[学习笔记][Python机器学习：预测分析核心算法][多变量回归：使用交叉验证来估计套索模型的样本外错误]

import numpy
from sklearn import datasets, linear_model
from sklearn.linear_model import LassoCV
from math import sqrt
import matplotlib.pyplot as plot

#read data into iterable
#target_url = "http://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-red.csv"
#data = urllib2.urlopen(target_url)
target_url_file = open('winequality-red.csv','r')
data = target_url_file.readlines()
target_url_file.close()

xList = []
labels = []
names = []
firstLine = True
for line in data:
    if firstLine:
        names = line.strip().split(";")
        firstLine = False
    else:
        #split on semi-colon
        row = line.strip().split(";")
        #put labels in separate array
        labels.append(float(row[-1]))
        #remove label from row
        row.pop()
        #convert row to floats
        floatRow = [float(num) for num in row]
        xList.append(floatRow)

#Normalize columns in x and labels
#Note: be careful about normalization.
#Some penalized regression packages include it and some don't.

nrows = len(xList)
ncols = len(xList[0])

#calculate means and variances
xMeans = []
xSD = []
for i in range(ncols):
    col = [xList[j][i] for j in range(nrows)]
    mean = sum(col)/nrows
    xMeans.append(mean)
    colDiff = [(xList[j][i] - mean) for j in range(nrows)]
    sumSq = sum([colDiff[i] * colDiff[i] for i in range(nrows)])
    stdDev = sqrt(sumSq/nrows)
    xSD.append(stdDev)

#use calculate mean and standard deviation to normalize xList
xNormalized = []
for i in range(nrows):
    rowNormalized = [(xList[i][j] - xMeans[j])/xSD[j] for j in range(ncols)]
    xNormalized.append(rowNormalized)

#Normalize labels
meanLabel = sum(labels)/nrows
sdLabel = sqrt(sum([(labels[i] - meanLabel) * (labels[i] - meanLabel) for i in range(nrows)])/nrows)

labelNormalized = [(labels[i] - meanLabel)/sdLabel for i in range(nrows)]

#Convert list of list to np array for input to sklearn packages

#Unnormalized labels
Y = numpy.array(labels)

#normalized lables
Y = numpy.array(labelNormalized)

#Unnormalized X's
X = numpy.array(xList)

#Normlized Xss
X = numpy.array(xNormalized)

#Call LassoCV from sklearn.linear_model
#10折交叉验证
wineModel = LassoCV(cv=10).fit(X, Y)

# Display results


plot.figure()
plot.figure(figsize=(12,8))
#随着alpha值的变化，均方误差的变化曲线
plot.plot(wineModel.alphas_, wineModel.mse_path_, ':')
#验证过程中，随着alpha值的变化，均方误差的平均曲线，并设置的alpha变化区域
plot.plot(wineModel.alphas_, wineModel.mse_path_.mean(axis=-1),
          label='Average MSE Across Folds', linewidth=2)
#最佳的alpha值,每次验证系统认为的最合适的alpha值
plot.axvline(wineModel.alpha_, linestyle='dotted',label='CV Estimate of Best alpha')
#这种轴半对数刻度曲线是将自变量对10取对数，可以有效的看出数据指数型变化时的衰变情况。
plot.semilogx()
#为图表打标注
plot.legend()
#当前的图表和子图可以使用plt.gcf()和plt.gca()获得，分别表示Get Current Figure和Get Current Axes。
ax = plot.gca()
#x轴反向
ax.invert_xaxis()

plot.xlabel('alpha')
plot.ylabel('Mean Square Error')
plot.axis('tight')
plot.show()

#print out the value of alpha that minimizes the Cv-error
print("alpha Value that Minimizes CV Error  ",wineModel.alpha_)
print("Minimum MSE  ", min(wineModel.mse_path_.mean(axis=-1)))

alpha Value that Minimizes CV Error   0.013561387700964642
Minimum MSE   0.6655849206002853