From cd9f3825856e38d8c55641cc6caee8886213f9bb Mon Sep 17 00:00:00 2001 From: Deyu Ming Date: Fri, 13 Dec 2024 23:24:49 +0000 Subject: [PATCH] Doc and Vignettes updates 1. Doc updates. 2 Add a BO vignette. --- .Rbuildignore | 1 + R/serialization.R | 6 +- _pkgdown.yml | 39 +---- man/deserialize.Rd | 3 + man/serialize.Rd | 5 +- vignettes/bayes_opt.Rmd | 258 ++++++++++++++++++++++++++++++++ vignettes/dgpsi.Rmd | 2 +- vignettes/images/bo_design.png | Bin 0 -> 50061 bytes vignettes/images/bo_tracker.png | Bin 0 -> 28962 bytes vignettes/images/shubert.png | Bin 0 -> 71302 bytes vignettes/references.bib | 7 + 11 files changed, 285 insertions(+), 36 deletions(-) create mode 100644 vignettes/bayes_opt.Rmd create mode 100644 vignettes/images/bo_design.png create mode 100644 vignettes/images/bo_tracker.png create mode 100644 vignettes/images/shubert.png diff --git a/.Rbuildignore b/.Rbuildignore index 920b614..66d2d32 100644 --- a/.Rbuildignore +++ b/.Rbuildignore @@ -16,4 +16,5 @@ ^vignettes/linked_DGP.Rmd$ ^vignettes/seq_design.Rmd$ ^vignettes/seq_design_2.Rmd$ +^vignettes/bayes_opt.Rmd$ ^LICENSE\.md$ diff --git a/R/serialization.R b/R/serialization.R index 62a6aa0..4453f2c 100644 --- a/R/serialization.R +++ b/R/serialization.R @@ -14,8 +14,9 @@ #' #' @details See further examples and tutorials at <`r get_docs_url()`>. #' @note Since the constructed emulators are 'python' objects, they cannot be directly exported to other R processes for parallel -#' processing in multi-session workers. This function provides a way to convert the emulators into serialized objects, which can be -#' restored using [deserialize()] for multi-session processing. +#' processing in multi-session workers created through spawning. This function provides a solution by converting the emulators +#' into serialized objects, which can be restored using [deserialize()] for multi-session processing. Note that in forking, +#' serialization is generally not required. #' @examples #' \dontrun{ #' @@ -113,6 +114,7 @@ serialize <- function(object, light = TRUE) { #' @return The S3 class of a GP emulator, a DGP emulator, a linked (D)GP emulator, or a bundle of (D)GP emulators. #' #' @details See further examples and tutorials at <`r get_docs_url()`>. +#' @note See the *Note* section in [serialize()]. #' @examples #' \dontrun{ #' diff --git a/_pkgdown.yml b/_pkgdown.yml index 0665c42..0553907 100644 --- a/_pkgdown.yml +++ b/_pkgdown.yml @@ -23,47 +23,24 @@ development: mode: auto articles: -- title: DGP Emulation with the Heteroskedastic Gaussian Likelihood - desc: DGP modeling of the motorcycle accident data. - navbar: ~ - contents: - - motorcycle - - title: A Quick Guide to dgpsi - desc: A quick guide to dgpsi by emulating a step function. + desc: A quick introduction to dgpsi by emulating a step function. navbar: ~ contents: - dgpsi -- title: Linked (D)GP Emulation - desc: Linked (D)GP emulation of a synthetic system of three linked computer models. +- title: A Deep Dive to dgpsi + desc: > + These articles provide an in-depth exploration of dgpsi and its diverse capabilities. navbar: ~ contents: + - large_scale_emulation - linked_DGP - -- title: Sequential Design I - desc: Sequential design and dynamic pruning for the DGP emulator of a non-stationary simulator. - navbar: ~ - contents: + - motorcycle + - classification - seq_design - -- title: Sequential Design II - desc: Sequential design for a bundle of DGP emulators with a stopping rule. - navbar: ~ - contents: - seq_design_2 - -- title: Large-scale