# tests/b-spline-lidar.R In weiyaw/blackbox: A SMC-SA Algorithm for Constrained Optimisation

```## Proposal distribution and number of iterations depend on the cooling schedule and problem at hand.

######## fit a constrained model. ########
## Visualise the dataset
rm(list = ls())
## K: number of inner knots
get_bs_design <- function(x, K, deg, EPS = 1e-6) {
dist <- diff(range(x)) / (K + 1)
knots <- seq(min(x) - (deg * dist) - EPS, max(x) + (deg * dist) + EPS,
len = K + 2 * (deg + 1))
res <- list()
res\$design <- splines::splineDesign(knots, x, ord = deg + 1)
res\$knots <- knots
return(res)
}

if (NROW(y) != NROW(design_mat)) {
stop("Number of rows for y and design matrix mismatch.")
}
function(beta) {
beta <- as.matrix(beta)
colSums((y - design_mat %*% beta)^2)
}
}

#### LIDAR, monotonic decreasing quadratic spline ####
is_beta_decreasing <- function(betas) {
res <- rep(NA, NCOL(betas))
for (i in seq_along(res)) {
res[i] <- all(diff(betas[, i]) <= 0)
}
res
}

rtrw_hmc_97 <- function(states, k) {
if (k == 0) { sd <- 100 } else { sd <- 1 }
fraction <- 0.97
sigma <- (sd * fraction^k)^2 * diag(NROW(states))
F <- diag(NROW(states))
F[row(F) + 1 == col(F)] <- -1
F <- F[1:(NROW(states) - 1), ]
lower <- rep(0, len = NROW(F))
initial <- seq(NROW(states), 1)

res <- matrix(NA, NROW(states), NCOL(states))
for (i in 1:NCOL(states)) {
res[, i] <- tnorm::rmvtnorm(1, states[, i], cov = sigma, g = lower, F = F,
initial = initial, burn = 10)
}
res
}

rtrw_hmc_998 <- function(states, k) {
if (k == 0) { sd <- 100 } else { sd <- 1 }
fraction <- 0.97
sigma <- (sd * fraction^k)^2 * diag(NROW(states))
F <- diag(NROW(states))
F[row(F) + 1 == col(F)] <- -1
F <- F[1:(NROW(states) - 1), ]
lower <- rep(0, len = NROW(F))
initial <- seq(NROW(states), 1)

res <- matrix(NA, NROW(states), NCOL(states))
for (i in 1:NCOL(states)) {
res[, i] <- tnorm::rmvtnorm(1, states[, i], cov = sigma, g = lower, F = F,
initial = initial, burn = 10)
}
res
}

scaled_lidar <- as.data.frame(scale(lidar, FALSE, apply(abs(lidar), 2, max)))
plot(y ~ range, data = scaled_lidar, main = "Light Detection and Ranging (LIDAR)",
cex = 1.3, cex.lab = 1.3, cex.axis = 1.3)

## Construct loss functions
Bmat <- get_bs_design(scaled_lidar\$range, 4, 2)\$design

## generate an arbitrary starting value
rand_eta <- NCOL(Bmat):1

library(doParallel)
registerDoParallel(cores = 8)

recip_time <- system.time(recip_lidar <- foreach(i = 1:40) %dopar% {
## Randomly generate 1000 starting values arounf rar_hyper
set.seed(500 + i)
starting <- get_feasibles(rand_eta, is_beta_decreasing, 1000, dist_para = list(scale = 2))

## SMCSA, reciprocal, fraction = 0.97, sd = 1, 500 iter, N = 3000, 2 comp
## Use a more aggresive proposal
rtnorm_rw <- rtnorm_rw_comp_fac(is_beta_decreasing, sd = 1, fraction = 0.97, n_pertub = 2)
runtime <- system.time(bs1 <- SMCSA(loss, rtnorm_rw, starting, recip_schedule, 3000, 1000, FALSE, TRUE))
bs1\$runtime <- runtime
bs1
})
cat("RECIP DONE.", recip_time[3], "\n")
