使用MIC进行变量选择

如果有很多自变量，我们能在很多自变量中选出几个对因变量影响最大的吗?或许MIC可以解决这个问题哦。

# -*- coding: utf-8 -*-"""Created on Mon Mar 14 19:52:57 2016@author: Luyixiao"""import numpy as npfrom minepy import MINEimport matplotlib.pyplot as pltdef print_stats(mine):    print "MIC", mine.mic()#    print "MAS", mine.mas()#detecting periodic relationships with unknown frequencies#    print "MEV", mine.mev()#    print "MCN (eps=0)", mine.mcn(0)#    print "MCN (eps=1-MIC)", mine.mcn_general()x1 = np.linspace(0, 1, 1000)x2 = np.random.randn(x1.shape[0])+0.5x3 = np.random.randn(x1.shape[0])#normal mean = 0,dev = 1x4 = np.random.random_sample(x1.shape[0])#randomx5 = 2*np.random.randn(x1.shape[0])+10 #normal mean = 10,dev = 2x6 = 4*np.random.random_sample(x1.shape[0])#random*4y = np.sin(10 * np.pi * x1) + x2#y = np.sin(10 * np.pi * x1) + x2*0.01mine = MINE(alpha=0.6, c=15)print "MIC between y and x1:"mine.compute_score(x1, y)print_stats(mine)plt.scatter(x1, y,  color='red')plt.show()print "MIC between y and x2:"mine.compute_score(x2, y)print_stats(mine)plt.scatter(x2, y,  color='blue')plt.show()print "MIC between y and x3(normal disturbtion):"mine.compute_score(x3, y)print_stats(mine)print "MIC between y and x4(random disturbtion):"mine.compute_score(x4, y)print_stats(mine)print "MIC between y and x3(normal disturbtion):"mine.compute_score(x5, y)print_stats(mine)print "MIC between y and x4(random disturbtion):"mine.compute_score(x6, y)print_stats(mine)

这里，y只与x1，x2有关。函数表达式是y=sin（10*3.14*x1）+x2。

运行之后的效果是这样的。

首先是x1变量与y的MIC值

MIC between y and x1:
MIC 0.34578174965

散点图是

然后是x2的：

MIC between y and x2:
MIC 0.583633971634

散点图是

那么还有几个变量呢？

MIC between y and x3(normal disturbtion):
MIC 0.125493013005
MIC between y and x4(random disturbtion):
MIC 0.126849697109
MIC between y and x3(normal disturbtion):
MIC 0.134937129482
MIC between y and x4(random disturbtion):
MIC 0.147182587126

相比较而言，这几个无关变量与y的MIC值都是比较小的，不管这些无关系数的范围在什么区间。