Emulation with the Vecchia Approximation - desc: Large-scale DGP emulation using a Vecchia implementation under the SI. - navbar: ~ - contents: - - large_scale_emulation - -- title: DGP Classification using dgpsi - desc: DGP classification of the iris data set. - navbar: ~ - contents: - - classification + - bayes_opt reference: - title: "Initalization" diff --git a/man/deserialize.Rd b/man/deserialize.Rd index 556c8ea..03b7c35 100644 --- a/man/deserialize.Rd +++ b/man/deserialize.Rd @@ -20,6 +20,9 @@ This function restores the serialized emulator created by \code{\link[=serialize \details{ See further examples and tutorials at \url{https://mingdeyu.github.io/dgpsi-R/dev/}. } +\note{ +See the \emph{Note} section in \code{\link[=serialize]{serialize()}}. +} \examples{ \dontrun{ diff --git a/man/serialize.Rd b/man/serialize.Rd index bf6d4d9..b73d4f0 100644 --- a/man/serialize.Rd +++ b/man/serialize.Rd @@ -25,8 +25,9 @@ See further examples and tutorials at \url{https://mingdeyu.github.io/dgpsi-R/de } \note{ Since the constructed emulators are 'python' objects, they cannot be directly exported to other R processes for parallel -processing in multi-session workers. This function provides a way to convert the emulators into serialized objects, which can be -restored using \code{\link[=deserialize]{deserialize()}} for multi-session processing. +processing in multi-session workers created through spawning. This function provides a solution by converting the emulators +into serialized objects, which can be restored using \code{\link[=deserialize]{deserialize()}} for multi-session processing. Note that in forking, +serialization is generally not required. } \examples{ \dontrun{ diff --git a/vignettes/bayes_opt.Rmd b/vignettes/bayes_opt.Rmd new file mode 100644 index 0000000..32daf6a --- /dev/null +++ b/vignettes/bayes_opt.Rmd @@ -0,0 +1,258 @@ +--- +title: "Customized Sequential Design for Bayesian Optimization" +output: rmarkdown::html_vignette +bibliography: references.bib +description: > + Customized sequential design to implement Bayesian optimization for the Shubert function. +vignette: > + %\VignetteIndexEntry{Customized Sequential Design for Bayesian Optimization} + %\VignetteEngine{knitr::rmarkdown} + %\VignetteEncoding{UTF-8} +--- + +```{r setup, include = FALSE} +knitr::opts_chunk$set( + echo = TRUE, + eval = FALSE +) +``` + +This vignette demonstrates how to utilize and repurpose my favorite `design()` function in `dgpsi` to implement Bayesian optimization using the (D)GP surrogate models provided by the package. + +## Load the packages + +```{r} +library(tidyverse) +library(lhs) +library(patchwork) +library(ggplot2) +library(dgpsi) +``` + +## Define the target function + +We consider a version of the Shubert function [@surjanovic] defined over the domain $[0,1]^2$ as follows: + +```{r} +shubert <- function(x) +{ + N <- nrow(x) + x1 <- x[,1] * 4 - 2 + x2 <- x[,2] * 4 - 2 + ii <- c(1:5) + + y <- sapply(1:N, function(i) { + sum(ii * cos((ii+1)*x1[i]+ii)) * sum(ii * cos((ii+1)*x2[i]+ii)) + }) + + y <- matrix(y, ncol = 1) + return(y) +} +``` + +To pass the Shubert function to `design()`, we defined it such that both its input `x` and output are matrices. Next, we generate the contour of the Shubert function: + +```{r} +x1 <- seq(0, 1, length.out = 200) +x2 <- seq(0, 1, length.out = 200) +dat <- expand_grid(x1 = x1, x2 = x2) +dat <- mutate(dat, f = shubert(cbind(x1, x2))) +ggplot(dat, aes(x1, x2, fill = f)) + geom_tile() + + scale_fill_continuous(type = "viridis") +``` + +![](https://raw.githubusercontent.com/mingdeyu/dgpsi-R/master/vignettes/images/shubert.png){width=100%} + +From the figure above, we can observe that the Shubert function has several local minima and two global minima located at $(0.1437, 0.2999)$ and $(0.2999, 0.1437)$, both with values around $-186.7309$. In the remainder of this vignette, we will use Expected Improvement (EI) as the acquisition function to identify the global minima. + +## Initial emulator construction + +To ensure the reproducibility of this vignette, we set a seed using the `set_seed()` function from the package: + +```{r} +set_seed(99) +``` + +Next, we generate an initial design of 20 points using the maximin Latin hypercube sampler: + +```{r} +X <- maximinLHS(20, 2) +Y <- shubert(X) +``` + +to construct the initial DGP surrogate model of the Shubert function: + +```{r} +m <- dgp(X, Y, name = 'matern2.5') +``` + +``` +## Auto-generating a 2-layered DGP structure ... done +## Initializing the DGP emulator ... done +## Training the DGP emulator: +## Iteration 500: Layer 2: 100%|██████████| 500/500 [00:02<00:00, 249.19it/s] +## Imputing ... done +``` + +## Bayesian optimization using Expected Improvement (EI) + +To begin Bayesian optimization with `design()`, we first need to define the Expected Improvement (EI) acquisition function, adhering to the rules specified for the `method` argument in `design()`: + +```{r} +ei <- function(object, limits, n_starts = 10, ...) { + # Expected Improvement (EI) function + ei_function <- function(x) { + x <- matrix(x, nrow = 1) + # Extract mean and variance from the 'object' + pred <- predict(object, x, ...)$results + mu <- pred$mean + sigma <- sqrt(pred$var) + + # Handle numerical precision issues with very small sigma values + sigma[sigma < 1e-10] <- 1e-10 + + # Best observed minimum value + best_value <- min(object$data$Y) + + # Calculate improvement + improvement <- best_value - mu + + # Calculate Expected Improvement (EI) + z <- improvement / sigma + ei <- improvement * pnorm(z) + sigma * dnorm(z) + ei <- ifelse(ei < 0, 0, ei) # Ensure non-negative EI + + return(-ei) # Return negative EI because `optim()` minimizes by default + } + + # Number of input dimensions + num_dims <- nrow(limits) + + # Generate initial points using Latin Hypercube Sampling (LHS) + lhd_samples <- maximinLHS(n_starts, num_dims) + lhd_points <- sapply(1:num_dims, function(i) { + limits[i, 1] + lhd_samples[, i] * (limits[i, 2] - limits[i, 1]) + }) + + # Perform optimization with multiple starts using `optim()` + results <- lapply(1:n_starts, function(i) { + optim( + par = lhd_points[i, ], + fn = ei_function, + method = "L-BFGS-B", + lower = limits[, 1], + upper = limits[, 2] + ) + }) + + # Find the result with the minimum (most negative) EI + best_result <- results[[which.min(sapply(results, `[[`, "value"))]] + + # Return the next best point `x` as a single-row matrix + return(matrix(best_result$par, nrow = 1)) +} + +``` + +The `ei` function defined above takes the emulator as its first argument, `object`, along with the additional arguments: `limits`, a two-column matrix where the first column specifies the lower bounds and the second column specifies the upper bounds of the input dimensions, and `n_starts`, which defines the number of multi-start points used to search for the location corresponding to the minimum (most negative) EI. You can, of course, replace `ei` with your own acquisition function, provided it adheres to the rules of the `method` argument in `design()` (see `?design` for details). + +To track the identified minimum value of the Shubert function during Bayesian optimization, we define a monitor function, `opt_monitor`, to be passed to the `eval` argument of `design()`: + +```{r} +opt_monitor <- function(object) { + return(min(object$data$Y)) +} +``` + +The domain of the input parameters for our Bayesian optimization, within which the global minima are searched, is defined as $[0,1]^2$: + +```{r} +lim <- rbind(c(0, 1), c(0, 1)) +``` + +With all the ingredients ready, we can now run the Bayesian optimization using `design()` with 80 iterations: + +```{r} +m <- design(m, N = 80, limits = lim, f = shubert, method = ei, eval = opt_monitor) +``` + +``` +## Initializing ... done +## * Metric: -125.203479 +## Iteration 1: +## - Locating ... done +## * Next design point: 0.352375 0.142570 +## - Updating and re-fitting ... done +## - Validating ... done +## * Metric: -125.203479 +## +## ... +## +## Iteration 6: +## - Locating ... done +## * Next design point: 0.299331 0.125606 +## - Updating and re-fitting ... done +## - Transiting to a GP emulator ... done +## - Validating ... done +## * Metric: -186.039545 +## +## ... +## +## Iteration 80: +## - Locating ... done +## * Next design point: 0.907645 0.000000 +## - Updating and re-fitting ... done +## - Validating ... done +## * Metric: -186.728582 +``` + +During the Bayesian optimization, our dynamic pruning mechanism transitioned the DGP emulator to a GP emulator at iteration 6, leading to faster optimizations in the remaining iterations while maintaining the emulator's quality. After 80 iterations, we identified a minimum of the Shubert function with a value of $-186.7286$, which is very close to the global minimum of $-186.7309$. We can inspect the progress of the minima search conducted by `design()` by applying `draw()` to `m`: + +```{r} +draw(m) + + plot_annotation(title = 'Bayesian Optimization Tracker') + + labs(y = "Minimum Value") + + # Add a horizontal line to represent the global minimum for benchmarking + geom_hline( + aes(yintercept = y, linetype = "Global Minimum"), # Global minimum + data = data.frame(y = -186.7309), + color = "#E31A1C", + size = 0.5 + ) + + scale_linetype_manual( + values = c("Global Minimum" = "dashed"), + name = "" # Remove the legend title + ) +``` + +![](https://raw.githubusercontent.com/mingdeyu/dgpsi-R/master/vignettes/images/bo_tracker.png){width=100%} + +The figure above shows that Bayesian optimization using our (D)GP emulator quickly identifies a low value of the Shubert function within 5 iterations. Notably, the lowest value, $-186.7286$, was achieved by `design()` after 48 iterations. + +We can also inspect the locations identified during the process by applying `draw()` to `m` with `type = 'design'`: + +```{r} +draw(m, type = 'design') + + plot_annotation(title = 'Bayesian Optimization Design') + + # Highlight the global minima on the design plot + geom_point( + data = data.frame( + .panel_x = c("X1", "X2"), # x labels of panels + .panel_y = c("X2", "X1"), # y labels of panels + X1 = c(0.1437, 0.2999), # X1 values for the global minima + X2 = c(0.2999, 0.1437) # X2 values for the global minima + ), + aes(x = .panel_x, y = .panel_y), + size = 1.25, + shape = 6, + color = "#E31A1C" + ) +``` + +![](https://raw.githubusercontent.com/mingdeyu/dgpsi-R/master/vignettes/images/bo_design.png){width=100%} + +The figure above illustrates that Bayesian optimization successfully identifies the regions around the two global