# plot(y ~ range, data = scaled_lidar, main = "Light Detection and Ranging (LIDAR)",
#      cex = 1.3, cex.lab = 1.3, cex.axis = 1.3)
# lines((Bmat %*% bs1\$state) ~ scaled_lidar\$range, col = 'red')
saveRDS(recip_lidar, "~/Dropbox/honours/extras/lidar/recip_lidar.rds")

recip85_time <- system.time(recip85_lidar <- foreach(i = 1:40) %dopar% {
## Randomly generate 1000 starting values arounf rar_hyper
set.seed(500 + i)
starting <- get_feasibles(rand_eta, is_beta_decreasing, 1000, dist_para = list(scale = 2))

## SMCSA, reciprocal, fraction = 0.97, sd = 1, 500 iter, N = 3000, 2 comp
## Use a more aggresive proposal
rtnorm_rw <- rtnorm_rw_comp_fac(is_beta_decreasing, sd = 1, fraction = 0.97, n_pertub = 2)
runtime <- system.time(bs1 <- SMCSA(loss, rtnorm_rw, starting, recip_schedule_0.85, 3000, 1000, FALSE, TRUE))
bs1\$runtime <- runtime
bs1
})
cat("RECIP DONE.", recip85_time[3], "\n")
# plot(y ~ range, data = scaled_lidar, main = "Light Detection and Ranging (LIDAR)",
#      cex = 1.3, cex.lab = 1.3, cex.axis = 1.3)
# lines((Bmat %*% bs1\$state) ~ scaled_lidar\$range, col = 'red')
saveRDS(recip85_lidar, "~/Dropbox/honours/extras/lidar/recip85_lidar.rds")

log_time <- system.time(log_lidar <- foreach(i = 1:40) %dopar% {
## Randomly generate 1000 starting values arounf rar_hyper
set.seed(500 + i)
starting <- get_feasibles(rand_eta, is_beta_decreasing, 1000, dist_para = list(scale = 2))

## SMCSA, log, fraction = 0.998, sd = 1, 3000 iter, N = 1000, 2 comp
rtnorm_rw <- rtnorm_rw_comp_fac(is_beta_decreasing, sd = 1, fraction = 0.998, n_pertub = 2)
runtime <- system.time(bs2 <- SMCSA(loss, rtnorm_rw, starting, log_schedule, 1000, 3000, FALSE, TRUE))
bs2\$runtime <- runtime
bs2
})
cat("LOG DONE.", log_time[3], "\n")
# plot(y ~ range, data = scaled_lidar, main = "Light Detection and Ranging (LIDAR)",
#      cex = 1.3, cex.lab = 1.3, cex.axis = 1.3)
# lines((Bmat %*% bs1\$state) ~ scaled_lidar\$range, col = 'red')
saveRDS(log_lidar, "~/Dropbox/honours/extras/lidar/log_lidar.rds")
## plot_rat(bs2\$state[1:3], c(1, bs2\$state[4:5]), col = 'blue')

lidar_pilot <- solve(crossprod(Bmat)) %*% crossprod(Bmat, scaled_lidar\$y)

cepso_time <- system.time(cepso_lidar <- foreach(i = 1:40) %dopar% {
## Randomly generate 1000 starting values arounf rar_hyper
set.seed(500 + i)
starting <- get_feasibles(rand_eta, is_beta_decreasing, 1000, dist_para = list(scale = 2))

## CEPSO, 2000 iter, N = 3000, neighbour = 3000/5
## OLS as pilot estimate
runtime <- system.time(bs3 <- CEPSO(starting, loss, lidar_pilot, is_beta_decreasing, iter = 2000, N = 3000, verbose = TRUE))
bs3\$runtime <- runtime
bs3
})
cat("CEPSO DONE.", cepso_time[3], "\n")
## plot(y ~ range, data = scaled_lidar, main = "Light Detection and Ranging (LIDAR)",
##      cex = 1.3, cex.lab = 1.3, cex.axis = 1.3)
## lines((Bmat %*% lidar_pilot) ~ scaled_lidar\$range, col = 'blue')
saveRDS(cepso_lidar, "~/Dropbox/honours/extras/lidar/cepso_lidar.rds")
```
weiyaw/blackbox documentation built on June 7, 2019, 5:12 a.m.