我正在尝试在下面运行以下模拟。请注意,这确实需要安装 Mosek 和 RMosek!
我不断收到错误
KWDual(A, d, w, ...) 中的错误:Mosek 错误:MSK_RES_TRM_STALL:优化器因进度缓慢而终止。
如何解决MSK_RES_TRM_STALL
错误?
进一步的研究
在查找此文档时,我发现了这一点:
优化器因进度缓慢而终止。停滞意味着数值问题会阻止优化器取得合理的进展,并且继续下去是没有意义的。在许多情况下,如果问题规模严重不足或条件不佳,就会发生这种情况。无法保证解决方案是可行的或最优的。然而,停顿经常发生在最佳值附近,并且返回的解决方案可能质量很好。因此,建议检查解决方案的状态。如果解决方案状态是最佳的,则解决方案很可能对于大多数实际目的来说已经足够好了。请注意,如果使用打开基础识别的内点优化器解决线性优化问题,即使优化器停止,返回的基本解决方案也可能具有较高的准确性。
所以我检查了最终值A
,但里面什么都没有。我发现如果我将模拟从 1000 更改为 30,我确实会得到值 ( A <- sim1(30, 30, setting = 1)
),但这是次优的。
可重现的脚本
KFE <- function(y, T = 300, lambda = 1/3){
# Kernel Fourier Estimator: Stefanski and Carroll (Statistics, 1990)
ks <- function(s,x) exp(s^2/2) * cos(s * x)
K <- function(t, y, lambda = 1/3){
k <- y
for(i in 1:length(y)){
k[i] <- integrate(ks, 0, 1/lambda, x = (y[i] - t))$value/pi
}
mean(k)
}
eps <- 1e-04
if(length(T) == 1) T <- seq(min(y)-eps, max(y)+eps, length = T)
g <- T
for(j in 1:length(T))
g[j] <- K(T[j], y, lambda = lambda)
list(x = T, y = g)
}
BDE <- function(y, T = 300, df = 5, c0 = 1){
# Bayesian Deconvolution Estimator: Efron (B'ka, 2016)
require(splines)
eps <- 1e-04
if(length(T) == 1) T <- seq(min(y)-eps, max(y)+eps, length = T)
X <- ns(T, df = df)
a0 <- rep(0, ncol(X))
A <- dnorm(outer(y,T,"-"))
qmle <- function(a, X, A, c0){
g <- exp(X %*% a)
g <- g/sum(g)
f <- A %*% g
-sum(log(f)) + c0 * sum(a^2)^.5
}
ahat <- nlm(qmle, a0, X=X, A=A, c0 = c0)$estimate
g <- exp(X %*% ahat)
g <- g/integrate(approxfun(T,g),min(T),max(T))$value
list(x = T,y = g)
}
W <- function(G, h, interp = FALSE, eps = 0.001){
#Wasserstein distance: ||G-H||_W
H <- cumsum(h$y)
H <- H/H[length(H)]
W <- integrate(approxfun(h$x, abs(G(h$x) - H)),min(h$x),max(h$x))$value
list(W=W, H=H)
}
biweight <- function(x0, x, bw){
t <- (x - x0)/bw
(1-t^2)^2*((t> -1 & t<1)-0) *15/16
}
Wasser <- function(G, h, interp = FALSE, eps = 0.001, bw = 0.7){
#Wasserstein distance: ||G-H||_W
if(interp == "biweight"){
yk = h$x
for (j in 1:length(yk))
yk[j] = sum(biweight(h$x[j], h$x, bw = bw)*h$y/sum(h$y))
H <- cumsum(yk)
H <- H/H[length(H)]
}
else {
H <- cumsum(h$y)
H <- H/H[length(H)]
}
W <- integrate(approxfun(h$x, abs(G(h$x) - H)),min(h$x),max(h$x),
rel.tol = 0.001, subdivisions = 500)$value
list(W=W, H=H)
}
sim1 <- function(n, R = 10, setting = 0){
A <- matrix(0, 4, R)
if(setting == 0){
G0 <- function(t) punif(t,0,6)/8 + 7 * pnorm(t, 0, 0.5)/8
rf0 <- function(n){
s <- sample(0:1, n, replace = TRUE, prob = c(1,7)/8)
rnorm(n) + (1-s) * runif(n,0,6) + s * rnorm(n,0,0.5)
}
}
else{
G0 <- function(t) 0 + 7 * (t > 0)/8 + (t > 2)/8
rf0 <- function(n){
s <- sample(0:1, n, replace = TRUE, prob = c(1,7)/8)
rnorm(n) + (1-s) * 2 + s * 0
}
}
for(i in 1:R){
y <- rf0(n)
g <- BDE(y)
Wg <- Wasser(G0, g)
h <- GLmix(y)
Wh <- Wasser(G0, h)
Whs <- Wasser(G0, h, interp = "biweight")
k <- KFE(y)
Wk <- Wasser(G0, k)
A[,i] <- c(Wg$W, Wk$W, Wh$W, Whs$W)
}
A
}
require(REBayes)
set.seed(12)
A <- sim1(1000, 1000, setting = 1)