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JGPR.R
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JGPR <- function(inputs, outputs, kern = NULL, init.params = NaN, fix.noise = F, inp = NaN, out = NaN, MaxIter = 100, break.tol = F, e = 0.25, init.rate = 0.1){
#inputs: train inputs
#outputs: train outputs
#kern: user define kernel
#init.params: initializing of kernel parameters and noise kernel
#inp: preprocessing of inputs
#out: preprocessing of outputs
#MaxIter: maximum Iteration for training
#break.tol: if true Iteration stops with special condition
#e: multiply parameter to Back tracking line search
require(Deriv)
require(rdist)
require(progress)
require(R.utils)
grad <- function(params){
grad.kerns = array(0, dim = c(L, N, N))
lst_params = as.list(setNames(params[1:(L-1)], op_vars), all.names = T)
for(i in 1:(L-1)){
grad.kerns[i,,] = doCall(kern_gxs[[i]], args = c(lst_params, list(d = d, ip = ip)))
}
grad.kerns[L,,] = diag(2*params[L], nrow = N)
# m = 0
# for(i in 1:MO){
# alpha = inv.kernl %*% as.matrix(outputs[,i])
# m = m + alpha %*% t(alpha) - inv.kernl
# }
alpha = inv.kernl %*% outputs
m = alpha %*% t(alpha) - MO * inv.kernl
grad.direction = matrix(0, nrow = L, ncol = 1)
for(i in 1:L){
grad.direction[i] = -1/2 * sum(diag( m %*% grad.kerns[i,,] ))
}
return(grad.direction)
}
predict <- function(newInputs, sigma.opt = NULL){
#newInputs: new inputs for predicting output
#sigma.opt: Noise kernel parameter
newInputs = as.matrix(newInputs)
N.ts = nrow(newInputs)
if(inp == 'st'){
newInputs = sweep(newInputs, 2, mean.in, "-")
newInputs = sweep(newInputs, 2, sd.in, "/")
}else if(inp == 'norm'){
newInputs = sweep(newInputs, 2, min.in, "-")
newInputs = sweep(newInputs, 2, (max.in-min.in), "/")
}
params = as.matrix(optimized.params)
if(!is.null(sigma.opt)){
params = params[,ncol(params)]
params[length(params)] = sigma.opt
lst_params = as.list(setNames(params[1:(L-1)], op_vars), all.names = T)
train.kernl = doCall(kern_fx, args = c(lst_params, list(d = d, ip = ip)))
if(!fix.noise){
train.kernl = train.kernl + diag(params[L]^2, nrow = N)
}else{
train.kernl = train.kernl + diag(init.params[L]^2, nrow = N)
}
inv.kernl = solve(train.kernl)
}
d.ts = dist(newInputs, method = "euclidean", diag = T, upper = T)
d.ts = as.matrix(d.ts)
ip.ts = newInputs %*% t(newInputs)
lst_params = as.list(setNames(params[1:(L-1)], op_vars), all.names = T)
test.kernl = doCall(kern_fx, args = c(lst_params, list(d = d.ts, ip = ip.ts)))
if(!fix.noise){
test.kernl = test.kernl + diag(params[L]^2, nrow = N.ts)
}else{
test.kernl = test.kernl + diag(init.params[L]^2, nrow = N.ts)
}
d.trs = cdist(newInputs, inputs)
ip.trs = newInputs %*% t(inputs)
lst_params = as.list(setNames(params[1:(L-1)], op_vars), all.names = T)
test.train.kernl = doCall(kern_fx, args = c(lst_params, list(d = d.trs, ip = ip.trs)))
pred.mu = pred.sd = matrix(0, nrow = nrow(newInputs), ncol = MO)
if(out == 'st'){
for(i in 1:MO){
pred.mu[,i] = test.train.kernl %*% inv.kernl %*% outputs[,i]
pred.mu[,i] = pred.mu[,i] * sd.ou[i] + mean.ou[i]
pred.sd[,i] = sqrt(diag(test.kernl - test.train.kernl %*% inv.kernl %*% t(test.train.kernl)))
pred.sd[,i] = pred.sd[,i] * sd.ou[i]
}
}else if(out == 'norm'){
for(i in 1:MO){
pred.mu[,i] = test.train.kernl %*% inv.kernl %*% outputs[,i]
pred.mu[,i] = pred.mu[,i] * (max.ou[i]-min.ou[i]) + min.ou[i]
pred.sd[,i] = sqrt(diag(test.kernl - test.train.kernl %*% inv.kernl %*% t(test.train.kernl)))
pred.sd[,i] = pred.sd[,i] * abs(max.ou[i]-min.ou[i])
}
}else{
for(i in 1:MO){
pred.mu[,i] = test.train.kernl %*% inv.kernl %*% outputs[,i]
pred.sd[,i] = sqrt(diag(test.kernl - test.train.kernl %*% inv.kernl %*% t(test.train.kernl)))
}
}
return(list(pred.mu = pred.mu, pred.sd = pred.sd))
}
all_vars = all.vars(kern)
op_vars = all_vars
if(sum(all_vars=="d")){
d = dist(inputs, method = "euclidean", diag = T, upper = T)
d = as.matrix(d)
op_vars = op_vars[! op_vars %in% c("d")]
}else{
d = 0
}
