使用Python实现小批量梯度下降算法的代码逻辑

import numpy as npimport matplotlib.pyplot as pltmean=np.array([5.0,6.0])cov=np.array([[1.0,0.95],[0.95,1.2]])data=np.random.multivariate_normal(mean,cov,8000)plt.scatter(data[:500,0],data[:500,1],marker='.')plt.show()data=np.hstack((np.ones((data.shape[0],1)),data))split_factor=0.90split=int(split_factor*data.shape[0])X_train=data[:split,:-1]y_train=data[:split,-1].reshape((-1,1))X_test=data[split:,:-1]y_test=data[split:,-1].reshape((-1,1))print(& quot Number of examples in training set= % d & quot % (X_train.shape[0]))print(& quot Number of examples in testing set= % d & quot % (X_test.shape[0]))

def hypothesis(X,theta):    return np.dot(X,theta)def gradient(X,y,theta):    h=hypothesis(X,theta)    grad=np.dot(X.transpose(),(h-y))    return graddef cost(X,y,theta):    h=hypothesis(X,theta)    J=np.dot((h-y).transpose(),(h-y))    J/=2    return J[0]def create_mini_batches(X,y,batch_size):    mini_batches=[]    data=np.hstack((X,y))    np.random.shuffle(data)    n_minibatches=data.shape[0]//batch_size    i=0    for i in range(n_minibatches+1):        mini_batch=data[i*batch_size:(i+1)*batch_size,:]        X_mini=mini_batch[:,:-1]        Y_mini=mini_batch[:,-1].reshape((-1,1))        mini_batches.append((X_mini,Y_mini))    if data.shape[0]%batch_size!=0:       mini_batch=data[i*batch_size:data.shape[0]]       X_mini=mini_batch[:,:-1]       Y_mini=mini_batch[:,-1].reshape((-1,1))       mini_batches.append((X_mini,Y_mini))    return mini_batchesdef gradientDescent(X,y,learning_rate=0.001,batch_size=32):    theta=np.zeros((X.shape[1],1))    error_list=[]    max_iters=3    for itr in range(max_iters):        mini_batches=create_mini_batches(X,y,batch_size)        for mini_batch in mini_batches:            X_mini,y_mini=mini_batch            theta=theta-learning_rate*gradient(X_mini,y_mini,theta)            error_list.append(cost(X_mini,y_mini,theta))    return theta,error_list

theta,error_list=gradientDescent(X_train,y_train)print("Bias=",theta[0])print("Coefficients=",theta[1:])plt.plot(error_list)plt.xlabel("Number of iterations")plt.ylabel("Cost")plt.show()

y_pred=hypothesis(X_test,theta)plt.scatter(X_test[:,1],y_test[:,],marker='.')plt.plot(X_test[:,1],y_pred,color='orange')plt.show()error=np.sum(np.abs(y_test-y_pred)/y_test.shape[0])print(& quot Mean absolute error=&quot,error)