5.2 グラフィカルLasso
inner.prod <- function(x, y) {
return(sum(x * y))
} ## 既出
soft.th <- function(lambda, x) {
return(sign(x) * pmax(abs(x) - lambda, 0))
} ## 既出
graph.lasso <- function(s, lambda = 0) {
W <- s
p <- ncol(s)
beta <- matrix(0, nrow = p - 1, ncol = p)
beta.out <- beta
eps.out <- 1
while (eps.out > 0.01) {
for (j in 1:p) {
a <- W[-j, -j]
b <- s[-j, j]
beta.in <- beta[, j]
eps.in <- 1
while (eps.in > 0.01) {
for (h in 1:(p - 1)) {
cc <- b[h] - inner.prod(a[h, -h], beta[-h, j])
beta[h, j] <- soft.th(lambda, cc) / a[h, h]
}
eps.in <- max(beta[, j] - beta.in)
beta.in <- beta[, j]
}
W[-j, j] <- W[-j, -j] %*% beta[, j]
}
eps.out <- max(beta - beta.out)
beta.out <- beta
}
theta <- matrix(nrow = p, ncol = p)
for (j in 1:p) {
theta[j, j] <- 1 / (W[j, j] - W[j, -j] %*% beta[, j])
theta[-j, j] <- -beta[, j] * theta[j, j]
}
return(theta)
}
例47
library(MultiRNG)
## Warning: package 'MultiRNG' was built under R version 4.0.3
Theta <- matrix(c( 2, 0.6, 0, 0, 0.5, 0.6, 2, -0.4, 0.3, 0,
0, -0.4, 2, -0.2, 0, 0, 0.3, -0.2, 2, -0.2,
0.5, 0, 0, -0.2, 2),
nrow = 5)
Sigma <- solve(Theta)
meanvec <- rep(0, 5)
dat <- draw.d.variate.normal(no.row = 20, d = 5,
mean.vec = meanvec, cov.mat = Sigma)
# 平均mean.vec,共分散行列cov.mat,サンプル数no.row,変数の個数dから
# サンプル行列を生成
s <- t(dat) %*% dat / nrow(dat)
Theta
## [,1] [,2] [,3] [,4] [,5]
## [1,] 2.0 0.6 0.0 0.0 0.5
## [2,] 0.6 2.0 -0.4 0.3 0.0
## [3,] 0.0 -0.4 2.0 -0.2 0.0
## [4,] 0.0 0.3 -0.2 2.0 -0.2
## [5,] 0.5 0.0 0.0 -0.2 2.0
graph.lasso(s)
## [,1] [,2] [,3] [,4] [,5]
## [1,] 4.5026572 0.9818782 0.60009124 -2.0466927 1.33991063
## [2,] 0.9751595 1.9353862 -0.23683861 0.1526158 0.10016728
## [3,] 0.5963550 -0.2364995 2.00318046 0.2183919 0.09857318
## [4,] -2.0529957 0.1479875 0.21616558 3.4705123 -0.92298628
## [5,] 1.3409907 0.1029790 0.09968043 -0.9214949 1.87734886
graph.lasso(s, lambda = 0.015)
## [,1] [,2] [,3] [,4] [,5]
## [1,] 3.9201795 0.83909586 0.4968786 -1.6663040 1.00974904
## [2,] 0.8419598 1.86659378 -0.2258595 0.1875745 0.01679017
## [3,] 0.4997081 -0.22613987 1.9474979 0.2293072 0.02867895
## [4,] -1.6599229 0.18933948 0.2312845 3.1619637 -0.69464559
## [5,] 1.0079087 0.01586028 0.0280105 -0.6952598 1.73576457
graph.lasso(s, lambda = 0.03)
## [,1] [,2] [,3] [,4] [,5]
## [1,] 3.5384878 0.7691536 0.4401780 -1.3900787 0.7967628
## [2,] 0.7678327 1.8114040 -0.2103822 0.1852676 0.0000000
## [3,] 0.4410263 -0.2110721 1.9023682 0.2157557 0.0000000
## [4,] -1.3890172 0.1847097 0.2163867 2.9235424 -0.5134782
## [5,] 0.7972078 0.0000000 0.0000000 -0.5137533 1.6430676
graph.lasso(s, lambda = 0.05)
## [,1] [,2] [,3] [,4] [,5]
## [1,] 3.1732901 0.6937337 0.3898361 -1.1235715 0.5997789
## [2,] 0.6921656 1.7451215 -0.1881856 0.1691241 0.0000000
## [3,] 0.3893990 -0.1888305 1.8497121 0.1808854 0.0000000
## [4,] -1.1237883 0.1683662 0.1809569 2.6903188 -0.3216729
## [5,] 0.6006711 0.0000000 0.0000000 -0.3218116 1.5604271
例48
