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04_b_App_Sparse.R
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04_b_App_Sparse.R
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source('00_system.R')
load('Datasets/app_dataset.RData')
# First model
if(T){
list_formulas <- list("mean" = as.formula(" ~ 1 + wind + new_wind + BIO04 + BIO15 + cloud_c + elevation + lati + long"),
"std.dev" = as.formula(" ~ 1 + log_cloud + log_elevation + log_wind + log_lati + log_long"),
"scale" = as.formula(" ~ 1 + log_cloud + log_elevation + log_wind + log_lati + log_long"),
"aniso" = 0,
"tilt" = 0,
"smooth" = as.formula(" ~ 1 + log_cloud + log_elevation + log_wind + log_lati + log_long"),
"nugget" = -Inf)
test_coco <- coco(type = 'sparse',
data = all_dfs[[3]],
locs = as.matrix(all_dfs[[3]][, 1:2]),
z = all_dfs[[3]]$prec,
model.list = list_formulas,
info = list('lambda' = 0.0125 * sqrt(8),
'taper' = spam::cov.wend2,
'delta' = 0.23,
'smooth_limits' = c(0.5, 2.5))
)
# Tailored boundaries
if(T){
boundaries_A <- getBoundariesV2(coco.object = test_coco,
mean.limits = c(-2, 0, 2),
std.dev.limits = c(-2.5, 0, 2.5),
scale.limits = c(-2, 0, 2),
aniso.limits = c(-2, 0, 2),
tilt.limits = c(-2, 0, 2),
smooth.limits = c(-2, 0, 2),
nugget.limits = c(NA, NA, NA))
boundaries_A$theta_init[1] <- mean(test_coco@z)
boundaries_A$theta_upper[1] <- boundaries_A$theta_init[1] + 2
boundaries_A$theta_lower[1] <- boundaries_A$theta_init[1] - 2
first_var <- which(names(boundaries_A$theta_init) == "std.dev.limits")[1]
first_range <- which(names(boundaries_A$theta_init) == "scale.limits")[1]
first_smooth <- which(names(boundaries_A$theta_init) == "smooth.limits")[1]
boundaries_A$theta_upper[c(first_var, first_range)] <- c(2, 4)
boundaries_A$theta_lower[c(first_var, first_range)] <- c(-5.5, -7.5)
boundaries_A$theta_upper[first_smooth] <- 2
boundaries_A$theta_lower[first_smooth] <- -2.5
boundaries_A$theta_init[first_smooth] <- -2.5
}
time_T_A <- system.time({Model_T_A <- cocoOptim(coco.object = test_coco,
ncores = ncores,
boundaries = boundaries_A,
optim.type = 'mle')})
save(Model_T_A, time_T_A, file = 'RData/Model_T_A.RData')
}
# Classic model
if(T){
list_formulas <- list("mean" = as.formula(" ~ 1 + wind + new_wind + BIO04 + BIO15 + cloud_c +
elevation + lati + long"),
"std.dev" = as.formula("~ 1"),
"scale" = as.formula("~ 1"),
"aniso" = 0,
"tilt" = 0,
"smooth" = as.formula("~ 1"),
"nugget" = -Inf)
OT_classic <- coco(type = 'sparse',
data = all_dfs[[3]],
locs = as.matrix(all_dfs[[3]][, 1:2]),
z = all_dfs[[3]]$prec,
model.list = list_formulas,
info = list('lambda' = 0.0125 * sqrt(8),
'taper' = spam::cov.wend1,
'delta' = 0.23,
'smooth_limits' = c(0.25, 1.5))
)
# Tailored boundaries
if(T){
Boundaries_B <- getBoundariesV2(coco.object = OT_classic,
mean.limits = c(-2, 0, 2),
