examples/gwish/gwish_decomp.R
In echuu/hybridml:
## 5/10:
## Split the calculation in to blocks, since each block of G_5 gives a very
## easy calculation for both the gradient and the hessian.
## This will require separate functions for both the gradient and the hessian
## that are specific to this problem. In addition, we have to modify
## globalMode() so that the correct params_G5 is passed into the grad and hess
## functions, as well as hybridml(), so that the correct params_G5 is passed
## into the grad and hess functions
source("examples/gwish/gwish_density.R")
library(BDgraph)
library(dplyr)
#### initialize graphs ---------------------------------------------------------
### create parameters for a single G_5 -----------------------------------------
p1 = 5
G_5 = matrix(c(1,1,0,1,1,
1,1,1,0,0,
0,1,1,1,1,
1,0,1,1,1,
1,0,1,1,1), p1, p1)
G_5 = matrix(1,5,5)
p1 = 10
n = 3
G_5 = matrix(c(0, 1, 0, 0, 0, 0, 0, 1, 0, 0,
1, 0, 1, 0, 0, 0, 1, 0, 0, 0,
0, 1, 0, 1, 0, 1, 0, 0, 0, 0,
0, 0, 1, 0, 1, 0, 0, 0, 0, 0,
0, 0, 0, 1, 0, 1, 0, 0, 0, 0,
0, 0, 1, 0, 1, 0, 1, 0, 0, 0,
0, 1, 0, 0, 0, 1, 0, 1, 0, 0,
1, 0, 0, 0, 0, 0, 1, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0), 10, 10)
diag(G_5) = 1
p1 = 6
G_5 = matrix(1,6,6)
G_5[6,] = 0
G_5[,6] = 0
G_5[6,6] = 1
gnorm(G_5, 3, 3*diag(6), 100)
b = 5
n = 3
V_5 = n * diag(1, p1)
P = chol(solve(V_5)) # upper cholesky factor; D^(-1) = TT' in Atay paper
FREE_PARAMS_ALL = c(upper.tri(diag(1, p1), diag = T) & G_5)
edgeInd = G_5[upper.tri(G_5, diag = TRUE)] %>% as.logical
## construct A matrix so that we can compute k_i
A = (upper.tri(diag(1, p1), diag = F) & G_5) + 0
k_i = colSums(A) # see step 2, p. 329 of Atay
nu_i = rowSums(A) # see step 2, p. 329 of Atay
b_i = nu_i + k_i + 1
b_i
# S = matrix(0, p, p)
D = sum(edgeInd) # number of free parameters / dimension of parameter space
index_mat = matrix(0, p1, p1)
index_mat[upper.tri(index_mat, diag = T)][edgeInd] = 1:D
index_mat[upper.tri(index_mat, diag = T)]
t_ind = which(index_mat!=0,arr.ind = T)
t_ind
index_mat[lower.tri(index_mat)] = NA
vbar = which(index_mat==0,arr.ind = T) # non-free elements
n_nonfree = nrow(vbar)
params_G5 = list(G = G_5, P = P, p = p1, D = D, edgeInd = edgeInd,
b = b, nu_i = nu_i, b_i = b_i,
t_ind = t_ind, n_nonfree = n_nonfree, vbar = vbar,
n_graphs = 1)
################################################################################
### create parameters for stacked G_5's so we can sample, and compute psi ------
n_G5 = 1 # number of G_5 graphs we want to stack
G = diag(1, n_G5) %x% G_5
p = ncol(G)
V = n * diag(1, p)
## try computing the normalizing constant of G_9 first as sanity check
FREE_PARAMS_ALL = c(upper.tri(diag(1, p), diag = T) & G)
edgeInd = G[upper.tri(G, diag = TRUE)] %>% as.logical
## construct A matrix so that we can compute k_i
A = (upper.tri(diag(1, p), diag = F) & G) + 0
k_i = colSums(A) # see step 2, p. 329 of Atay
nu_i = rowSums(A) # see step 2, p. 329 of Atay
b_i = nu_i + k_i + 1
b_i
set.seed(1)
Omega_G = rgwish(1, G, b, V) # generate the true precision matrix
P = chol(solve(V)) # upper cholesky factor; D^(-1) = TT' in Atay paper