if(sum(all_vars=="ip")){
ip = inputs %*% t(inputs)
op_vars = op_vars[! op_vars %in% c("ip")]
}else{
ip = 0
}
args = setNames(rep(NA,length(all_vars)), all_vars)
kern_fx = as.function(c(args, kern)) #define function of filling kernel
n_op_vars = length(op_vars) #number of optimization parameters
kern_gxs = vector("list", n_op_vars)
for(i in 1:n_op_vars){
g = D(kern, op_vars[i]) #get gradient of kernel with respect to i'th variable
sg = Simplify(g) #simplify gradient
gx <- as.function(c(args, sg)) #convert it to function
kern_gxs[[i]] = gx #save gradient functions into list
}
inputs = as.matrix(inputs)
outputs = as.matrix(outputs)
N = nrow(inputs)
MI = ncol(inputs)
MO = ncol(outputs)
L = length(init.params)
if(inp == 'st'){
mean.in = apply(inputs, 2, mean)
sd.in = apply(inputs, 2, sd)
inputs = sweep(inputs, 2, mean.in, "-")
inputs = sweep(inputs, 2, sd.in, "/")
}else if(inp == 'norm'){
max.in = apply(inputs, 2, max)
min.in = apply(inputs, 2, min)
inputs = sweep(inputs, 2, min.in, "-")
inputs = sweep(inputs, 2, (max.in-min.in), "/")
}
if(out == 'st'){
mean.ou = apply(outputs, 2, mean)
sd.ou = apply(outputs, 2, sd)
outputs = sweep(outputs, 2, mean.ou, "-")
outputs = sweep(outputs, 2, sd.ou, "/")
}else if(out == 'norm'){
max.ou = apply(outputs, 2, max)
min.ou = apply(outputs, 2, min)
outputs = sweep(outputs, 2, min.ou, "-")
outputs = sweep(outputs, 2, (max.ou-min.ou), "/")
}
rate1 = rep(0, MaxIter)
rate2 = rep(0, MaxIter)
rate2[1] = init.rate
Ta = 0.1
log.max = rep(0, MaxIter+1)
log.max2 = 0
params = matrix(0, nrow = L, ncol = MaxIter+1)
params[, 1] = init.params
if(fix.noise){
params[L, 1] = 0
}
grads = matrix(0, nrow = L, ncol = MaxIter+1)
p = matrix(0, nrow = L, ncol = MaxIter+1)
lst_params = as.list(setNames(params[1:(L-1),1], op_vars), all.names = T)
kernl = doCall(kern_fx, args = c(lst_params, list(d = d, ip = ip)))
if(!fix.noise){
kernl = kernl + diag(params[L,1]^2, nrow = N)
}else{
kernl = kernl + diag(init.params[L]^2, nrow = N)
}
R = chol(kernl)
inv.kernl = chol2inv(R)
grads[,1] = grad(params[,1])
p[,1] = -grads[,1]
log.det.kernl = sum(2*log(diag(R)))
for(i in 1:MO){
log.max[1] = log.max[1] + 1/2*(log.det.kernl + t(outputs[,i]) %*% inv.kernl %*% outputs[,i] + N*log(2*pi))
}
print(sprintf("Iter %i ==> log.lik = %f", 0, log.max[1]))
pb <- progress_bar$new(
format = "rate::new_rate loglik::loglik it::current [:bar] :percent eta: :eta",
total = MaxIter, clear = FALSE, width = 100)
#----------------------------------------------------------------------------------
#find optimum parameters
for(it in 1:MaxIter){
#----------------------------------------
#back tracking line search with wolf condition
for(j in 1:11){
new.params = params[, it] + rate2[j] * p[,it]
lst_params = as.list(setNames(new.params[1:(L-1)], op_vars), all.names = T)
kernl = doCall(kern_fx, args = c(lst_params, list(d = d, ip = ip)))
if(!fix.noise){
kernl = kernl + diag(new.params[L]^2, nrow = N)
}else{
kernl = kernl + diag(init.params[L]^2, nrow = N)
}
R = chol(kernl)
inv.kernl = chol2inv(R)
log.det.kernl = sum(2*log(diag(R)))
log.max2 = 0
for(i in 1:MO){
log.max2 = log.max2 + 1/2*(log.det.kernl+ t(outputs[,i]) %*% inv.kernl %*% outputs[,i] + N*log(2*pi))
}
if(log.max2 < log.max[it] + rate2[j]*e*(t(grads[,it])%*%p[,it])) break()
rate2[j+1] = Ta * rate2[j]
}
rate1[it] = rate2[j] #initialize new rate
#-----------------------------------------
params[,it+1] = new.params
log.max[it+1] = log.max2
pb$tick(tokens = list(new_rate = rate1[it], loglik = log.max[it+1]))
grads[,it+1] = grad(params[,it+1])
Beta = t(grads[,it+1])%*%(grads[,it+1]-grads[,it]) / t(grads[,it])%*%(grads[,it])
Beta = max(0, Beta)
p[,it+1] = -grads[,it+1] + c(Beta) * p[,it]
if(break.tol & abs(log.max[it+1] - log.max[it]) < break.tol) break()
}
cat("\n")
log.max = log.max[log.max!=0]
optimized.params = params[,it+1]
if(fix.noise) params[L,] = init.params[L]
return(list(predict = predict, params = params[,1:(it+1)], logLikelihood = log.max))
}