梯度下降法實現最簡單線性迴歸問題python實現

梯度下降法是非常常見的優化方法，在神經網路的深度學習中更是必會方法，但是直接從深度學習去實現，會比較複雜。本文試圖使用梯度下降來優化最簡單的LSR線性迴歸問題，作為進一步學習的基礎。

import numpy as np
import pandas as pd
from numpy import *
from pandas import *
import matplotlib.pyplot as plt


x = np.array([[1,2],[2,1],[3,2.5],[4,3],
              [5,4],[6,5],[7,2.7],[8,4.5],
              [9,2]])

m, n = np.shape(x)
x_data = np.ones((m,n))
x_data[:,:-1] = x[:,:-1]
y_data = x[:,-1]

print(x_data.shape)
print(y_data.shape)
m, n = np.shape(x_data)
theta = np.ones(n)


def batchGradientDescent(maxiter,x,y,theta,alpha):
    xTrains = x.transpose()
    for i in range(0,maxiter):
        hypothesis = np.dot(x,theta)
        loss = (hypothesis-y)
        gradient = np.dot(xTrains,loss)/m
        theta = theta - alpha * gradient
        cost = 1.0/2*m*np.sum(np.square(np.dot(x,np.transpose(theta))-y))
        print("cost: %f"%cost)
    return theta

result = batchGradientDescent(10,x_data,y_data,theta,0.01)
print(result)
newy = np.dot(x_data,result)
fig, ax = plt.subplots()
ax.plot(x[:,0],newy, 'k--')
ax.plot(x[:,0],x[:,1], 'ro')
plt.show()
print("final: " + result)