# params = list(G = G, P = P, p = p, edgeInd = edgeInd,
# b = b, nu_i = nu_i, b_i = b_i)
# N = 0
S = matrix(0, p, p)
D = sum(edgeInd) # number of free parameters / dimension of parameter space
index_mat = matrix(0, p, p)
index_mat[upper.tri(index_mat, diag = T)][edgeInd] = 1:D
index_mat[upper.tri(index_mat, diag = T)]
t_ind = which(index_mat!=0,arr.ind = T)
# t_ind
index_mat[lower.tri(index_mat)] = NA
vbar = which(index_mat==0,arr.ind = T) # non-free elements
n_nonfree = nrow(vbar)
params = list(G = G, P = P, p = p, D = D, edgeInd = edgeInd,
b = b, nu_i = nu_i, b_i = b_i,
t_ind = t_ind, n_nonfree = n_nonfree, vbar = vbar)
J = 200
samps = samplegw(J, G, b, 0, V, S, solve(P), FREE_PARAMS_ALL)
u_samps = samps$Psi_free %>% data.frame
# u_df = preprocess(u_samps, D, params) # J x (D_u + 1)
u_df = gwish_preprocess(u_samps, D, params_G5) # J x (D_u + 1)
u_df %>% head
I_G = function(delta) {
7/2 * log(pi) + lgamma(delta + 5/2) - lgamma(delta + 3) +
lgamma(delta + 1) + lgamma(delta + 3/2) + 2 * lgamma(delta + 2) +
lgamma(delta + 5/2)
}
(Z_5 = log(2^(0.5*p1*b + 7)) + I_G(0.5*(b-2)) + (-0.5 * p1 * b - 7) * log(n))
Z = n_G5 * Z_5
Z
gnorm(G, b, V, J) # gnorm estimate of the entire (appended graph)
# ------------------------------------------------------------------------------
#### compute the hybrid approximation, bridge sampling estimator
## numerical versions of the grad and hess -- included here just as a comparison
## for smaller dimension to make sure the analytical gradient and hessian
## are computed correctly
# grad = function(u, params) { pracma::grad(psi, u, params = params) }
# hess = function(u, params) { pracma::hessian(psi, u, params = params) }
# u_star = hybridml::globalMode(u_df) ## slow version
# u_star_numer = u_star
grad = function(u, params) { fast_grad(u, params) }
hess = function(u, params) { fast_hess(u, params) }
u_star = gwish_globalMode(u_df, params, params_G5)
## laplace estimator
0.5*(D)*log(2*pi) -
0.5*log_det(hess(u_star, params_G5)$H) -
gwish_psi(c(u_star), params_G5)
# u_star
# u_star_closed = u_star
# cbind(u_star_numer, u_star_closed)
logzhat = hybml_gwish(u_df, params_G5, psi = psi, grad = grad, hess = hess, u_0 = u_star)$logz
logzhat = hybml_gwish(u_df, params_G5, psi = psi, grad = grad, hess = hess)$logz
logzhat # hybrid
Z # truth
J = 2000
samps = samplegw(J, G, b, 0, V, S, solve(P), FREE_PARAMS_ALL)
u_samps = samps$Psi_free %>% data.frame
u_df = gwish_preprocess(u_samps, D, params_G5) # J x (D_u + 1)
logzhat = hybml_gwish(u_df, params_G5, psi = gwish_psi, grad = grad, hess = hess, u_0 = u_star)$logz
logzhat # hybrid
abs(logzhat - Z)
## bridge calculation
log_density = function(u, data) {
-psi(u, data)
}
log_density = function(u, data) {
-gwish_psi(u, data)
}
u_samp = as.matrix(u_samps)
colnames(u_samp) = names(u_df)[1:D]
# prepare bridge_sampler input()
lb = rep(-Inf, D)
ub = rep(Inf, D)
names(lb) <- names(ub) <- colnames(u_samp)
bridge_result = bridgesampling::bridge_sampler(samples = u_samp,
log_posterior = log_density,
data = params_G5,
lb = lb, ub = ub,
method = 'normal',
silent = TRUE)
bridge_result = bridgesampling::bridge_sampler(samples = u_samp,
log_posterior = log_density,
data = params,
lb = lb, ub = ub,