library(glasso)
## Warning: package 'glasso' was built under R version 4.0.3
solve(s)
## [,1] [,2] [,3] [,4] [,5]
## [1,] 4.4996092 0.9759424 0.59616546 -2.0504223 1.33984091
## [2,] 0.9759424 1.9340685 -0.23601615 0.1513602 0.10110823
## [3,] 0.5961655 -0.2360162 2.00218014 0.2187106 0.09831414
## [4,] -2.0504223 0.1513602 0.21871064 3.4723473 -0.92260766
## [5,] 1.3398409 0.1011082 0.09831414 -0.9226077 1.87722288
glasso(s, rho = 0)
## Warning in glasso(s, rho = 0): With rho=0, there may be convergence problems if the input matrix
## is not of full rank
## $w
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.4840149 -0.2783125 -0.1957499 0.25901256 -0.19291794
## [2,] -0.2783125 0.6915990 0.1823482 -0.19050703 0.05820960
## [3,] -0.1957499 0.1823482 0.5950644 -0.15503142 0.02253190
## [4,] 0.2590126 -0.1905070 -0.1550314 0.47706857 0.06798044
## [5,] -0.1929179 0.0582096 0.0225319 0.06798044 0.69949020
##
## $wi
## [,1] [,2] [,3] [,4] [,5]
## [1,] 4.4996218 0.9759768 0.59618930 -2.0504188 1.33983912
## [2,] 0.9759458 1.9340837 -0.23601549 0.1513473 0.10111612
## [3,] 0.5961611 -0.2360212 2.00218797 0.2187012 0.09831833
## [4,] -2.0504304 0.1513429 0.21869822 3.4723342 -0.92260025
## [5,] 1.3398450 0.1011183 0.09832162 -0.9226041 1.87721935
##
## $loglik
## [1] NA
##
## $errflag
## [1] 0
##
## $approx
## [1] FALSE
##
## $del
## [1] 1.422557e-06
##
## $niter
## [1] 1
glasso(s, rho = 0.015)
## $w
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.4990149 -0.26331132 -0.18074581 0.24401373 -0.17791758
## [2,] -0.2633113 0.70659903 0.16734523 -0.17550769 0.07320939
## [3,] -0.1807458 0.16734523 0.61006437 -0.14003150 0.03753097
## [4,] 0.2440137 -0.17550769 -0.14003150 0.49206857 0.05298044
## [5,] -0.1779176 0.07320939 0.03753097 0.05298044 0.71449020
##
## $wi
## [,1] [,2] [,3] [,4] [,5]
## [1,] 3.6395267 0.780865279 0.46547486 -1.4920883 0.912469153
## [2,] 0.7808639 1.805685316 -0.21995497 0.1935040 0.006634033
## [3,] 0.4654826 -0.219960606 1.88779032 0.2255145 0.022562388
## [4,] -1.4920810 0.193502603 0.22551594 2.9724949 -0.623636388
## [5,] 0.9124746 0.006634729 0.02256159 -0.6236402 1.671194883
##
## $loglik
## [1] NA
##
## $errflag
## [1] 0
##
## $approx
## [1] FALSE
##
## $del
## [1] 1.391914e-06
##
## $niter
## [1] 2
glasso(s, rho = 0.030)
## $w
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.5140149 -0.24830961 -0.16574571 0.22901326 -0.16291838
