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test_ess_with_observations_nd.R
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require("RZigZag")
generate.logistic.data <- function(beta, nobs) {
ncomp <- length(beta)
dataX <- matrix(rnorm((ncomp -1) * nobs), nrow = ncomp -1);
vals <- beta[1] + colSums(dataX * as.vector(beta[2:ncomp]))
generateY <- function(p) { rbinom(1, 1, p)}
dataY <- sapply(1/(1 + exp(-vals)), generateY)
return(list(dataX, dataY))
}
n.dimension <- 16
beta <- rep(1, n.dimension)
#set.seed(38)
n.experiments <- 10
exponents <- 7:13
n.epochs <- 1e5
malastepsizes <- 29.2/(2.2)^exponents
ess_zigzag_means <- matrix(nrow = length(exponents), ncol = 1)
ess_upperbound_means <- matrix(nrow = length(exponents), ncol = 1)
ess_subsampling_means <- matrix(nrow = length(exponents), ncol = 1)
ess_cv_means <- matrix(nrow = length(exponents), ncol = 1)
ess_zigzag_sds <- matrix(nrow = length(exponents), ncol = 1)
ess_upperbound_sds <- matrix(nrow = length(exponents), ncol = 1)
ess_subsampling_sds <- matrix(nrow = length(exponents), ncol = 1)
ess_cv_sds <- matrix(nrow = length(exponents), ncol = 1)
ess_MALA_means <- matrix(nrow = length(exponents), ncol = 1)
ess_MALA_sds <- matrix(nrow = length(exponents), ncol = 1)
essps_zigzag_means <- matrix(nrow = length(exponents), ncol = 1)
essps_upperbound_means <- matrix(nrow = length(exponents), ncol = 1)
essps_subsampling_means <- matrix(nrow = length(exponents), ncol = 1)
essps_cv_means <- matrix(nrow = length(exponents), ncol = 1)
essps_zigzag_sds <- matrix(nrow = length(exponents), ncol = 1)
essps_upperbound_sds <- matrix(nrow = length(exponents), ncol = 1)
essps_subsampling_sds <- matrix(nrow = length(exponents), ncol = 1)
essps_cv_sds <- matrix(nrow = length(exponents), ncol = 1)
essps_MALA_means <- matrix(nrow = length(exponents), ncol = 1)
essps_MALA_sds <- matrix(nrow = length(exponents), ncol = 1)
require("batchmeans")
source("asvar.R")
for (j in 1:length(exponents)) {
n.observations <- 2^exponents[j]
cat(n.observations,'observations.\n')
ess_zigzag <- matrix(nrow = n.experiments, ncol = 1)
ess_upperbound <- matrix(nrow = n.experiments, ncol = 1)
ess_subsampling <- matrix(nrow = n.experiments, ncol = 1)
ess_cv <- matrix(nrow = n.experiments, ncol = 1)
ess_MALA <- matrix(nrow = n.experiments, ncol = 1)
essps_zigzag <- matrix(nrow = n.experiments, ncol = 1)
essps_upperbound <- matrix(nrow = n.experiments, ncol = 1)
essps_subsampling <- matrix(nrow = n.experiments, ncol = 1)
essps_cv <- matrix(nrow = n.experiments, ncol = 1)
essps_MALA <- matrix(nrow = n.experiments, ncol = 1)
n.batches <- 200
for (i in 1:n.experiments) {
# new data set
logisticData <- generate.logistic.data(beta, n.observations)
# canonical zig zag
ptm.start <- proc.time()[3]
result.ZZ <- ZigZagLogistic(logisticData[[1]], logisticData[[2]], n.epochs, subsampling=FALSE, controlvariates=FALSE, beta0 = beta, n_samples=0, n_batches = n.batches, computeCovariance=FALSE)
ptm.stop <- proc.time()[3]
ess_zigzag[i] <- result.ZZ$ESS[1]
essps_zigzag[i] <- ess_zigzag[i]/(ptm.stop - ptm.start)
# zig zag with global bound
ptm.start <- proc.time()[3]
result.upperbound <- ZigZagLogistic(logisticData[[1]], logisticData[[2]], n.epochs, subsampling=FALSE, controlvariates=FALSE, beta0 = beta, n_samples=0, n_batches = n.batches, computeCovariance=FALSE, upperbound=TRUE)
ptm.stop <- proc.time()[3]
ess_upperbound[i] <- result.upperbound$ESS[1]
essps_upperbound[i] <- ess_upperbound[i]/(ptm.stop - ptm.start)