method = 'normal',
silent = TRUE)
bridge_result$logml
abs(bridge_result$logml - Z)
gnorm(G, b, V, J) # gnorm estimate of the entire (appended graph)
abs(gnorm(G, b, V, J) - Z)
abs(bridge_result$logml - Z)
abs(logzhat - Z)
### run simulations
# initialize storage for each of the estimators
n_sims = 100
hyb = numeric(n_sims)
# hyb_old = numeric(n_sims)
gnorm_approx = numeric(n_sims)
bridge = numeric(n_sims)
bridge_warp = numeric(n_sims)
j = 1
J = 1000
set.seed(1)
while (j <= n_sims) {
samps = samplegw(J, G, b, N, V, S, solve(P), FREE_PARAMS_ALL)
u_samps = samps$Psi_free %>% data.frame
### hyb estimator ------------------------------------------------------------
u_df = gwish_preprocess(u_samps, D, params_G5) # J x (D_u + 1)
logzhat = hybml_gwish(u_df, params_G5, psi = psi, grad = grad, hess = hess,
u_0 = u_star)$logz
hyb[j] = logzhat # hybrid
### bridge estimator ---------------------------------------------------------
u_samp = as.matrix(u_samps)
colnames(u_samp) = names(u_df)[1:D]
lb = rep(-Inf, D)
ub = rep(Inf, D)
names(lb) <- names(ub) <- colnames(u_samp)
bridge_result = bridgesampling::bridge_sampler(samples = u_samp,
log_posterior = log_density,
data = params_G5,
lb = lb, ub = ub,
silent = TRUE)
bridge[j] = bridge_result$logml
bridge_result = bridgesampling::bridge_sampler(samples = u_samp,
log_posterior = log_density,
data = params_G5,
lb = lb, ub = ub,
method = 'warp3',
silent = TRUE)
bridge_warp[j] = bridge_result$logml
### gnorm estimator ----------------------------------------------------------
gnorm_approx[j] = gnorm(G, b, V, J)
### display some information about the running avg of the estimator + error
print(paste('iter ', j, ': ',
'hyb = ', round(mean(hyb[hyb!=0]), 3),
' (error = ', round(mean((Z - hyb[hyb!=0])), 3), '), ',
'bse = ', round(mean(bridge[bridge!=0]), 3),
' (error = ', round(mean((Z - bridge[bridge!=0])), 3), '), ',
'wbse = ', round(mean((bridge_warp[bridge_warp!=0])), 3),
' (error = ', round(mean(Z - bridge_warp[bridge_warp!=0]), 3), '), ',
sep = ''))
j = j + 1
}
mean(abs(Z - hyb[hyb != 0]))
mean(abs(Z - bridge[bridge != 0]))
mean(abs(Z - bridge_warp[bridge_warp != 0]))
mean(abs(Z - hyb[hyb != 0])^2)
mean(abs(Z - bridge[bridge != 0])^2)
mean(abs(Z - bridge_warp[bridge_warp != 0])^2)
truth = Z
approx = data.frame(truth, hyb = hyb, gnorm = gnorm_approx, bridge = bridge,
bridge_warp = bridge_warp)
approx_long = reshape2::melt(approx, id.vars = 'truth')
truth = Z
res_tbl =
data.frame(logz = colMeans(approx),
approx_sd = apply(approx, 2, sd),
avg_error = colMeans(truth - approx), # avg error
mae = colMeans(abs(truth - approx)), # mean absolute error
rmse = sqrt(colMeans((truth - approx)^2))) # root mean square error
model_name = paste("gw_", 'p_', p, '_D_', D, '_stack_', n_G5, sep = '')
results_obj = list(name = model_name,
p = p,
D = D,
truth = truth,
results = res_tbl,
nMCMC = J,
n = n,
delta = b,
all_approx = approx,
Omega_G = Omega_G)
save_loc = 'C:/Users/ericc/Documents/sim_results/'
paste(save_loc, model_name, ".rds", sep = '')
saveRDS(results_obj, file = paste(save_loc, model_name, ".rds", sep = ''))
echuu/hybridml documentation built on Dec. 20, 2021, 3:13 a.m.
