関連の検出 MIC HSIC

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• 関連の検出手法としてMIC HSICの話
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• MIC-> Rではminervaパッケージ

library(minerva)
A <- matrix(runif(50),nrow=5)
mine(x=A, master=1)
mine(x=A, master=c(1,3,5,7,8:10))

x <- runif(10); y <- 3*x+2; plot(x,y,type="l")
mine(x,y)
# MIC = 1 
# MAS = 0
# MEV = 1
# MCN = 2
# MIC-R2 = 0

set.seed(100); x <- runif(10); y <- 3*x+2+rnorm(10,mean=2,sd=5); plot(x,y)
mine(x,y)
# rounded values of MINE statistics
# MIC = 0.61
# MAS = 0
# MEV = 0.61
# MCN = 2
# MIC-R2 = 0.13

t <-seq(-2*pi,2*pi,0.2); y1 <- sin(2*t); plot(t,y1,type="l")
mine(t,y1)
# rounded values of MINE statistics
# MIC = 0.66 
# MAS = 0.37
# MEV = 0.66
# MCN = 3.58
# MIC-R2 = 0.62

y2 <- sin(4*t); plot(t,y2,type="l")
mine(t,y2)
# rounded values of MINE statistics
# MIC = 0.32 
# MAS = 0.18
# MEV = 0.32
# MCN = 3.58
# MIC-R2 = 0.31

# Note that for small n it is better to increase alpha
mine(t,y1,alpha=1)
# rounded values of MINE statistics
# MIC = 1 
# MAS = 0.59
# MEV = 1
# MCN = 5.67
# MIC-R2 = 0.96

mine(t,y2,alpha=1)
# rounded values of MINE statistics
# MIC = 1 
# MAS = 0.59
# MEV = 1
# MCN = 5
# MIC-R2 = 0.99

# Some examples from SOM
x <- runif(n=1000, min=0, max=1)

# Linear relationship
y1 <- x; plot(x,y1,type="l"); mine(x,y1)
# MIC = 1 
# MAS = 0
# MEV = 1
# MCN = 4
# MIC-R2 = 0

# Parabolic relationship
y2 <- 4*(x-0.5)^2; plot(sort(x),y2[order(x)],type="l"); mine(x,y2)
# rounded values of MINE statistics
# MIC = 1 
# MAS = 0.68
# MEV = 1
# MCN = 5.5
# MIC-R2 = 1

# Sinusoidal relationship (varying frequency)
y3 <- sin(6*pi*x*(1+x)); plot(sort(x),y3[order(x)],type="l"); mine(x,y3)
# rounded values of MINE statistics
# MIC = 1 
# MAS = 0.85
# MEV = 1
# MCN = 4.6
# MIC-R2 = 0.96

# Circle relationship
t <- seq(from=0,to=2*pi,length.out=1000)
x4 <- cos(t); y4 <- sin(t); plot(x4, y4, type="l",asp=1)
mine(x4,y4)
# rounded values of MINE statistics
# MIC = 0.68 
# MAS = 0.01
# MEV = 0.32
# MCN = 5.98
# MIC-R2 = 0.68

data(Spellman)
Spellman <- as.matrix(Spellman)
res <- mine(Spellman,master=1,n.cores=1)

## Not run: ## example of multicore computation
require(parallel)
res <- mine(Spellman,master=1,n.cores=parallel::detectCores()-1)
## End(Not run)