std.dev.limits = c(-2.5, 0, 2.5),
scale.limits = c(-2, 0, 2),
aniso.limits = c(-2, 0, 2),
tilt.limits = c(-2, 0, 2),
smooth.limits = c(-2, 0, 2),
nugget.limits = c(NA, NA, NA))
Boundaries_B$theta_init[1] <- mean(OT_classic@z)
Boundaries_B$theta_upper[1] <- Boundaries_B$theta_init[1] + 2
Boundaries_B$theta_lower[1] <- Boundaries_B$theta_init[1] - 2
first_var <- which(names(Boundaries_B$theta_init) == "std.dev.limits")[1]
first_range <- which(names(Boundaries_B$theta_init) == "scale.limits")[1]
first_smooth <- which(names(Boundaries_B$theta_init) == "smooth.limits")[1]
Boundaries_B$theta_upper[c(first_var, first_range)] <- c(2, 4)
Boundaries_B$theta_lower[c(first_var, first_range)] <- c(-4, -6)
Boundaries_B$theta_upper[first_smooth] <- 2
Boundaries_B$theta_lower[first_smooth] <- -2.5
Boundaries_B$theta_init[first_smooth] <- -2.5
}
Time_T_B <- system.time({ Model_T_B <- cocoOptim(coco.object = OT_classic,
ncores = 4,
optim.type = 'mle',
boundaries = Boundaries_B)})
save(Model_T_B, Time_T_B, file = 'RData/Model_T_B.RData')
}
# Global smoothness based on reduced model
if(T){
list_formulas <- list("mean" = as.formula(" ~ 1 + wind + new_wind + BIO04 + BIO15 + cloud_c + elevation + lati + long"),
"std.dev" = as.formula(" ~ 1 + log_cloud + log_elevation + log_wind + log_lati + log_long"),
"scale" = as.formula(" ~ 1 + log_cloud + log_elevation + log_wind + log_lati + log_long"),
"aniso" = 0,
"tilt" = 0,
"smooth" = as.formula(" ~ 1"),
"nugget" = -Inf)
test_coco <- coco(type = 'sparse',
data = all_dfs[[3]],
locs = as.matrix(all_dfs[[3]][, 1:2]),
z = all_dfs[[3]]$prec,
model.list = list_formulas,
info = list('lambda' = 0.0125 * sqrt(8),
'taper' = spam::cov.wend2,
'delta' = 0.23,
'smooth_limits' = c(0.5, 2.5))
)
# Boundaries
if(T){
boundaries_taper_C <- getBoundariesV2(coco.object = test_coco,
mean.limits = c(-2, 0, 2),
std.dev.limits = c(-2.5, 0, 2.5),
scale.limits = c(-2, 0, 2),
aniso.limits = c(-2, 0, 2),
tilt.limits = c(-2, 0, 2),
smooth.limits = c(-2, 0, 2),
nugget.limits = c(NA, NA, NA))
boundaries_taper_C$theta_init[1] <- mean(test_coco@z)
boundaries_taper_C$theta_upper[1] <- boundaries_taper_C$theta_init[1] + 2
boundaries_taper_C$theta_lower[1] <- boundaries_taper_C$theta_init[1] - 2
first_var <- which(names(boundaries_taper_C$theta_init) == "std.dev.limits")[1]
first_range <- which(names(boundaries_taper_C$theta_init) == "scale.limits")[1]
first_smooth <- which(names(boundaries_taper_C$theta_init) == "smooth.limits")[1]
boundaries_taper_C$theta_upper[c(first_var, first_range)] <- c(2, 4)
boundaries_taper_C$theta_lower[c(first_var, first_range)] <- c(-5.5, -7.5)
boundaries_taper_C$theta_upper[first_smooth] <- 2
boundaries_taper_C$theta_lower[first_smooth] <- -2.5
boundaries_taper_C$theta_init[first_smooth] <- -2.5
}
Time_T_C <- system.time({Model_T_C <- cocoOptim(coco.object = test_coco,
