descent=alpha * 1/m * error

这是梯度下降算法中的一个公式，用于更新模型参数。其中，alpha表示学习率，m表示样本数量，error表示模型预测值与真实值之间的误差。这个公式的作用是根据误差的大小，调整模型参数的取值，使得模型的预测值更加接近真实值。具体来说，公式中的1/m表示对所有样本的误差进行平均，以避免单个样本对模型参数更新的影响过大。最终，通过多轮迭代，不断调整模型参数，使得模型的预测结果不断优化，达到最佳的预测效果。

相关问题

def gradientDescent(X,y,theta,alpha,num_iters,Lambda):

This is a Python function for performing gradient descent algorithm with regularization on a given dataset.

- X: Input feature matrix of size (m, n+1) where m is the number of training examples and n is the number of features. The first column of X is usually all ones for the bias term.
- y: Output vector of size (m, 1) containing the target values for each training example.
- theta: Parameter vector of size (n+1, 1) containing the initial values for the model parameters.
- alpha: Learning rate for the gradient descent algorithm.
- num_iters: Number of iterations to run the gradient descent algorithm.
- Lambda: Regularization parameter for controlling the trade-off between fitting the training data well and avoiding overfitting.

The function returns the optimized parameter vector theta after running the gradient descent algorithm.

Here's the code:

def gradientDescent(X,y,theta,alpha,num_iters,Lambda):
    m = len(y)
    for i in range(num_iters):
        h = X.dot(theta)
        error = h - y
        reg_term = (Lambda/m) * np.sum(theta[1:]**2)
        grad = (1/m) * (X.T.dot(error) + reg_term)
        theta[0] -= alpha * grad[0]
        theta[1:] -= alpha * grad[1:]
    return theta

给出下面代码注释def batch_gradientDescent(X, y, w, alpha, iters): temp = np.matrix(np.zeros(w.shape)) parameters = int(w.ravel().shape[1]) cost = np.zeros(iters) for i in range(iters): error = (X * w.T) - y for j in range(parameters): term = np.multiply(error, X[:, j]) temp[0, j] = w[0, j] - ((alpha / len(X)) * np.sum(term)) w = temp cost[i] = computeCost(X, y, w) return w, cost

这是一个批量梯度下降算法的实现代码，用于优化线性回归模型的参数。下面是代码的注释：

def batch_gradientDescent(X, y, w, alpha, iters):
    # 初始化一个全零矩阵用于存储每次迭代的更新值
    temp = np.matrix(np.zeros(w.shape))
    # 获取参数的个数
    parameters = int(w.ravel().shape[1])
    # 初始化损失函数的值
    cost = np.zeros(iters)

    for i in range(iters):
        # 计算预测值与实际值之间的误差
        error = (X * w.T) - y
        for j in range(parameters):
            # 计算每个参数的梯度，并更新到temp矩阵中
            term = np.multiply(error, X[:, j])
            temp[0, j] = w[0, j] - ((alpha / len(X)) * np.sum(term))

        # 将更新后的参数赋值给w
        w = temp
        # 计算当前迭代下的损失函数值
        cost[i] = computeCost(X, y, w)

    # 返回最终优化后的参数与损失函数值
    return w, cost

其中，X是输入数据的特征矩阵，y是对应的标签向量，w是线性回归模型的参数（权重向量），alpha是学习率，iters是迭代次数。注释中还提到了一个computeCost函数，用于计算损失函数的值。