kaggle gradient_descent

kaggle gradient_descent

1.描述

自写梯度下降

2.代码

import numpy as np
import matplotlib.pyplot as plt

# train_X = np.array([[1,2,3,4,5,6,7,8,9,10],[1,2,3,4,5,6,7,8,9,10]]).T
# train_y = np.array([2,4,6,8,10,12,14,16,18,20]).T
# test_X = np.array([[2,4,12,11],[3,6,3,9]]).T # 5 10 15 20

train_X = np.random.randn(1000,10)
train_y = np.random.randn(1000,1)
test_X =  np.random.randn(1000,10)

step_len = 0.1
max_iterations = 100000
epsilon = 1e-7

def ComputeCost(X,y,theta):
    tmp = X.dot(theta)-y.reshape(y.shape[0],1)
    return 1/(2*len(y))*sum((tmp*tmp))

def GradientDescent(X,y,step_len,max_iterations):
    X = np.array(X)
    y = np.array(y)
    X = np.column_stack( (np.ones((len(y),1)),X))
    theta = np.zeros((X.shape[1],1))
    m = len(y)
    J_his = []
    for i in range(0,max_iterations):
        tmp = X.dot(theta)-y.reshape(y.shape[0],1)
        theta = theta - step_len / m * X.T.dot(tmp)
        J_his.append(ComputeCost(X,y,theta))
        #print(J_his[-1])
        if(len(J_his)>=2 and J_his[-2] - J_his[-1] >= 0 and J_his[-2] - J_his[-1] <= epsilon):
            print('已收敛')
            break
        if(len(J_his)>=2 and J_his[-1] - J_his[-2] >= 0):
            print('步长过大')
            break
    return theta,J_his

def Predict(X,theta):
    one = np.ones((X.shape[0],1))
    X = np.column_stack(( one,X ))
    return X.dot(theta)

def Normalizetion(x):
    sum_tmp = np.sum(x,axis=0)
    max_tmp = np.max(x,axis=0)
    min_tmp = np.min(x,axis=0)
    ave_tmp = np.average(x,axis=0)
    return (x - ave_tmp)/(max_tmp-min_tmp)
#############################################################################

train_X = Normalizetion(train_X)
theta,J_his = GradientDescent(train_X,train_y,step_len,max_iterations)
# print('theta =',theta,'\n')

# print(Predict(test_X,theta))

train_time = range(0,len(J_his))
plt.plot(train_time, J_his)
plt.xlabel('train_time')
plt.ylabel('cost_fun_J')
plt.show()