批量梯度下降实现线性回归

import numpy as np

def Gradient_Descent(X, Y, theta, alpha = 0.01, interations = 200):
    m, n = X.shape
    theta = np.zeros(n)+0.1*np.random.randn()
    for i in range(interations):
        Y_predict = X.dot(theta.T)
        loss = Y - Y_predict
        loss_grad = np.sum(loss*X, axis=0)/m
        theta = theta + alpha*loss_grad
    return theta

def Prediction(X, theta):
    return X.dot(theta.T)

随机梯度下降实现线性回归

import numpy as np

def Gradient_Descent(X, Y, theta, alpha = 0.01, interations = 200):
    m, n = X.shape
    theta = np.zeros(n)+0.1*np.random.randn()
    for i in range(interations):
        rand = np.random.randint(m)
        x = X[rand]
        y = Y[rand]
        y_predict = x.dot(theta.T)
        loss = y - y_predict
        loss_grad = loss*x
        theta = theta + alpha*loss_grad
    return theta

def Prediction(X, theta):
    return X.dot(theta.T)

小批量梯度下降实现线性回归

import numpy as np

def Gradient_Descent(X, Y, batch_size, theta, alpha = 0.01, interations = 200):
    m, n = X.shape
    theta = np.zeros(n)+0.1*np.random.randn()
    if m%batch_size != 0:
        X = np.concatenate((X,X[:m%batch_size]), axis=0)
    for i in range(interations):
        batch_num = m/batch_size
        for j in range(batch_num):
            mini_X = X[j*batch_size:j*(batch_size+1)]
            Y_predict = mini_X.dot(theta.T)
            loss = Y - Y_predict
            loss_grad = np.sum(loss*mini_X, axis=0)/batch_size
            theta = theta + alpha*loss_grad
    return theta

def Prediction(X, theta):
    return X.dot(theta.T)