# sub-sampling with global bound
ptm.start <- proc.time()[3]
result.SS <- ZigZagLogistic(logisticData[[1]], logisticData[[2]], n.epochs, subsampling=TRUE, controlvariates=FALSE, beta0 = beta, n_samples=0, n_batches = n.batches, computeCovariance=FALSE)
ptm.stop <- proc.time()[3]
ess_subsampling[i] <- result.SS$ESS[1]
essps_subsampling[i] <- ess_subsampling[i]/(ptm.stop - ptm.start)
# sub-sampling with control variates
ptm.start <- proc.time()[3]
result.CV <- ZigZagLogistic(logisticData[[1]], logisticData[[2]], n.epochs, subsampling=TRUE, controlvariates=TRUE, beta0 = beta, n_samples=0, n_batches = n.batches, computeCovariance=FALSE)
ptm.stop <- proc.time()[3]
ess_cv[i] <- result.CV$ESS[1]
essps_cv[i] <- ess_cv[i]/(ptm.stop - ptm.start)
ptm.start <- proc.time()[3]
result.MALA <- MALALogistic(logisticData[[1]], logisticData[[2]], n.epochs, beta, malastepsizes[j])
ess_MALA[i] <- bm_ess(result.MALA$beta[1,])
ptm.stop <- proc.time()[3]
essps_MALA[i] <- ess_MALA[i]/(ptm.stop - ptm.start)
}
ess_zigzag_means[j] <- mean(ess_zigzag)/n.epochs
ess_zigzag_sds[j] <- sd(ess_zigzag)/n.epochs
ess_upperbound_means[j] <- mean(ess_upperbound)/n.epochs
ess_upperbound_sds[j] <- sd(ess_upperbound)/n.epochs
ess_subsampling_means[j] <- mean(ess_subsampling)/n.epochs
ess_subsampling_sds[j] <- sd(ess_subsampling)/n.epochs
ess_cv_means[j] <- mean(ess_cv)/n.epochs
ess_cv_sds[j] <- sd(ess_cv)/n.epochs
ess_MALA_means[j] <- mean(ess_MALA)/n.epochs
ess_MALA_sds[j] <- sd(ess_MALA)/n.epochs
essps_zigzag_means[j] <- mean(essps_zigzag)
essps_zigzag_sds[j] <- sd(essps_zigzag)
essps_upperbound_means[j] <- mean(essps_upperbound)
essps_upperbound_sds[j] <- sd(essps_upperbound)
essps_subsampling_means[j] <- mean(essps_subsampling)
essps_subsampling_sds[j] <- sd(essps_subsampling)
essps_cv_means[j] <- mean(essps_cv)
essps_cv_sds[j] <- sd(essps_cv)
essps_MALA_means[j] <- mean(essps_MALA)
essps_MALA_sds[j] <- sd(essps_MALA)
}
plot(result.MALA$beta[1,],result.MALA$beta[2,],'p',asp = 1)
## SAVE USEFUL DATA
SAVEPATH = "./"
rm(logisticData)
rm(result.CV, result.SS, result.upperbound, result.ZZ, result.MALA)
filename <- paste(SAVEPATH, Sys.Date(), "-ESSpE-", n.dimension, "d.Rdata", sep="")
save.image(filename)
## FIRST: ESSpE
y_max = log(max(ess_zigzag_means+ess_zigzag_sds, ess_subsampling_means + ess_subsampling_sds, ess_cv_means + ess_cv_sds, ess_upperbound_means+ess_upperbound_sds, ess_MALA_means+ess_MALA_sds),2)
y_min = log(min(ess_zigzag_means-ess_zigzag_sds, ess_subsampling_means - ess_subsampling_sds, ess_cv_means - ess_cv_sds, ess_upperbound_means - ess_upperbound_sds, ess_MALA_means-ess_MALA_sds),2)
filename <- paste(SAVEPATH, Sys.Date(), "-ESSpE-", n.dimension, "d.pdf", sep="")
pdf(filename)
require("Hmisc")
errbar(exponents, log(ess_zigzag_means,2), log(ess_zigzag_means+ess_zigzag_sds,2), log(ess_zigzag_means-ess_zigzag_sds,2), add=FALSE, pch=1, ylim=c(-9.0, -2.0), cap=.015, ann=FALSE)
errbar(exponents, log(ess_upperbound_means,2), log(ess_upperbound_means+ess_upperbound_sds,2), log(ess_upperbound_means-ess_upperbound_sds,2), add=TRUE, pch=1, cap=.015, xlog = TRUE, ylog=TRUE,
col = 'red', errbar.col = 'red', ann=FALSE)
errbar(exponents, log(ess_subsampling_means,2), log(ess_subsampling_means+ess_subsampling_sds,2), log(ess_subsampling_means-ess_subsampling_sds,2), add=TRUE, pch=1, cap=.015, xlog = TRUE, ylog=TRUE,
col = 'blue', errbar.col = 'blue', ann=FALSE)
errbar(exponents, log(ess_cv_means,2), log(ess_cv_means+ess_cv_sds,2), log(ess_cv_means-ess_cv_sds,2),add=TRUE, pch=1, cap=.015,