ncores = ncores,
boundaries = boundaries_taper_C,
optim.type = 'mle')})
save(Model_T_C, Time_T_C, file = 'RData/Model_T_C.RData')
}
# Predictions
if(T){
newdataset <- all_dfs[[1]]
newlocs <- all_dfs[[1]][,1:2]
z_values <- all_dfs[[1]]$prec
# Create holdouts
if(T){
set.seed(100621)
hetero_holdouts <- kmeans(as.data.frame(scale(newdataset[,c(1,2,4:9)])),centers = 100,iter.max = 100)
groups <- as.factor(hetero_holdouts$cluster)
quilt.plot(newlocs, hetero_holdouts$cluster, nx = 150, ny = 150)
}
Pred_Model_T_A <- cocoPredict(coco.object = Model_T_A,
newdataset = newdataset,
newlocs = newlocs,
type = 'pred')
Pred_Model_T_B <- cocoPredict(coco.object = Model_T_B,
newdataset = newdataset,
newlocs = newlocs,
type = 'pred')
Pred_Model_T_C <- cocoPredict(coco.object = Model_T_C,
newdataset = newdataset,
newlocs = newlocs,
type = 'pred')
CRPS_T_A <- getCRPS(z_values,mean.pred = Pred_Model_T_A$trend + Pred_Model_T_A$mean,sd.pred = Pred_Model_T_A$sd.pred)
CRPS_T_B <- getCRPS(z_values,mean.pred = Pred_Model_T_B$trend + Pred_Model_T_B$mean,sd.pred = Pred_Model_T_B$sd.pred)
CRPS_T_C <- getCRPS(z_values,mean.pred = Pred_Model_T_C$trend + Pred_Model_T_C$mean,sd.pred = Pred_Model_T_C$sd.pred)
Logscore_T_A <- getLogRank(z_values,mean.pred = Pred_Model_T_A$trend + Pred_Model_T_A$mean,sd.pred = Pred_Model_T_A$sd.pred)
Logscore_T_B <- getLogRank(z_values,mean.pred = Pred_Model_T_B$trend + Pred_Model_T_B$mean,sd.pred = Pred_Model_T_B$sd.pred)
Logscore_T_C <- getLogRank(z_values,mean.pred = Pred_Model_T_C$trend + Pred_Model_T_C$mean,sd.pred = Pred_Model_T_C$sd.pred)
z_std_A <- (Pred_Model_T_A$trend + Pred_Model_T_A$mean - z_values) / Pred_Model_T_A$sd.pred
z_std_B <- (Pred_Model_T_B$trend + Pred_Model_T_B$mean - z_values) / Pred_Model_T_B$sd.pred
z_std_C <- (Pred_Model_T_C$trend + Pred_Model_T_C$mean - z_values) / Pred_Model_T_C$sd.pred
save(CRPS_T_A, CRPS_T_B, CRPS_T_C,
Logscore_T_A, Logscore_T_B, Logscore_T_C,
z_std_A,z_std_B,z_std_C,
Pred_Model_T_A,Pred_Model_T_B, Pred_Model_T_C,
file = 'RData/Pred_Taper.RData')
}
# Metrics
load('RData/Pred_Taper.RData')
if(T){
# RMSPE
if(T){
RMSPE_T_A <- numeric(100)
for(ii in 1:100){
RMSPE_T_A[ii] <- sqrt(mean((Pred_Model_T_A$mean[groups == levels(groups)[ii]] +
Pred_Model_T_A$trend[groups == levels(groups)[ii]] -
z_values[groups == levels(groups)[ii]])^2))
}
RMSPE_T_B <- numeric(100)
for(ii in 1:100){
RMSPE_T_B[ii] <- sqrt(mean((Pred_Model_T_B$mean[groups == levels(groups)[ii]] +
Pred_Model_T_B$trend[groups == levels(groups)[ii]] -
z_values[groups == levels(groups)[ii]])^2))
}
RMSPE_T_C <- numeric(100)
for(ii in 1:100){
RMSPE_T_C[ii] <- sqrt(mean((Pred_Model_T_C$mean[groups == levels(groups)[ii]] +
Pred_Model_T_C$trend[groups == levels(groups)[ii]] -
z_values[groups == levels(groups)[ii]])^2))
}
