机器学习（梯度下降python）

批量梯度下降

def gradient_descent(x, y, w, learning_rate, iterations):
    m = len(y)
    cost_history = np.zeros(iterations)
    
    for i in range(iterations):
        predictions = h(x, w)
        errors = predictions - y
        w -= (learning_rate / m) * np.dot(x.T, errors)  # 更新权重
        cost_history[i] = cost_function(x, y, w)  # 记录代价函数值
    
    return w, cost_history

小批量梯度下降

def mini_batch_gradient_descent(x, y, w, learning_rate, iterations, batch_size):
    m = len(y)
    cost_history = np.zeros(iterations)
    
    for i in range(iterations):
        # Shuffle the data
        indices = np.random.permutation(m)
        x_shuffled = x[indices]
        y_shuffled = y[indices]
        
        for j in range(0, m, batch_size):
            x_batch = x_shuffled[j:j + batch_size]
            y_batch = y_shuffled[j:j + batch_size]
            predictions = h(x_batch, w)
            errors = predictions - y_batch
            
            # Update weights
            w -= (learning_rate / batch_size) * np.dot(x_batch.T, errors)
        
        cost_history[i] = cost_function(x, y, w)

    return w, cost_history