grad_ram = function(par,ImpCov,SampCov,Areg,Sreg,A,S,
F,lambda,type,pars_pen,diff_par){
grad.out <- rep(0,length(par))
B = solve(diag(nrow(A)) - Areg)
C = diag(nrow(ImpCov)) - solve(ImpCov) %*% SampCov
E = B %*% Sreg %*% t(B)
# The S matrix gradients are exactly twice that of other methods
if(type=="none"){
for(i in 1:length(grad.out)){
A2 <- A == i;
A2[A2==T] <- 1
S2 <- S == i;
S2[S2==T] <- 1
deriv15 <- F %*% B %*% A2 %*% E %*% t(F) + F %*% B %*% S2 %*% t(B) %*% t(F)
# left out mean part
grad.out[i] <- trace(solve(ImpCov) %*% deriv15 %*% C)
}
}
else if(type=="lasso"){
for(i in 1:length(grad.out)){
A2 <- A == i;
A2[A2==T] <- 1
S2 <- S == i;
S2[S2==T] <- 1
deriv15 <- F %*% B %*% A2 %*% E %*% t(F) + F %*% B %*% S2 %*% t(B) %*% t(F)
# left out mean part
# grad.out[i] <- trace(solve(ImpCov) %*% deriv15 %*% C) + if(any(i==pars_pen)) lambda*sign(Areg[A==i]) else(0)# just penalize when A
#add <- 0
# soft threshold
# if(any(i==pars_pen)){
# if(Areg[A==i] >0 & abs(Areg[A==i]) < lambda){
# add <- Areg[A==i] - lambda
# }else if(Areg[A==i] < 0 & abs(Areg[A==i]) < lambda){
# add <- Areg[A==i] + lambda
# }else if(abs(Areg[A==i]) <= lambda){
# add <- 0
# }
# }
# if(any(i==pars_pen)){
# add = sign(Areg[A==i]) * max(abs(Areg[A==i])-lambda,0)
# }else{
# add <- 0
# }
grad.out[i] <- trace(solve(ImpCov) %*% deriv15 %*% C) #+ add
}
}
else if(type=="ridge"){
for(i in 1:length(grad.out)){
A2 <- A == i;
A2[A2==T] <- 1
S2 <- S == i;
S2[S2==T] <- 1
deriv15 <- F %*% B %*% A2 %*% E %*% t(F) + F %*% B %*% S2 %*% t(B) %*% t(F)
# left out mean part
grad.out[i] <- trace(solve(ImpCov) %*% deriv15 %*% C) +
if(any(i==pars_pen)) 2*lambda*Areg[A==i] else(0)
}
}
else if(type=="diff_lasso"){
count=0
for(i in 1:length(grad.out)){
A2 <- A == i;
A2[A2==T] <- 1
S2 <- S == i;
S2[S2==T] <- 1
deriv15 <- F %*% B %*% A2 %*% E %*% t(F) + F %*% B %*% S2 %*% t(B) %*% t(F)
# left out mean part
grad.out[i] <- trace(solve(ImpCov) %*% deriv15 %*% C) +
if(any(i==pars_pen)){
count=count+1
lambda*sign(Areg[A==i]-diff_par[count])
}else(0)
}
}
grad.out[(max(A)+1):max(S)] = grad.out[(max(A)+1):max(S)] *0.5
#grad.out[min(S[S!=0],0):max(S)] = grad.out[min(S[S!=0],0):max(S)] *0.5
grad.out
}
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