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AOGD-ALD.R
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AOGD-ALD.R
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setwd("D:/experiment/Conference Paper/ICML/ICML2023/code")
rm(list = ls())
d_index <- 9
dpath <- file.path("D:/experiment/online learning dataset/regression/")
Dataset <- c("elevators_all","bank_all", "Year_test","ailerons_all","calhousing","N-cpusmall",
"N-parkinsons","N-TomsHardware")
savepath1 <- paste0("D:/experiment/Conference Paper/ICML/ICML2023/result/",
paste0("AOGD-ALD-",Dataset[d_index],".txt"))
traindatapath <- file.path(dpath, paste0(Dataset[d_index], ".train"))
traindatamatrix <- as.matrix(read.table(traindatapath))
trdata <- traindatamatrix[ ,-1]
ylabel <- traindatamatrix[ ,1]
length_tr <- nrow(trdata)
feature_tr <- ncol(trdata)
##############################################################################
# -4 -3 -2 -1 0 1 2 3 4
sigma <- 12
B0 <- round(sqrt(feature_tr^2+4*feature_tr*length_tr)/2-feature_tr/2)
U <- 2
reptimes <- 10
runtime <- c(rep(0, reptimes))
errorrate <- c(rep(0, reptimes))
All_bud <- c(rep(0, reptimes))
sumtdelta <- c(rep(0, reptimes))
bar_t <- c(rep(length_tr, reptimes))
for( re in 1:reptimes)
{
order <- sample(1:length_tr,length_tr,replace = F) #dis
# order <- c(1:length_tr)
k <- 0
error <- 0
alpha <- 5/length_tr^(1/2)
alpha_t <- 0
sum_delta <- 0
sum_t_delta<- 1
eta_t <- U
Norm <- 0
svmat <- matrix(0,nrow = feature_tr,ncol=1)
Inver_K <- matrix(0,nrow = 1,ncol=1) # The inverse kernel matrix
Gram <- matrix(0,nrow = 1,ncol=1) # The inverse kernel matrix
beta_ast <- array(0,1) # The optimal parameter d
delta <- 0 # The difference of f''-f'
kt <- array(0,1)
indx <- array(0,1)
svpara <- array(0,1)
t1 <- proc.time() #proc.time()
### the first instance
error <- (ylabel[order[1]])^2
svmat[,1] <- trdata[order[1], ]
k <- 1
Inver_K[1,1] <- 1
Gram[1,1] <- 1
sum_t_delta <- sum_t_delta+4*(ylabel[order[1]])^2
eta_t <- U/sqrt(sum_t_delta)
svpara[1] <- -eta_t*2*(0-ylabel[order[1]])
Norm <- abs(svpara[1])
i <- 1
### from the second instance
while(bar_t[re]>=length_tr && i< length_tr)
{
i=i+1
diff <- svmat- trdata[order[i], ]
tem <- colSums(diff*diff)
kt <- exp(tem/(-2*(sigma)^2))
fx <- crossprod(svpara[1:k],kt)[1,1]
error <- error + (fx - ylabel[order[i]])^2
#### compute alpha_t
beta_ast <- Inver_K%*%kt
alpha_t <- 1-crossprod(beta_ast,kt)[1,1]
if(alpha_t<0)
alpha_t <- 0
sq_alpha_t <- sqrt(alpha_t)
if(sq_alpha_t <= alpha)
{
tem <- Gram%*%beta_ast
tem1 <- crossprod(tem,beta_ast)[1,1]
sum_t_delta <- sum_t_delta+4*(fx - ylabel[order[i]])^2*tem1
eta_t <- U/sqrt(sum_t_delta)
tem3 <- crossprod(tem,svpara)[1,1]
g_t <- eta_t*2*(fx-ylabel[order[i]])
svpara <- svpara - g_t*as.vector(beta_ast)
Norm <- sqrt(Norm^2-2*g_t*tem3+g_t^2*tem1)
if(Norm >U)
{
svpara <- svpara*U/Norm
Norm <- U
}
}else{
k <- k+1
svmat <- cbind(svmat,trdata[order[i],])
sum_t_delta <- sum_t_delta+4*(fx - ylabel[order[i]])^2
eta_t <- U/sqrt(sum_t_delta)
g_t <- eta_t*2*(fx-ylabel[order[i]])
svpara[k] <- -g_t
# update the inverse kernel matrix
tem_d <- beta_ast
tem_d[k] <- -1
incre <- tem_d %*% t(tem_d)/alpha_t
incre[1:(k-1),1:(k-1)] <- incre[1:(k-1),1:(k-1)]+Inver_K
Inver_K <- incre
Gram <- cbind(Gram,kt)
Gram <- rbind(Gram,c(kt,1))
Norm <- sqrt(Norm^2-2*g_t*fx+g_t^2)
if(Norm >U)
{
svpara <- svpara*U/Norm
Norm <- U
}
}
if(k==B0)
bar_t[re] <- i
}
if(bar_t[re]<length_tr)
{
for(t in (i+1):length_tr)
{
diff <- svmat- trdata[order[t], ]
kt <- exp(colSums(diff*diff)/(-2*(sigma)^2))
fx <- crossprod(svpara[1:k],kt)[1,1]
error <- error + (fx - ylabel[order[t]])^2
#### compute alpha_t
k <- k+1
svmat <- cbind(svmat,trdata[order[t],])
sum_t_delta <- sum_t_delta + 4*(fx - ylabel[order[t]])^2
eta_t <- U/sqrt(sum_t_delta)
g_t <- eta_t*2*(fx-ylabel[order[t]])
svpara[k] <- -g_t
Norm <- sqrt(Norm^2-2*g_t*fx+g_t^2)
if(Norm > U)
{
svpara <- svpara*U/Norm
Norm <- U
}
}
}
t2 <- proc.time()
runtime[re] <- (t2 - t1)[3]
errorrate[re] <- error/length_tr
All_bud[re] <- k
}
save_result <- list(
note = c("the next term are:alg_name--dataname--sam_num--sigma--sv_num--run_time--err_num--tot_run_time--ave_run_time--ave_err_rate--sd_time--sd_err"),
alg_name = c("AOGD-ALD-"),
dataname = paste0(Dataset[d_index], ".train"),
ker_para = sigma,
sv_num = sum(All_bud)/re,
run_time = as.character(runtime),
err_num = errorrate,
tot_run_time = sum(runtime),
ave_run_time = sum(runtime)/reptimes,
ave_err_rate = sum(errorrate)/reptimes,
sd_time <- sd(runtime),
sd_err <-sd(errorrate)
)
write.table(save_result,file=savepath1,row.names =TRUE, col.names =FALSE, quote = T)
sprintf("the candidate kernel parameter are :")
sprintf("%.5f", sigma)
sprintf("the number of sample is %d", length_tr)
sprintf("the number of support vectors is %d", round(sum(All_bud)/re))
sprintf("total training time is %.4f in dataset", sum(runtime))
sprintf("average training time is %.5f in dataset", sum(runtime)/reptimes)
sprintf("the average MSE is %f", sum(errorrate)/reptimes)
sprintf("standard deviation of run_time is %.5f in dataset", sd(runtime))
sprintf("standard deviation of MSE is %.5f in dataset", sd(errorrate))