我正在尝试使用多个变量（实际上只有 2 个）实现线性回归。我正在使用来自斯坦福大学 ML-Class 的数据。我让它在单变量情况下正常工作。相同的代码应该适用于多个，但是，没有。
链接到数据：
http://s3.amazonaws.com/mlclass-resources/exercises/mlclass-ex1.zip
特征归一化：
''' This is for the regression with multiple variables problem . You have to normalize features before doing anything. Lets get started'''
from __future__ import division
import os,sys
from math import *
def mean(f,col):
#This is to find the mean of a feature
sigma = 0
count = 0
data = open(f,'r')
for line in data:
points = line.split(",")
sigma = sigma + float(points[col].strip("\n"))
count+=1
data.close()
return sigma/count
def size(f):
count = 0
data = open(f,'r')
for line in data:
count +=1
data.close()
return count
def standard_dev(f,col):
#Calculate the standard_dev . Formula : Sqrt ( Sigma ( x - x') ** (x-x') ) / N )
data = open(f,'r')
sigma = 0
mean = 0
if(col==0):
mean = mean_area
else:
mean = mean_bedroom
for line in data:
points = line.split(",")
sigma = sigma + (float(points[col].strip("\n")) - mean) ** 2
data.close()
return sqrt(sigma/SIZE)
def substitute(f,fnew):
''' Take the old file.
1. Subtract the mean values from each feature
2. Scale it by dividing with the SD
'''
data = open(f,'r')
data_new = open(fnew,'w')
for line in data:
points = line.split(",")
new_area = (float(points[0]) - mean_area ) / sd_area
new_bedroom = (float(points[1].strip("\n")) - mean_bedroom) / sd_bedroom
data_new.write("1,"+str(new_area)+ ","+str(new_bedroom)+","+str(points[2].strip("\n"))+"\n")
data.close()
data_new.close()
global mean_area
global mean_bedroom
mean_bedroom = mean(sys.argv[1],1)
mean_area = mean(sys.argv[1],0)
print 'Mean number of bedrooms',mean_bedroom
print 'Mean area',mean_area
global SIZE
SIZE = size(sys.argv[1])
global sd_area
global sd_bedroom
sd_area = standard_dev(sys.argv[1],0)
sd_bedroom=standard_dev(sys.argv[1],1)
substitute(sys.argv[1],sys.argv[2])
我在代码中实现了均值和标准差，而不是使用 NumPy/SciPy。将值存储在文件中后，其快照如下：
X1 X2 X3 COST OF HOUSE
1,0.131415422021,-0.226093367578,399900
1,-0.509640697591,-0.226093367578,329900
1,0.507908698618,-0.226093367578,369000
1,-0.743677058719,-1.5543919021,232000
1,1.27107074578,1.10220516694,539900
1,-0.0199450506651,1.10220516694,299900
1,-0.593588522778,-0.226093367578,314900
1,-0.729685754521,-0.226093367578,198999
1,-0.789466781548,-0.226093367578,212000
1,-0.644465992588,-0.226093367578,242500
我对其进行回归以找到参数。代码如下：
''' The plan is to rewrite and this time, calculate cost each time to ensure its reducing. Also make it enough to handle multiple variables '''
from __future__ import division
import os,sys
def computecost(X,Y,theta):
#X is the feature vector, Y is the predicted variable
h_theta=calculatehTheta(X,theta)
delta = (h_theta - Y) * (h_theta - Y)
return (1/194) * delta
def allCost(f,no_features):
theta=[0,0]
sigma=0
data = open(f,'r')
for line in data:
X=[]
Y=0
points=line.split(",")
for i in range(no_features):
X.append(float(points[i]))
Y=float(points[no_features].strip("\n"))
sigma=sigma+computecost(X,Y,theta)
return sigma
def calculatehTheta(points,theta):
#This takes a file which has (1,feature1,feature2,so ... on)
#print 'Points are',points
sigma = 0
for i in range(len(theta)):
sigma = sigma + theta[i] * float(points[i])
return sigma
def gradient_Descent(f,no_iters,no_features,theta):
''' Calculate ( h(x) - y ) * xj(i) . And then subtract it from thetaj . Continue for 1500 iterations and you will have your answer'''
X=[]
Y=0
sigma=0
alpha=0.01
for i in range(no_iters):
for j in range(len(theta)):
data = open(f,'r')
for line in data:
points=line.split(",")
for i in range(no_features):
X.append(float(points[i]))
Y=float(points[no_features].strip("\n"))
h_theta = calculatehTheta(points,theta)
delta = h_theta - Y
sigma = sigma + delta * float(points[j])
data.close()
theta[j] = theta[j] - (alpha/97) * sigma
sigma = 0
print theta
print allCost(sys.argv[1],2)
print gradient_Descent(sys.argv[1],1500,2,[0,0,0])
它打印以下作为参数：
[-3.8697149722857996e-14, 0.02030369056348706, 0.979706406501678]
这三个都是可怕的错误:(完全相同的事情适用于 Single variable 。
谢谢 ！