matrix_to_show <- t(round(cbind(c(mean(RMSPE_T_B), mean(RMSPE_T_A), mean(RMSPE_T_C)),
c(sd(RMSPE_T_B), sd(RMSPE_T_A), sd(RMSPE_T_C))), 3))
rownames(matrix_to_show) <- c('mean', 'se')
colnames(matrix_to_show) <- c('M-STAT-T', 'T-NS-T', 'M-NS-T-G')
cat('RMSPE\n')
print(matrix_to_show)
cat('------\n')
}
# CRPS
if(T){
CRPS_A_holdout <- numeric(100)
for(ii in 1:100){
CRPS_A_holdout[ii] <- mean(CRPS_T_A[groups == levels(groups)[ii]])
}
CRPS_B_holdout <- numeric(100)
for(ii in 1:100){
CRPS_B_holdout[ii] <- mean(CRPS_T_B[groups == levels(groups)[ii]])
}
CRPS_C_holdout <- numeric(100)
for(ii in 1:100){
CRPS_C_holdout[ii] <- mean(CRPS_T_C[groups == levels(groups)[ii]])
}
matrix_to_show <- t(round(cbind(c(mean(CRPS_B_holdout),mean(CRPS_A_holdout),mean(CRPS_C_holdout)),
c(sd(CRPS_B_holdout),sd(CRPS_A_holdout),sd(CRPS_C_holdout))),3))
rownames(matrix_to_show) <- c('mean', 'se')
colnames(matrix_to_show) <- c('M-STAT-T', 'T-NS-T', 'M-NS-T-G')
cat('CRPS\n')
print(matrix_to_show)
cat('------\n')
}
# Q_0.9 CRPS
if(T){
Q_CRPS_A <- numeric(100)
for(ii in 1:100){
Q_CRPS_A[ii] <- quantile(CRPS_T_A[groups == levels(groups)[ii]],probs = 0.95)
}
Q_CRPS_B <- numeric(100)
for(ii in 1:100){
Q_CRPS_B[ii] <- quantile(CRPS_T_B[groups == levels(groups)[ii]],probs = 0.95)
}
Q_CRPS_C <- numeric(100)
for(ii in 1:100){
Q_CRPS_C[ii] <- quantile(CRPS_T_C[groups == levels(groups)[ii]],probs=0.95)
}
matrix_to_show <- t(round(cbind(c(mean(Q_CRPS_B), mean(Q_CRPS_A), mean(Q_CRPS_C)),
c(sd(Q_CRPS_B), sd(Q_CRPS_A), sd(Q_CRPS_C))), 3))
rownames(matrix_to_show) <- c('mean', 'se')
colnames(matrix_to_show) <- c('M-STAT-T', 'T-NS-T', 'M-NS-T-G')
cat('0.95 Quantile CRPS\n')
print(matrix_to_show)
cat('---------\n')
}
# D_n
if(T){
KS_A <- numeric(100)
for(ii in 1:100){
KS_A[ii] <- ks.test(z_std_A[groups == levels(groups)[ii]],y = pnorm)$statistic
}
KS_B <- numeric(100)
for(ii in 1:100){
KS_B[ii] <- ks.test(z_std_B[groups == levels(groups)[ii]],
y = pnorm)$statistic
}
KS_C <- numeric(100)
for(ii in 1:100){
KS_C[ii] <- ks.test(z_std_C[groups == levels(groups)[ii]],
y = pnorm)$statistic
}
matrix_to_show <- t(round(cbind(c(mean(KS_B), mean(KS_A), mean(KS_C)),
c(sd(KS_B), sd(KS_A), sd(KS_C))),3))
rownames(matrix_to_show) <- c('mean', 'se')
colnames(matrix_to_show) <- c('M-STAT-T', 'T-NS-T', 'M-NS-T-G')
cat('KS statistic \n')
print(matrix_to_show)
cat('--------\n')
}
# Coverage_prob
if(T){
Cov_prob_A <- numeric(100)
for(ii in 1:100){
upper_bound <- Pred_Model_T_A$trend[groups == levels(groups)[ii]] +
Pred_Model_T_A$mean[groups == levels(groups)[ii]] +
qnorm(1 - 0.025) * Pred_Model_T_A$sd.pred[groups == levels(groups)[ii]]
lower_bound <- Pred_Model_T_A$trend[groups == levels(groups)[ii]] +
Pred_Model_T_A$mean[groups == levels(groups)[ii]] -
qnorm(1 - 0.025) * Pred_Model_T_A$sd.pred[groups == levels(groups)[ii]]
