python实现线性回归
本帖最后由 糖逗 于 2020-11-14 13:01 编辑参考书籍：《机器学习实战》
1.传统线性回归
import numpy as np
def loadDataSet(fileName):
numFeat = len(open(fileName).readline().split('\t')) - 1
dataMat = []
labelMat = []
fr = open(fileName)
for line in fr.readlines():
lineArr = []
curLine = line.strip().split('\t')
for i in range(numFeat):
lineArr.append(float(curLine))
dataMat.append(lineArr)
labelMat.append(float(curLine[-1]))
return dataMat, labelMat
def standRegres(xArr, yArr):
xMat = np.mat(xArr)
yMat = np.mat(yArr).T
xTx = xMat.T * xMat
if np.linalg.det(xTx) == 0:#矩阵不可逆,矩阵行列式为0
print("This matrix is singular, cannot do inverse")
return
ws = np.linalg.inv(xTx)*(xMat.T * yMat)
return ws
if __name__ == "__main__":
import matplotlib.pyplot as plt
xArr, yArr = loadDataSet(r'C:\...\ex0.txt')
ws = standRegres(xArr, yArr)
xMat = np.mat(xArr)
yMat = np.mat(yArr)
yHat = xMat * ws
fig = plt.figure()
ax = fig.add_subplot(111)
#https://blog.csdn.net/lilong117194/article/details/78288795
ax.scatter(xMat[:, 1].flatten().A, yMat.T[:, 0].flatten().A)
xCopy = xMat.copy()
xCopy.sort(0)#升序
yHat = xCopy * ws
ax.plot(xCopy[:, 1], yHat)
plt.show()
2.局部加权线性回归
import numpy as np
def loadDataSet(fileName):
numFeat = len(open(fileName).readline().split('\t')) - 1
dataMat = []
labelMat = []
fr = open(fileName)
for line in fr.readlines():
lineArr = []
curLine = line.strip().split('\t')
for i in range(numFeat):
lineArr.append(float(curLine))
dataMat.append(lineArr)
labelMat.append(float(curLine[-1]))
return dataMat, labelMat
def lwlr(testPoint, xArr, yArr, k = 1.0):
xMat = np.mat(xArr)
yMat = np.mat(yArr).T
m = np.shape(xMat)
weights = np.mat(np.eye((m)))
for j in range(m):
diffMat = testPoint - xMat
weights = np.exp(diffMat * diffMat.T/(-2.0*k**2))#径向基核函数
xTx = xMat.T * (weights * xMat)
if np.linalg.det(xTx) == 0.0:
print("This matrix is singular, cannot do inverse")
return
ws = np.linalg.inv(xTx) * (xMat.T * weights * yMat)
return testPoint * ws
def lwlrTest(testArr, xArr, yArr, k = 1.0):
m = np.shape(testArr)
yHat = np.zeros(m)
for i in range(m):
yHat = lwlr(testArr,xArr,yArr,k)
return yHat
if __name__ == "__main__":
xArr, yArr = loadDataSet(r'C:\...\ex0.txt')
lwlr(xArr, xArr, yArr, 1)#单个点的估计
yHat = lwlrTest(xArr, xArr, yArr, 0.003)
xMat = np.mat(xArr)
srtInd = xMat[:, 1].argsort(0)
xSort = xMat[:, 0, :]
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(xSort[:, 1], yHat)
ax.scatter(xMat[:, 1].flatten().A, np.mat(yArr).T.flatten().A,
s = 2, c = 'red')
plt.show()
3.岭回归
import numpy as np
def loadDataSet(fileName):
numFeat = len(open(fileName).readline().split('\t')) - 1
dataMat = []
labelMat = []
fr = open(fileName)
for line in fr.readlines():
lineArr = []
curLine = line.strip().split('\t')
for i in range(numFeat):
lineArr.append(float(curLine))
dataMat.append(lineArr)
labelMat.append(float(curLine[-1]))
return dataMat, labelMat
def ridgeRegres(xMat, yMat, lam = 0.2):
xTx = xMat.T * xMat
denom = xTx + np.eye(np.shape(xMat)) * lam
if np.linalg.det(denom) == 0:
print("This matrix is singular, cannot do inverse")
return
ws = np.linalg.inv(denom) * (xMat.T * yMat)
return ws
def ridgeTest(xArr, yArr):
xMat = np.mat(xArr)
yMat = np.mat(yArr).T
yMean = np.mean(yMat,0)
yMat = yMat - yMean
xMeans = np.mean(xMat,0)