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## 5/10:
## Split the calculation in to blocks, since each block of G_5 gives a very
## easy calculation for both the gradient and the hessian.
## This will require separate functions for both the gradient and the hessian
## that are specific to this problem. In addition, we have to modify
## globalMode() so that the correct params_G5 is passed into the grad and hess
## functions, as well as hybridml(), so that the correct params_G5 is passed
## into the grad and hess functions
source("examples/gwish/gwish_density.R")
library(BDgraph)
library(dplyr)
#### initialize graphs ---------------------------------------------------------
### create parameters for a single G_5 -----------------------------------------
p1 = 5
G_5 = matrix(c(1,1,0,1,1,
1,1,1,0,0,
0,1,1,1,1,
1,0,1,1,1,
1,0,1,1,1), p1, p1)
G_5 = matrix(1,5,5)
p1 = 10
n = 3
G_5 = matrix(c(0, 1, 0, 0, 0, 0, 0, 1, 0, 0,
1, 0, 1, 0, 0, 0, 1, 0, 0, 0,
0, 1, 0, 1, 0, 1, 0, 0, 0, 0,
0, 0, 1, 0, 1, 0, 0, 0, 0, 0,
0, 0, 0, 1, 0, 1, 0, 0, 0, 0,
0, 0, 1, 0, 1, 0, 1, 0, 0, 0,
0, 1, 0, 0, 0, 1, 0, 1, 0, 0,
1, 0, 0, 0, 0, 0, 1, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0), 10, 10)
diag(G_5) = 1
p1 = 6
G_5 = matrix(1,6,6)
G_5[6,] = 0
G_5[,6] = 0
G_5[6,6] = 1
gnorm(G_5, 3, 3*diag(6), 100)
b = 5
n = 3
V_5 = n * diag(1, p1)
P = chol(solve(V_5)) # upper cholesky factor; D^(-1) = TT' in Atay paper
FREE_PARAMS_ALL = c(upper.tri(diag(1, p1), diag = T) & G_5)
edgeInd = G_5[upper.tri(G_5, diag = TRUE)] %>% as.logical
## construct A matrix so that we can compute k_i
A = (upper.tri(diag(1, p1), diag = F) & G_5) + 0
k_i = colSums(A) # see step 2, p. 329 of Atay
nu_i = rowSums(A) # see step 2, p. 329 of Atay
b_i = nu_i + k_i + 1
b_i
# S = matrix(0, p, p)
D = sum(edgeInd) # number of free parameters / dimension of parameter space
index_mat = matrix(0, p1, p1)
index_mat[upper.tri(index_mat, diag = T)][edgeInd] = 1:D
index_mat[upper.tri(index_mat, diag = T)]
t_ind = which(index_mat!=0,arr.ind = T)
t_ind
index_mat[lower.tri(index_mat)] = NA
vbar = which(index_mat==0,arr.ind = T) # non-free elements
n_nonfree = nrow(vbar)
params_G5 = list(G = G_5, P = P, p = p1, D = D, edgeInd = edgeInd,
b = b, nu_i = nu_i, b_i = b_i,
t_ind = t_ind, n_nonfree = n_nonfree, vbar = vbar,
n_graphs = 1)
################################################################################
### create parameters for stacked G_5's so we can sample, and compute psi ------
n_G5 = 1 # number of G_5 graphs we want to stack
G = diag(1, n_G5) %x% G_5
p = ncol(G)
V = n * diag(1, p)
## try computing the normalizing constant of G_9 first as sanity check
FREE_PARAMS_ALL = c(upper.tri(diag(1, p), diag = T) & G)
edgeInd = G[upper.tri(G, diag = TRUE)] %>% as.logical
## construct A matrix so that we can compute k_i
A = (upper.tri(diag(1, p), diag = F) & G) + 0
k_i = colSums(A) # see step 2, p. 329 of Atay
nu_i = rowSums(A) # see step 2, p. 329 of Atay
b_i = nu_i + k_i + 1
b_i
set.seed(1)
Omega_G = rgwish(1, G, b, V) # generate the true precision matrix
P = chol(solve(V)) # upper cholesky factor; D^(-1) = TT' in Atay paper