minima, represented as red inverted triangles, by adding design points concentrated near these two locations. + +### References + + diff --git a/vignettes/dgpsi.Rmd b/vignettes/dgpsi.Rmd index f55b6b5..d7efd15 100644 --- a/vignettes/dgpsi.Rmd +++ b/vignettes/dgpsi.Rmd @@ -30,7 +30,7 @@ get_article_url <- function(article) { } ``` -The `dgpsi` package offers a flexible toolbox for Gaussian process (GP), deep Gaussian process (DGP), and linked (D)GP emulation. In this guide, we show how to use the package to emulate a step function using a three-layered DGP structure. Additional examples showcasing the package's functionality are available in the [Articles](`r get_article_url("/articles/index.html")`) section of the package website. Topics include [linked DGPs](`r get_article_url("/articles/linked_DGP.html")`), [scalable DGPs](`r get_article_url("/articles/large_scale_emulation.html")`), [DGPs for classification](`r get_article_url("/articles/classification.html")`), [non-Gaussian problems](`r get_article_url("/articles/motorcycle.html")`), and [sequential design and active learning for DGPs](`r get_article_url("/articles/seq_design.html")`). A detailed reference for all available functions is provided in the [Reference](`r get_article_url("/reference/index.html")`) section of the package website. +The `dgpsi` package offers a flexible toolbox for Gaussian process (GP), deep Gaussian process (DGP), and linked (D)GP emulation. In this guide, we show how to use the package to emulate a step function using a three-layered DGP structure. Additional examples showcasing the package's functionality are available in the [Articles](`r get_article_url("/articles/index.html")`) section of the package website. Topics include [linked DGPs](`r get_article_url("/articles/linked_DGP.html")`), [scalable DGPs](`r get_article_url("/articles/large_scale_emulation.html")`), [DGPs for classification](`r get_article_url("/articles/classification.html")`), [non-Gaussian problems](`r get_article_url("/articles/motorcycle.html")`), [sequential design and active learning for (D)GPs](`r get_article_url("/articles/seq_design.html")`), and [Bayesian optimization with (D)GPs](`r get_article_url("/articles/bayes_opt.html")`). A detailed reference for all available functions is provided in the [Reference](`r get_article_url("/reference/index.html")`) section of the package website. ## Load the package diff --git a/vignettes/images/bo_design.png b/vignettes/images/bo_design.png new file mode 100644 index 0000000000000000000000000000000000000000..68533a6abb229b12790758bba0e75b3cc976b914 GIT binary patch literal 50061 zcmb5V2Q=K#*C?v@mI$IpNDwW8NYo&R9t6=w5GC3~AHDa8Ac!7BFB82DW(a~HdKt!y z8g+g;(eB9q`|kVJUF*K}-Ws!JX8+DU`|NUdJ4eh*ZB=Rt779E(JZiNU&-L)|h#`1* zgqCE4IEcd>w-fGz$WB2^0S~V_f%4pv8220BT~AdJuWE>G9XAs1rRFQ;&CSj2?d{#& z-GhUJ!^6Xii;Lsqc@YsLQKgq_*hSl^HmJNfzf zPNlmJ#XHQ*%m@VH*RNlqqN4BKy{oRS$;ruiSG4oKV$Y>~Z{^P>SLEiO_06Y=SjQ6V z!otGZ+S(EqTSD`8S65d`N{Wq*jjO9`OG^t1h5FjLH90xyQnLMfZgXjAi6?reva&Kb zI2gIOIWRC#TwH8qWaQ-J6j8U`*Vi{XGFn$xH;vwe{oYz!-7MYLu0o12Sm*p7^h zw6d~FPfzdZ>3R9`rB}sv*Tj~#wsyex?Qh?{p;op{O-;v9TQM;)tdTo51zYarJ7HmA z6B83YRomX)-etX8pIf&R6BB>`{yjZCt(!ClgTZQlZTb58($LUk!M8)Ix5>%LJ32au 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year={1935} } + +@misc{surjanovic, + author = {Surjanovic, Simon and Bingham, Derek}, + title = {Virtual Library of Simulation Experiments: Test Functions and Datasets}, + howpublished = {\url{https://www.sfu.ca/~ssurjano/index.html}}, + note = {Accessed: 13 December, 2024} +}