正则化

一、正则化的线性回归模型

1.成本函数

def compute_cost(X, y, w, b, lambda_):
    m = X.shape[0]
    n = len(w)
    cost = 0.
    for i in range(m):
        z_i = np.dot(X[i], w) + b
        cost += (z_i - y[i]) ** 2
    cost = cost / (2 * m)
    reg_cost = 0
    for j in range(n):
        reg_cost += w[j] ** 2
    reg_cost = (lambda_ / (2 * m)) * reg_cost
    return cost + reg_cost

2.梯度下降函数

二、正则化的逻辑回归模型

1.成本函数

def sigmoid(x):
    return 1 / (1 + np.exp(-x))


def compute_cost(X, y, w, b, lambda_):
    m = X.shape[0]
    n = len(w)
    cost = 0.

    for i in range(m):
        z_i = np.dot(X, w) + b
        f_wb_i = sigmoid(z_i)
        cost += y[i] * np.log(f_wb_i) + (1 - y[i]) * np.log(1 - f_wb_i)
    cost = cost / (-m)

    reg_cost = 0
    for j in range(n):
        reg_cost += w[j] ** 2

    reg_cost = (lambda_ / (2 * m)) * reg_cost
    return cost + reg_cost

2.梯度下降函数

def compute_gradient(X, y, w, b, lambda_):
    m, n = X.shape[0]
    df_dw = np.zeros((n,))
    df_db = 0.0
    for i in range(m):
        z_i = np.dot(X, w) + b
        f_wb_i = sigmoid(z_i)
        err = f_wb_i - y[i]
        for j in range(m):
            df_dw[j] += err * X[i, j]
        df_db += err
    df_dw = df_dw / m
    df_db = df_db / m

    for j in range(n):
        df_dw[j] = df_dw[j] + (lambda_ / m) * w[j]
    return df_dw, df_db