# params = list(G = G, P = P, p = p, edgeInd = edgeInd,
# b = b, nu_i = nu_i, b_i = b_i)
# N = 0
S = matrix(0, p, p)
D = sum(edgeInd) # number of free parameters / dimension of parameter space
index_mat = matrix(0, p, p)
index_mat[upper.tri(index_mat, diag = T)][edgeInd] = 1:D
index_mat[upper.tri(index_mat, diag = T)]
t_ind = which(index_mat!=0,arr.ind = T)
# t_ind
index_mat[lower.tri(index_mat)] = NA
vbar = which(index_mat==0,arr.ind = T) # non-free elements
n_nonfree = nrow(vbar)
params = list(G = G, P = P, p = p, D = D, edgeInd = edgeInd,
b = b, nu_i = nu_i, b_i = b_i,
t_ind = t_ind, n_nonfree = n_nonfree, vbar = vbar)
J = 200
samps = samplegw(J, G, b, 0, V, S, solve(P), FREE_PARAMS_ALL)
u_samps = samps$Psi_free %>% data.frame
# u_df = preprocess(u_samps, D, params) # J x (D_u + 1)
u_df = gwish_preprocess(u_samps, D, params_G5) # J x (D_u + 1)
u_df %>% head
I_G = function(delta) {
7/2 * log(pi) + lgamma(delta + 5/2) - lgamma(delta + 3) +
lgamma(delta + 1) + lgamma(delta + 3/2) + 2 * lgamma(delta + 2) +
lgamma(delta + 5/2)
}
(Z_5 = log(2^(0.5*p1*b + 7)) + I_G(0.5*(b-2)) + (-0.5 * p1 * b - 7) * log(n))
Z = n_G5 * Z_5
Z
gnorm(G, b, V, J) # gnorm estimate of the entire (appended graph)
# ------------------------------------------------------------------------------
#### compute the hybrid approximation, bridge sampling estimator
## numerical versions of the grad and hess -- included here just as a comparison
## for smaller dimension to make sure the analytical gradient and hessian
## are computed correctly
# grad = function(u, params) { pracma::grad(psi, u, params = params) }
# hess = function(u, params) { pracma::hessian(psi, u, params = params) }
# u_star = hybridml::globalMode(u_df) ## slow version
# u_star_numer = u_star
grad = function(u, params) { fast_grad(u, params) }
hess = function(u, params) { fast_hess(u, params) }
u_star = gwish_globalMode(u_df, params, params_G5)
## laplace estimator
0.5*(D)*log(2*pi) -
0.5*log_det(hess(u_star, params_G5)$H) -
gwish_psi(c(u_star), params_G5)
# u_star
# u_star_closed = u_star
# cbind(u_star_numer, u_star_closed)
logzhat = hybml_gwish(u_df, params_G5, psi = psi, grad = grad, hess = hess, u_0 = u_star)$logz
logzhat = hybml_gwish(u_df, params_G5, psi = psi, grad = grad, hess = hess)$logz
logzhat # hybrid
Z # truth
J = 2000
samps = samplegw(J, G, b, 0, V, S, solve(P), FREE_PARAMS_ALL)
u_samps = samps$Psi_free %>% data.frame
u_df = gwish_preprocess(u_samps, D, params_G5) # J x (D_u + 1)
logzhat = hybml_gwish(u_df, params_G5, psi = gwish_psi, grad = grad, hess = hess, u_0 = u_star)$logz
logzhat # hybrid
abs(logzhat - Z)
## bridge calculation
log_density = function(u, data) {
-psi(u, data)
}
log_density = function(u, data) {
-gwish_psi(u, data)
}
u_samp = as.matrix(u_samps)
colnames(u_samp) = names(u_df)[1:D]
# prepare bridge_sampler input()
lb = rep(-Inf, D)
ub = rep(Inf, D)
names(lb) <- names(ub) <- colnames(u_samp)
bridge_result = bridgesampling::bridge_sampler(samples = u_samp,
log_posterior = log_density,
data = params_G5,
lb = lb, ub = ub,
method = 'normal',
silent = TRUE)
bridge_result = bridgesampling::bridge_sampler(samples = u_samp,
log_posterior = log_density,
data = params,
