 + (hidden_layer_size * (input_layer_size + 1))):end), output_layer_size, (hidden_layer_size + 1));
m = size(X, 1);
J = 0;
Theta1_grad = zeros(size(Theta1));
Theta2_grad = zeros(size(Theta2));
a1 = [ones(m, 1) X];
z2 = a1 * Theta1';
a2 = [ones(size(z2, 1), 1) sigmoid(z2)];
z3 = a2 * Theta2';
h = sigmoid(z3);
J = (1 / m) * sum(sum((-y .* log(h)) - ((1 - y) .* log(1 - h))));
J = J + ((lambda / (2 * m)) * (sum(sum(Theta1(:, 2:end) .^ 2)) + sum(sum(Theta2(:, 2:end) .^ 2))));
delta3 = h - y;
delta2 = (delta3 * Theta2) .* sigmoidGradient([ones(size(z2, 1), 1) z2]);
delta2 = delta2(:, 2:end);
Theta1_grad = (1 / m) * (delta2' * a1);
Theta2_grad = (1 / m) * (delta3' * a2);
Theta1_grad(:, 2:end) = Theta1_grad(:, 2:end) + ((lambda / m) * Theta1(:, 2:end));
Theta2_grad(:, 2:end) = Theta2_grad(:, 2:end) + ((lambda / m) * Theta2(:, 2:end));
grad = [Theta1_grad(:) ; Theta2_grad(:)];
end

% 定义sigmoid函数
function g = sigmoid(z)
g = 1.0 ./ (1.0 + exp(-z));
end

% 定义sigmoid函数的导数
function g = sigmoidGradient(z)
g = sigmoid(z) .* (1 - sigmoid(z));
end

% 预测函数
function p = predict(nn_params, input_layer_size, hidden_layer_size, output_layer_size, X)
Theta1 = reshape(nn_params(1:hidden_layer_size * (input_layer_size + 1)), hidden_layer_size, (input_layer_size + 1));
Theta2 = reshape(nn_params((1 + (hidden_layer_size * (input_layer_size + 1))):end), output_layer_size, (hidden_layer_size + 1));
m = size(X, 1);
p = zeros(m, 1);
a1 = [ones(m, 1) X];
z2 = a1 * Theta1';
a2 = [ones(size(z2, 1), 1) sigmoid(z2)];
z3 = a2 * Theta2';
h = sigmoid(z3);
p = h;
end