## [2,] -0.2483096 0.72159903 0.15234577 -0.16050791 0.06508705
## [3,] -0.1657457 0.15234577 0.62506437 -0.12503155 0.03856086
## [4,] 0.2290133 -0.16050791 -0.12503155 0.50706857 0.03798044
## [5,] -0.1629184 0.06508705 0.03856086 0.03798044 0.72949020
##
## $wi
## [,1] [,2] [,3] [,4] [,5]
## [1,] 3.1262203 0.6756426 0.3920615 -1.1521078 0.6771599
## [2,] 0.6756458 1.7012520 -0.1986007 0.1843966 0.0000000
## [3,] 0.3920730 -0.1986037 1.7926239 0.2020837 0.0000000
## [4,] -1.1521061 0.1843949 0.2020837 2.6322279 -0.4214819
## [5,] 0.6771633 0.0000000 0.0000000 -0.4214826 1.5439959
##
## $loglik
## [1] NA
##
## $errflag
## [1] 0
##
## $approx
## [1] FALSE
##
## $del
## [1] 2.075307e-06
##
## $niter
## [1] 2
glasso(s, rho = 0.045)
## $w
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.5290149 -0.23330907 -0.15074659 0.21401278 -0.14791839
## [2,] -0.2333091 0.73659903 0.13734602 -0.14550749 0.05551342
## [3,] -0.1507466 0.13734602 0.64006437 -0.11003147 0.03282273
## [4,] 0.2140128 -0.14550749 -0.11003147 0.52206857 0.02298044
## [5,] -0.1479184 0.05551342 0.03282273 0.02298044 0.74449020
##
## $wi
## [,1] [,2] [,3] [,4] [,5]
## [1,] 2.7652114 0.5917274 0.3395463 -0.9198957 0.5187054
## [2,] 0.5917283 1.6115062 -0.1773502 0.1692015 0.0000000
## [3,] 0.3395498 -0.1773516 1.7098944 0.1717574 0.0000000
## [4,] -0.9198980 0.1692008 0.1717572 2.3880891 -0.2766716
## [5,] 0.5187076 0.0000000 0.0000000 -0.2766721 1.4547997
##
## $loglik
## [1] NA
##
## $errflag
## [1] 0
##
## $approx
## [1] FALSE
##
## $del
## [1] 1.202403e-06
##
## $niter
## [1] 2
library(igraph)
## Warning: package 'igraph' was built under R version 4.0.3
##
## Attaching package: 'igraph'
## The following objects are masked from 'package:stats':
##
## decompose, spectrum
## The following object is masked from 'package:base':
##
## union
adj <- function(mat) {
p <- ncol(mat)
ad <- matrix(0, nrow = p, ncol = p)
for (i in 1:(p - 1)) {
for (j in (i + 1):p) {
if (mat[i, j] == 0) {
ad[i, j] <- 0
} else {
ad[i, j] <- 1
}
}
}
g <- graph.adjacency(ad, mode = "undirected")
plot(g)
}
例49
library(glasso)
library(igraph)
df <- read.csv("breastcancer.csv")
w <- matrix(nrow = 250, ncol = 1000)
for (i in 1:1000)
w[, i] <- as.numeric(df[[i]])
x <- w
s <- t(x) %*% x / 250
fit <- glasso(s, rho = 0.75)
sum(fit$wi == 0)
## [1] 992822
y <- NULL
z <- NULL
for (i in 1:999) {
for (j in (i + 1):1000) {
if (fit$wi[i, j] != 0) {
y <- c(y, i)
z <- c(z, j)
}
}
}
edges <- cbind(y, z)
write.csv(edges,"edges.csv")
5.3 疑似尤度を用いたグラフィカルモデルの推定
例50
library(glmnet)
## Warning: package 'glmnet' was built under R version 4.0.3
## Loading required package: Matrix
## Loaded glmnet 4.0-2
df <- read.csv("breastcancer.csv")
n <- 250
p <- 50
w <- matrix(nrow = n, ncol = p)
for (i in 1:p)
w[, i] <- as.numeric(df[[i]])
x <- w[, 1:p]
fm <- rep("gaussian", p)
lambda <- 0.1
fit <- list()
for (j in 1:p)
fit[[j]] <- glmnet(x[, -j], x[, j], family = fm[j], lambda = lambda)
ad <- matrix(0, p, p)
for (i in 1:p) {
for (j in 1:(p - 1)) {
k <- j
if (j >= i)
k <- j + 1
if (fit[[i]]$beta[j] != 0) {
ad[i, k] <- 1
} else {
ad[i, k] <- 0
}
}
}