Cov_prob_A[ii] <- 1 - length(which(z_values[groups == levels(groups)[ii]] < lower_bound |
z_values[groups == levels(groups)[ii]] > upper_bound )) /
length(z_values[groups == levels(groups)[ii]])
}
Cov_prob_B <- numeric(100)
for(ii in 1:100){
upper_bound <- Pred_Model_T_B$trend[groups == levels(groups)[ii]] +
Pred_Model_T_B$mean[groups == levels(groups)[ii]] +
qnorm(1 - 0.025) * Pred_Model_T_B$sd.pred[groups == levels(groups)[ii]]
lower_bound <- Pred_Model_T_B$trend[groups == levels(groups)[ii]] +
Pred_Model_T_B$mean[groups == levels(groups)[ii]] -
qnorm(1 - 0.025) * Pred_Model_T_B$sd.pred[groups == levels(groups)[ii]]
Cov_prob_B[ii] <- 1 - length(which(z_values[groups == levels(groups)[ii]] < lower_bound |
z_values[groups == levels(groups)[ii]] > upper_bound )) /
length(z_values[groups == levels(groups)[ii]])
}
Cov_prob_C <- numeric(100)
for(ii in 1:100){
upper_bound <- Pred_Model_T_C$trend[groups == levels(groups)[ii]] +
Pred_Model_T_C$mean[groups == levels(groups)[ii]] +
qnorm(1 - 0.025) * Pred_Model_T_C$sd.pred[groups == levels(groups)[ii]]
lower_bound <- Pred_Model_T_C$trend[groups == levels(groups)[ii]] +
Pred_Model_T_C$mean[groups == levels(groups)[ii]] -
qnorm(1 - 0.025) * Pred_Model_T_C$sd.pred[groups == levels(groups)[ii]]
Cov_prob_C[ii] <- 1 - length(which(z_values[groups == levels(groups)[ii]] < lower_bound |
z_values[groups == levels(groups)[ii]] > upper_bound )) /
length(z_values[groups == levels(groups)[ii]])
}
matrix_to_show <- t(round(cbind(c(mean(Cov_prob_B),mean(Cov_prob_A),mean(Cov_prob_C)),
c(sd(Cov_prob_B),sd(Cov_prob_A),sd(Cov_prob_C))),3))
rownames(matrix_to_show) <- c('mean', 'se')
colnames(matrix_to_show) <- c('M-STAT-T', 'T-NS-T', 'M-NS-T-G')
cat('coverage probability\n')
print(matrix_to_show)
cat('--------------\n')
}
# log-score
if(T){
LS_A <- numeric(100)
for(ii in 1:100){
LS_A[ii] <- mean(Logscore_T_A[groups == levels(groups)[ii]])
}
LS_B <- numeric(100)
for(ii in 1:100){
LS_B[ii] <- mean(Logscore_T_B[groups == levels(groups)[ii]])
}
LS_C <- numeric(100)
for(ii in 1:100){
LS_C[ii] <- mean(Logscore_T_C[groups == levels(groups)[ii]])
}
matrix_to_show <- t(round(cbind(c(mean(LS_B), mean(LS_A), mean(LS_C)),
c(sd(LS_B), sd(LS_A), sd(LS_C))), 3))
rownames(matrix_to_show) <- c('mean', 'se')
colnames(matrix_to_show) <- c('M-STAT-T', 'T-NS-T', 'M-NS-T-G')
cat('logscore\n')
print(matrix_to_show)
cat('--------\n')
}
# logliks
vector_to_show <- c(getLoglik(Model_T_B),getLoglik(Model_T_A),getLoglik(Model_T_C))
names(vector_to_show) <- c('M-STAT-T', 'T-NS-T', 'M-NS-T-G')
cat('Logliks\n')
print(vector_to_show)
cat('--------\n')
# times
vector_to_show <- round(c(Time_T_B[3]/60,time_T_A[3]/60,Time_T_C[3]/60),2)
names(vector_to_show) <- c('M-STAT-T', 'T-NS-T', 'M-NS-T-G')
cat('system times\n')
print(vector_to_show)
cat('--------\n')
}