/
1_illustration.R
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1_illustration.R
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## Higher-Order Total Variation (HOTV)
## A. Okuno (ISM, okuno@ism.ac.jp)
## Augst 3rd, 2023
## ----------------------------------------------------
working_dir = getwd()
## ----------------------------------------------------
## dependencies
require("progress")
require("parallel"); require("foreach"); require("doParallel"); require("doRNG")
## directories
dir = list(
main = (tmp <- working_dir),
scripts = paste0(tmp,"/A0_scripts"),
data = paste0(tmp,"/A1_data"),
computed = paste0(tmp,"/A2_computed")
)
lapply(dir, function(z) dir.create(z, showWarnings=FALSE))
## CPU cores for parallel computation
N.Cores = detectCores()
## number of experiments (random seeds)
n_seeds = 1
## loading scripts
source(paste0(dir$scripts,"/gen_data.R"))
source(paste0(dir$scripts,"/functions.R"))
## dataset
df = read.csv(paste0(dir$data,"/2_seed1.csv"), header=T)
x=df$x; mu=df$y; y=mu+df$e;
N=100
x=x[1:N]; y=y[1:N]; mu=mu[1:N]
constants = vector(mode='list', length=3)
## Baseline (no regularization)
constants[[1]] = list(L = 200, ## number of hidden units
lambda = 10**(-1), ## reg. coef. for beta
eta = c(0,0,0), ## reg. coef. for gamma
n = 5, ## num. of subsampling for alpha
m = 5, ## num. of subsampling for gamma
lr0 = 10**(-3), ## initial learning rate
lr_dr = 0.9, ## decay rate
lr_it = 25, ## decay interval
lr_period = 10**3, ## period of cyclic decay
n_itr = 2*10**4 ## num. of SGD iteration
)
## Baseline (ridge regularization)
constants[[2]] = list(L = 200, ## number of hidden units
lambda = 10**(-1), ## reg. coef. for beta
eta = c(0,0,0), ## reg. coef. for gamma
n = 5, ## num. of subsampling for alpha
m = 5, ## num. of subsampling for gamma
lr0 = 10**(-3), ## initial learning rate
lr_dr = 0.9, ## decay rate
lr_it = 25, ## decay interval
lr_period = 10**3, ## period of cyclic decay
n_itr = 2*10**4 ## num. of SGD iteration
)
## Baseline (ridge regularization)
constants[[3]] = list(L = 200, ## number of hidden units
lambda = 10**(-3), ## reg. coef. for beta
eta = c(0,0,0), ## reg. coef. for gamma
n = 5, ## num. of subsampling for alpha
m = 5, ## num. of subsampling for gamma
lr0 = 10**(-3), ## initial learning rate
lr_dr = 0.9, ## decay rate
lr_it = 25, ## decay interval
lr_period = 10**3, ## period of cyclic decay
n_itr = 2*10**4 ## num. of SGD iteration
)
## Proposal (variation regularization)
constants[[4]] = list(L = 200, ## number of hidden units
lambda = 10**(-5), ## reg. coef. for beta
eta = c(0,0,0), ## reg. coef. for gamma
n = 5, ## num. of subsampling for alpha
m = 5, ## num. of subsampling for gamma
lr0 = 10**(-3), ## initial learning rate
lr_dr = 0.9, ## decay rate
lr_it = 25, ## decay interval
lr_period = 10**3, ## period of cyclic decay
n_itr = 2*10**4 ## num. of SGD iteration
)
## Proposal (variation regularization)
constants[[5]] = list(L = 200, ## number of hidden units
lambda = 0, ## reg. coef. for beta
eta = c(10**(-1),0,0), ## reg. coef. for gamma
n = 5, ## num. of subsampling for alpha
m = 5, ## num. of subsampling for gamma
lr0 = 10**(-3), ## initial learning rate