## ANDの場合
for (i in 1:(p - 1)) {
for (j in (i + 1):p) {
if (ad[i, j] != ad[i, j]) {
ad[i, j] <- 0
ad[j, i] <- 0
}
}
}
u <- NULL
v <- NULL
for (i in 1:(p - 1)) {
for (j in (i + 1):p) {
if (ad[i, j] == 1) {
u <- c(u, i)
v <- c(v, j)
}
}
}
u
## [1] 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 3
## [26] 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 5 5 5 5 5 5 6 6 6
## [51] 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 8 8 8 8 8 8 9 9 9
## [76] 9 9 9 9 9 9 10 10 10 10 10 10 10 11 11 11 11 11 11 12 12 12 12 12 12
## [101] 12 12 13 13 13 13 13 13 13 13 13 14 14 15 15 15 16 16 16 16 16 16 16 16 16
## [126] 16 16 17 17 17 17 17 18 18 18 18 18 18 18 18 19 19 19 19 20 20 20 21 21 21
## [151] 21 21 22 22 22 22 22 22 23 23 23 23 23 23 23 24 24 24 24 24 24 25 25 25 25
## [176] 26 26 26 26 26 27 27 27 27 27 28 28 28 28 29 29 29 29 29 30 30 30 30 30 30
## [201] 31 31 31 31 31 31 31 32 32 33 33 34 34 34 35 35 36 36 36 37 37 37 38 38 38
## [226] 38 38 40 40 42 42 43 43 43 44 44 45 45 47 47 47 49
v
## [1] 2 12 13 18 22 23 24 28 41 46 48 50 4 5 10 16 18 21 23 26 27 34 37 43 9
## [26] 10 15 19 20 21 24 29 38 50 5 8 17 18 21 23 46 9 20 21 28 30 32 10 11 15
## [51] 21 24 25 31 33 39 41 45 8 12 14 18 30 36 44 47 12 13 15 17 41 49 10 14 18
## [76] 19 21 29 45 46 50 18 25 28 32 34 37 42 12 16 20 28 42 48 17 18 29 33 35 41
## [101] 43 47 20 22 25 28 39 40 43 45 50 15 16 17 25 45 18 23 26 27 30 31 32 41 46
## [126] 47 49 20 25 29 31 36 21 24 27 35 41 43 48 49 20 25 42 44 27 44 48 23 24 34
## [151] 37 42 23 29 30 35 36 50 25 28 32 35 37 47 50 28 33 35 40 41 42 29 39 45 48
## [176] 39 40 42 46 50 37 40 42 43 49 29 31 47 50 30 39 45 48 50 31 32 45 47 48 50
## [201] 34 36 39 44 47 49 50 33 45 37 49 35 36 45 41 42 38 39 45 38 42 46 39 45 46
## [226] 49 50 41 42 49 50 47 49 50 48 50 46 50 48 49 50 50
adj(ad)
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)
## ORの場合
for (i in 1:(p - 1)) {
for (j in (i + 1):p) {
if (ad[i, j] != ad[i, j]) {
ad[i, j] <- 1
ad[j, i] <- 1
}
}
}
adj(ad)
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)
例51
library(glmnet)
df <- read.csv("breastcancer.csv")
w <- matrix(nrow = 250, ncol = 1000)
for (i in 1:1000)
w[, i] <- as.numeric(df[[i]])
w <- (sign(w) + 1) / 2 ## 2値データに変換する
p <- 50
x <- w[, 1:p]
fm <- rep("binomial", p)
lambda <- 0.15
fit <- list()
for (j in 1:p)
fit[[j]] <- glmnet(x[, -j], x[, j], family = fm[j], lambda = lambda)
ad <- matrix(0, nrow = p, ncol = p)
for (i in 1:p) {
for (j in 1:(p - 1)) {
k <- j
if (j >= i)
k <- j + 1
if (fit[[i]]$beta[j] != 0) {
ad[i, k] <- 1
} else {
ad[i, k] <- 0
}
}
}
for (i in 1:(p - 1)) {
for (j in (i + 1):p) {
if (ad[i, j] != ad[i, j]) {
ad[i, j] <- 0
ad[j, i] <- 0
}
}
}
sum(ad)
## [1] 203
adj(ad)
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)
5.4 JointグラフィカルLasso