lb = lb, ub = ub,
method = 'normal',
silent = TRUE)
bridge_result$logml
abs(bridge_result$logml - Z)
gnorm(G, b, V, J) # gnorm estimate of the entire (appended graph)
abs(gnorm(G, b, V, J) - Z)
abs(bridge_result$logml - Z)
abs(logzhat - Z)
### run simulations
# initialize storage for each of the estimators
n_sims = 100
hyb = numeric(n_sims)
# hyb_old = numeric(n_sims)
gnorm_approx = numeric(n_sims)
bridge = numeric(n_sims)
bridge_warp = numeric(n_sims)
j = 1
J = 1000
set.seed(1)
while (j <= n_sims) {
samps = samplegw(J, G, b, N, V, S, solve(P), FREE_PARAMS_ALL)
u_samps = samps$Psi_free %>% data.frame
### hyb estimator ------------------------------------------------------------
u_df = gwish_preprocess(u_samps, D, params_G5) # J x (D_u + 1)
logzhat = hybml_gwish(u_df, params_G5, psi = psi, grad = grad, hess = hess,
u_0 = u_star)$logz
hyb[j] = logzhat # hybrid
### bridge estimator ---------------------------------------------------------
u_samp = as.matrix(u_samps)
colnames(u_samp) = names(u_df)[1:D]
lb = rep(-Inf, D)
ub = rep(Inf, D)
names(lb) <- names(ub) <- colnames(u_samp)
bridge_result = bridgesampling::bridge_sampler(samples = u_samp,
log_posterior = log_density,
data = params_G5,
lb = lb, ub = ub,
silent = TRUE)
bridge[j] = bridge_result$logml
bridge_result = bridgesampling::bridge_sampler(samples = u_samp,
log_posterior = log_density,
data = params_G5,
lb = lb, ub = ub,
method = 'warp3',
silent = TRUE)
bridge_warp[j] = bridge_result$logml
### gnorm estimator ----------------------------------------------------------
gnorm_approx[j] = gnorm(G, b, V, J)
### display some information about the running avg of the estimator + error
print(paste('iter ', j, ': ',
'hyb = ', round(mean(hyb[hyb!=0]), 3),
' (error = ', round(mean((Z - hyb[hyb!=0])), 3), '), ',
'bse = ', round(mean(bridge[bridge!=0]), 3),
' (error = ', round(mean((Z - bridge[bridge!=0])), 3), '), ',
'wbse = ', round(mean((bridge_warp[bridge_warp!=0])), 3),
' (error = ', round(mean(Z - bridge_warp[bridge_warp!=0]), 3), '), ',
sep = ''))
j = j + 1
}
mean(abs(Z - hyb[hyb != 0]))
mean(abs(Z - bridge[bridge != 0]))
mean(abs(Z - bridge_warp[bridge_warp != 0]))
mean(abs(Z - hyb[hyb != 0])^2)
mean(abs(Z - bridge[bridge != 0])^2)
mean(abs(Z - bridge_warp[bridge_warp != 0])^2)
truth = Z
approx = data.frame(truth, hyb = hyb, gnorm = gnorm_approx, bridge = bridge,
bridge_warp = bridge_warp)
approx_long = reshape2::melt(approx, id.vars = 'truth')
truth = Z
res_tbl =
data.frame(logz = colMeans(approx),
approx_sd = apply(approx, 2, sd),
avg_error = colMeans(truth - approx), # avg error
mae = colMeans(abs(truth - approx)), # mean absolute error
rmse = sqrt(colMeans((truth - approx)^2))) # root mean square error
model_name = paste("gw_", 'p_', p, '_D_', D, '_stack_', n_G5, sep = '')
results_obj = list(name = model_name,
p = p,
D = D,
truth = truth,
results = res_tbl,
nMCMC = J,
n = n,
delta = b,
all_approx = approx,
Omega_G = Omega_G)
save_loc = 'C:/Users/ericc/Documents/sim_results/'
paste(save_loc, model_name, ".rds", sep = '')
saveRDS(results_obj, file = paste(save_loc, model_name, ".rds", sep = ''))
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