xVar = np.var(xMat,0)
xMat = (xMat - xMeans)/xVar
numTestPts = 30#30个不同的lambda
wMat = np.zeros((numTestPts, np.shape(xMat)))
for i in range(numTestPts):
ws = ridgeRegres(xMat, yMat, np.exp(i-10))
wMat = ws.T
return wMat
if __name__ == "__main__":
abX, abY = loadDataSet(r'C:\...\abalone.txt')
ridgeWeights = ridgeTest(abX, abY)
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(ridgeWeights）#一共有八条线，代表不同lambda下8个特征的取值情况
plt.show()
4.前向逐步回归
import numpy as np
def loadDataSet(fileName):
numFeat = len(open(fileName).readline().split('\t')) - 1
dataMat = []
labelMat = []
fr = open(fileName)
for line in fr.readlines():
lineArr = []
curLine = line.strip().split('\t')
for i in range(numFeat):
lineArr.append(float(curLine))
dataMat.append(lineArr)
labelMat.append(float(curLine[-1]))
return dataMat, labelMat
def regularize(xMat):
inMat = xMat.copy()
inMeans = np.mean(inMat,0)
inVar = np.var(inMat,0)
inMat = (inMat - inMeans)/inVar
return inMat
def rssError(yArr, yHatArr):
return ((yArr-yHatArr)**2).sum()
def stageWise(xArr, yArr, eps = 0.01, numIt = 100):
xMat = np.mat(xArr)
yMat = np.mat(yArr).T
yMean = np.mean(yMat, 0)
yMat = yMat - yMean
xMat = regularize(xMat)
m, n = np.shape(xMat)
ws = np.zeros((n, 1))
returnMat = np.zeros((numIt, n))
wsMax = ws.copy()
for i in range(numIt):
lowestError = np.inf;
for j in range(n):
for sign in [-1, 1]:#增大或减少特征值
wsTest = ws.copy()
wsTest += eps * sign
yTest = xMat * wsTest
rssE = rssError(yMat.A,yTest.A)
if rssE < lowestError:
lowestError = rssE
wsMax = wsTest
ws = wsMax.copy()
returnMat = ws.T
return returnMat
if __name__ == "__main__":
xArr, yArr = loadDataSet(r'C:\...\abalone.txt')
res = stageWise(xArr, yArr, 0.01, 5000)
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(res)#一共有八条线，代表不同lambda下8个特征的取值情况
plt.show() {:10_248:} 补充一个知识点：python中x.I就是对矩阵x求逆矩阵 本帖最后由 糖逗 于 2020-12-7 16:20 编辑
基于批梯度参数更新的线性回归
import numpy as np
import matplotlib.pyplot as plt
#计算损失函数
def compute_error_for_line_given_points(b, w, points):
totalError = 0
for i in range(0, len(points)):
x = points
y = points
totalError += (y - (w * x + b)) ** 2
return totalError / len(points)
#计算梯度(批梯度下降，计算一次梯度使用所有样本)，更新参数
#一次参数更新计算
def step_gradient(b_current, w_current, points, learningRate):
b_gradient = 0
w_gradient = 0
N = len(points)
for i in range(N):
x = points
y = points
#grad_b = 2(wx + b - y)
b_gradient += (2 / N) * ((w_current * x + b_current) - y)
#grad_w = 2(wx+b-y)*x
w_gradient += (2/ N) * x * ((w_current * x + b_current) - y)
new_b = b_current - (learningRate * b_gradient)
new_w = w_current - (learningRate * w_gradient)
return
#多次梯度下降计算迭代
def gradient_descent_runner(points, starting_b, starting_w, learning_rate, num_iterations):
b = starting_b
w = starting_w
for i in range(num_iterations):
b, w = step_gradient(b, w, np.array(points), learning_rate)
return
if __name__ == "__main__":
points = [, , , , , , , ,]
plt.scatter(x = np.array(points)[:,0] , y = np.array(points)[:,1])
b, w = gradient_descent_runner(points, 100, -10, 0.02, 500)#初始化参数选取很重要，尤其是学习率
x = np.random.rand(100) * 10
y = np.array([])
for i in range(len(x)):
y = np.append(y, w * x + b)
plt.plot(x, y)
代码源自：《Tensorflow深度学习》（龙良曲）
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