xlog = TRUE, ylog=TRUE, col = 'magenta', errbar.col = 'magenta', ann=FALSE)
errbar(exponents, log(ess_MALA_means,2), log(ess_MALA_means+ess_MALA_sds,2), log(ess_MALA_means-ess_MALA_sds,2),add=TRUE, pch=1, cap=.015,
xlog = TRUE, ylog=TRUE, col = 'green', errbar.col = 'green', ann=FALSE)
basic.lm <- lm(log(ess_zigzag_means,2) ~ exponents)
upperbound.lm <- lm(log(ess_upperbound_means,2) ~ exponents)
subsampling.lm <- lm(log(ess_subsampling_means,2) ~ exponents)
cv.lm <- lm(log(ess_cv_means,2) ~ exponents)
MALA.lm <- lm(log(ess_MALA_means,2) ~ exponents)
abline(basic.lm$coefficients[[1]], basic.lm$coefficients[[2]],col = 'black')
abline(upperbound.lm$coefficients[[1]], upperbound.lm$coefficients[[2]],col = 'red')
abline(subsampling.lm$coefficients[[1]], subsampling.lm$coefficients[[2]], col = 'blue')
abline(cv.lm$coefficients[[1]], cv.lm$coefficients[[2]], col='magenta')
abline(MALA.lm$coefficients[[1]], MALA.lm$coefficients[[2]], col='green')
title(xlab="log(number of observations) base 2", ylab="log(ESS / epoch) base 2")
dev.off()
## BELOW: ESSps plot
y_max = log(max(essps_zigzag_means+essps_zigzag_sds, essps_subsampling_means + essps_subsampling_sds, essps_cv_means + essps_cv_sds, essps_upperbound_means+essps_upperbound_sds, essps_MALA_means+essps_MALA_sds),2)
y_min = log(min(essps_zigzag_means-essps_zigzag_sds, essps_subsampling_means - essps_subsampling_sds, essps_cv_means - essps_cv_sds, essps_upperbound_means - essps_upperbound_sds, essps_MALA_means-essps_MALA_sds),2)
filename <- paste(SAVEPATH, Sys.Date(), "-ESSps-", n.dimension, "d.pdf", sep="")
pdf(filename)
errbar(exponents, log(essps_zigzag_means,2), log(essps_zigzag_means+essps_zigzag_sds,2), log(essps_zigzag_means-essps_zigzag_sds,2), add=FALSE, pch=1, ylim=c(-1,10),cap=.015, ann=FALSE)
errbar(exponents, log(essps_upperbound_means,2), log(essps_upperbound_means+essps_upperbound_sds,2), log(essps_upperbound_means-essps_upperbound_sds,2), add=TRUE, pch=1, cap=.015, xlog = TRUE, ylog=TRUE,
col = 'red', errbar.col = 'red', ann=FALSE)
errbar(exponents, log(essps_subsampling_means,2), log(essps_subsampling_means+essps_subsampling_sds,2), log(essps_subsampling_means-essps_subsampling_sds,2), add=TRUE, pch=1, cap=.015, xlog = TRUE, ylog=TRUE,
col = 'blue', errbar.col = 'blue', ann=FALSE)
errbar(exponents, log(essps_cv_means,2), log(essps_cv_means+essps_cv_sds,2), log(essps_cv_means-essps_cv_sds,2),add=TRUE, pch=1, cap=.015,
xlog = TRUE, ylog=TRUE, col = 'magenta', errbar.col = 'magenta', ann=FALSE)
errbar(exponents, log(essps_MALA_means,2), log(essps_MALA_means+essps_MALA_sds,2), log(essps_MALA_means-essps_MALA_sds,2),add=TRUE, pch=1, cap=.015,xlog = TRUE, ylog=TRUE, col = 'green', errbar.col = 'green', ann=FALSE)
basic.lm <- lm(log(essps_zigzag_means,2) ~ exponents)
upperbound.lm <- lm(log(essps_upperbound_means,2) ~ exponents)
subsampling.lm <- lm(log(essps_subsampling_means,2) ~ exponents)
cv.lm <- lm(log(essps_cv_means,2) ~ exponents)
MALA.lm <- lm(log(essps_MALA_means,2) ~ exponents)
abline(basic.lm$coefficients[[1]], basic.lm$coefficients[[2]],col = 'black')
abline(upperbound.lm$coefficients[[1]], upperbound.lm$coefficients[[2]],col = 'red')
abline(subsampling.lm$coefficients[[1]], subsampling.lm$coefficients[[2]], col = 'blue')
abline(cv.lm$coefficients[[1]], cv.lm$coefficients[[2]], col='magenta')
abline(MALA.lm$coefficients[[1]], MALA.lm$coefficients[[2]], col='green')
title(xlab="log(number of observations) base 2", ylab="log(ESS per second) base 2")
dev.off()