# 大きさが3以上でないとgenlassoは稼働しない
b.fused <- function(y, lambda) {
if (y[1] > y[2] + 2 * lambda) {
a <- y[1] - lambda
b <- y[2] + lambda
} else if (y[1] < y[2] - 2 * lambda) {
a <- y[1] + lambda
b <- y[2] - lambda
} else {
a <- (y[1] + y[2]) / 2
b <- a
}
return(c(a, b))
}
# 隣接項だけではなく,離接するすべての値と比較するFused Lasso
fused <- function(y, lambda.1, lambda.2) {
K <- length(y)
if (K == 1) {
theta <- y
} else if (K == 2) {
theta <- b.fused(y, lambda.2)
} else {
L <- K * (K - 1) / 2
D <- matrix(0, nrow = L, ncol = K)
k <- 0
for (i in 1:(K - 1)) {
for (j in (i + 1):K) {
k <- k + 1
D[k, i] <- 1
D[k, j] <- -1
}
}
out <- genlasso(y, D = D)
theta <- coef(out, lambda = lambda.2)
}
theta <- soft.th(lambda.1, theta)
return(theta)
}
# Joint Graphical Lasso
jgl <- function(X, lambda.1, lambda.2) { # Xはリストで与える
K <- length(X)
p <- ncol(X[[1]])
n <- array(dim = K)
S <- list()
for (k in 1:K) {
n[k] <- nrow(X[[k]])
S[[k]] <- t(X[[k]]) %*% X[[k]] / n[k]
}
rho <- 1
lambda.1 <- lambda.1 / rho
lambda.2 <- lambda.2 / rho
Theta <- list()
for (k in 1:K)
Theta[[k]] <- diag(p)
Theta.old <- list()
for (k in 1:K)
Theta.old[[k]] <- diag(rnorm(p))
U <- list()
for (k in 1:K)
U[[k]] <- matrix(0, nrow = p, ncol = p)
Z <- list()
for (k in 1:K)
Z[[k]] <- matrix(0, nrow = p, ncol = p)
epsilon <- 0
epsilon.old <- 1
while (abs((epsilon - epsilon.old) / epsilon.old) > 0.0001) {
Theta.old <- Theta
epsilon.old <- epsilon
## (a)に関する更新
for (k in 1:K) {
mat <- S[[k]] - rho * Z[[k]] / n[k] + rho * U[[k]] / n[k]
svd.mat <- svd(mat)
V <- svd.mat$v
D <- svd.mat$d
DD <- n[k] / (2 * rho) * (-D + sqrt(D ^ 2 + 4 * rho / n[k]))
Theta[[k]] <- V %*% diag(DD) %*% t(V)
}
## (b)に関する更新
for (i in 1:p) {
for (j in 1:p) {
A <- NULL
for (k in 1:K)
A <- c(A, Theta[[k]][i, j] + U[[k]][i, j])
if (i == j) {
B <- fused(A, 0, lambda.2)
} else {
B <- fused(A, lambda.1, lambda.2)
}
for (k in 1:K)
Z[[k]][i, j] <- B[k]
}
}
## (c)に関する更新
for (k in 1:K)
U[[k]] <- U[[k]] + Theta[[k]] - Z[[k]]
## 収束したかどうかの検査
epsilon <- 0
for (k in 1:K) {
epsilon.new <- max(abs(Theta[[k]] - Theta.old[[k]]))
if (epsilon.new > epsilon)
epsilon <- epsilon.new
}
}
return(Z)
}
## (b)の更新の箇所を以下で置き換える。下記単独では動作しない。
for (i in 1:p) {
for (j in 1:p) {
A <- NULL
for (k in 1:K)
A <- c(A, Theta[[k]][i, j] + U[[k]][i, j])
if (i == j) {
B <- A
} else {
B <- soft.th(lambda.1 / rho,A) *
max(1 - lambda.2 / rho / sqrt(norm(soft.th(lambda.1 / rho, A), "2") ^ 2), 0)
}
for (k in 1:K)
Z[[k]][i, j] <- B[k]
}
}
例52
## データ生成と実行
p <- 10
K <- 2
N <- 100
n <- array(dim = K)
for (k in 1:K)
n[k] <- N / K
X <- list()
X[[1]] <- matrix(rnorm(n[k] * p), ncol = p)
for (k in 2:K)
X[[k]] <- X[[k - 1]] + matrix(rnorm(n[k] * p) * 0.1, ncol = p)
## lambda.1,lambda.2を変えて実行してみた
Theta <- jgl(X, 3, 0.01)
par(mfrow = c(1, 2))
adj(Theta[[1]])
adj(Theta[[2]])
![](data:image/png;base64,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)