lr_dr = 0.9, ## decay rate
lr_it = 25, ## decay interval
lr_period = 10**3, ## period of cyclic decay
n_itr = 2*10**4 ## num. of SGD iteration
)
## Proposal (variation regularization)
constants[[6]] = list(L = 200, ## number of hidden units
lambda = 0, ## reg. coef. for beta
eta = c(0,10**(-3),0), ## reg. coef. for gamma
n = 5, ## num. of subsampling for alpha
m = 5, ## num. of subsampling for gamma
lr0 = 10**(-3), ## initial learning rate
lr_dr = 0.9, ## decay rate
lr_it = 25, ## decay interval
lr_period = 10**3, ## period of cyclic decay
n_itr = 2*10**4 ## num. of SGD iteration
)
## Proposal (variation regularization)
constants[[7]] = list(L = 200, ## number of hidden units
lambda = 0, ## reg. coef. for beta
eta = c(0,0,10**(-5)), ## reg. coef. for gamma
n = 5, ## num. of subsampling for alpha
m = 5, ## num. of subsampling for gamma
lr0 = 10**(-3), ## initial learning rate
lr_dr = 0.9, ## decay rate
lr_it = 25, ## decay interval
lr_period = 10**3, ## period of cyclic decay
n_itr = 2*10**4 ## num. of SGD iteration
)
## Proposal (ridge + variation regularization)
constants[[8]] = list(L = 20, ## number of hidden units
lambda = 10**(-3), ## reg. coef. for beta
eta = c(0,0,0), ## reg. coef. for gamma
n = 5, ## num. of subsampling for alpha
m = 5, ## num. of subsampling for gamma
lr0 = 10**(-3), ## initial learning rate
lr_dr = 0.9, ## decay rate
lr_it = 25, ## decay interval
lr_period = 10**3, ## period of cyclic decay
n_itr = 2*10**4 ## num. of SGD iteration
)
## experiments
registerDoParallel(N.Cores)
registerDoRNG(123)
foreach(id = 1:8, .export="progress_bar") %dopar% {
## initialization: parameter
theta0 = theta.init(L=constants[[id]]$L, sd=1, sdx=sd(x))
## Variance-reduced SGD
.sgd = VRSGD(theta0=theta0, x=x, y=y, constants=constants[[id]])
save(file=paste0(dir$computed,"/",id,".RData"),
theta0, x, y, constants, .sgd)
}
stopImplicitCluster()
## plot
for(id in 1:8){
name = if(f_id==1) "linear" else if(f_id==2) "quadratic" else "cubic"
load(file=paste0(dir$computed,"/",name,"/",id,".RData"))
pdf(file=paste0(dir$computed,"/",name,"/",id,"_regression.pdf"),
width=4, height=4)
par(mar = c(4, 4, 1, 1), oma = c(0,0,0,0))
xl = c(-1/2, 1/2)
xx = seq(-1/2, 1/2, length.out=100)
yp = f(xx, .sgd$theta)
yl = range(y)
plot(x,y, xlim=xl, ylim=yl, xlab="x", ylab="y")
color = if(5 <= id && id <= 7) "blue" else "black"
par(new=T)
plot(xx, yp, col=color, type="l", xlim=xl, ylim=yl, xlab=" ", ylab=" ",
xaxt="n", yaxt="n", lwd=2)
dev.off()
pdf(file=paste0(dir$computed,"/",name,"/",id,"_variation.pdf"),
width=4, height=4)
par(mar = c(4, 4, 1, 1), oma = c(0,0,0,0))
xx = seq(-0.5, 0.5, 0.01)
y0 = f(xx, .sgd$theta, k=0)
y1 = f(xx, .sgd$theta, k=1)
y2 = f(xx, .sgd$theta, k=2)
y3 = f(xx, .sgd$theta, k=3)
yl = range(y0, y1, y2, y3)
plot(xx, y0, type="l", ylim=yl, lty=1, xlab="x", ylab="k-th variation")
par(new=T)
plot(xx, y1, type="l", ylim=yl, lty=2, xlab=" ", ylab=" ", xaxt="n", yaxt="n")
par(new=T)
plot(xx, y2, type="l", ylim=yl, lty=3, xlab=" ", ylab=" ", xaxt="n", yaxt="n")
par(new=T)
plot(xx, y3, type="l", ylim=yl, lty=4, xlab=" ", ylab=" ", xaxt="n", yaxt="n")
legend("topright",legend=c("k=0","k=1","k=2","k=3"),
lty=1:4)
dev.off()
}