From 9b906976a533e84fc8d7f6807772d0655f854c99 Mon Sep 17 00:00:00 2001 From: Aki Vehtari Date: Mon, 12 Oct 2026 16:23:09 +0300 Subject: [PATCH 1/2] Fix the inverse affine transformation in loo_moment_match_split() --- R/split_moment_matching.R | 7 +- tests/testthat/_snaps/loo_moment_matching.md | 2380 +++++++++--------- tests/testthat/test_loo_moment_matching.R | 41 + 3 files changed, 1236 insertions(+), 1192 deletions(-) diff --git a/R/split_moment_matching.R b/R/split_moment_matching.R index 8ae5c91f..383aeb05 100644 --- a/R/split_moment_matching.R +++ b/R/split_moment_matching.R @@ -56,12 +56,15 @@ loo_moment_match_split <- function(x, upars, cov, total_shift, total_scaling, attributes(upars_trans) <- attributes(upars) # inverse accumulated affine transformation - upars_trans_inv <- sweep(upars, 2, mean_original, "-") + # T(theta) = M diag(s) (theta - m) + m + shift, so + # T^-1(z) = diag(s)^-1 M^-1 (z - m - shift) + m: + # remove the shift first, then undo the mapping and the scaling. + upars_trans_inv <- sweep(upars, 2, mean_original + total_shift, "-") if (cov) { upars_trans_inv <- tcrossprod(upars_trans_inv, solve(total_mapping)) } upars_trans_inv <- sweep(upars_trans_inv, 2, total_scaling, "/") - upars_trans_inv <- sweep(upars_trans_inv, 2, mean_original - total_shift, "+") + upars_trans_inv <- sweep(upars_trans_inv, 2, mean_original, "+") attributes(upars_trans_inv) <- attributes(upars) # first half of upars_trans_half are T(theta) diff --git a/tests/testthat/_snaps/loo_moment_matching.md b/tests/testthat/_snaps/loo_moment_matching.md index 1a1d41dc..1a7be2f3 100644 --- a/tests/testthat/_snaps/loo_moment_matching.md +++ b/tests/testthat/_snaps/loo_moment_matching.md @@ -256,1192 +256,1192 @@ # loo_moment_match_split works - WAoAAAACAAQFAAACAwAAAAITAAAABAAAAA4AAA+gwCSZfNDtrTLAJQg4rmPuN8AlzHES4hut - wCIGBetDhYLAI0awRsFdk8AjINcUGsscwCXMUMW16IzAI/L2nOOyq8AqdhFsysKGwCYWOgEw - BijAI3cQGt4njsAgq4sZEnDQwChE2LymruHAJNOCW9qoWMAmI8sb5ckXwCGzOpKcK2zAJv7I - 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index 58325a29..b7791dbb 100644 --- a/tests/testthat/test_loo_moment_matching.R +++ b/tests/testthat/test_loo_moment_matching.R @@ -541,6 +541,47 @@ test_that("loo_moment_match_split works", { expect_false(anyNA(split3$lwi)) }) +test_that("loo_moment_match_split evaluates the inverse of its transformation", { + # The second half of the draws is untransformed. For these draws theta, + # the mixture proposal needs the density at T^-1(theta), where + # T(theta) = M diag(s) (theta - m) + m + shift. + shift <- c(-0.1, -0.2) + scaling <- c(0.7, 1.3) + m <- colMeans(upars) + second <- seq_len(S)[-seq_len(as.integer(0.5 * S))] + for (cov in c(FALSE, TRUE)) { + mapping <- if (cov) matrix(c(1, 0.1, 0.1, 1), 2, 2) else diag(2) + seen <- list() + log_prob_record <- function(x, upars, ...) { + seen[[length(seen) + 1]] <<- upars + log_prob_upars_test(x, upars, ...) + } + loo_moment_match_split( + x, + upars, + cov = cov, + total_shift = shift, + total_scaling = scaling, + total_mapping = mapping, + i = 1, + log_prob_upars = log_prob_record, + log_lik_i_upars = log_lik_i_upars_test, + cores = 1, + r_eff_i = 1, + is_method = "psis" + ) + # the second call evaluates the inverse-transformed draws + inv <- seen[[2]][second, , drop = FALSE] + fwd <- sweep(inv, 2, m, "-") + fwd <- sweep(fwd, 2, scaling, "*") + if (cov) { + fwd <- tcrossprod(fwd, mapping) + } + fwd <- sweep(fwd, 2, shift + m, "+") + expect_equal(unname(fwd), unname(upars[second, , drop = FALSE])) + } +}) + test_that("shift_and_scale is stable for large parameter values", { upars <- matrix(1e8 + c(-1, 0, 1), ncol = 1) result <- shift_and_scale(NULL, upars, rep(-log(3), 3)) From c2d4f4352ae67f8fdde46e6f14297baae5888fc5 Mon Sep 17 00:00:00 2001 From: Aki Vehtari Date: Mon, 12 Oct 2026 22:14:25 +0300 Subject: [PATCH 2/2] Compose moment matching steps in acceptance order; Jacobian uses the mapping only with cov; r_eff from both halves; tests --- R/loo_moment_matching.R | 51 +- R/split_moment_matching.R | 25 +- man/loo_moment_match_split.Rd | 11 +- tests/testthat/_snaps/loo_moment_matching.md | 2966 +++++++++--------- tests/testthat/test_loo_moment_matching.R | 64 +- 5 files changed, 1612 insertions(+), 1505 deletions(-) diff --git a/R/loo_moment_matching.R b/R/loo_moment_matching.R index 2d14e20b..91d17ee2 100644 --- a/R/loo_moment_matching.R +++ b/R/loo_moment_matching.R @@ -268,9 +268,11 @@ loo_moment_match_i <- function(i, lwfi <- rep(-matrixStats::logSumExp(rep(0, S)),S) # initialize objects that keep track of the total transformation - total_shift <- rep(0, npars) - total_scaling <- rep(1, npars) - total_mapping <- diag(npars) + total <- list( + shift = rep(0, npars), + scaling = rep(1, npars), + mapping = diag(npars) + ) # try several transformations one by one # if one does not work, do not apply it and try another one @@ -302,7 +304,7 @@ loo_moment_match_i <- function(i, } if (quantities_i$ki < ki) { uparsi <- trans$upars - total_shift <- total_shift + trans$shift + total <- add_step_to_total(total, trans, cov) lwi <- quantities_i$lwi lwfi <- quantities_i$lwfi @@ -332,8 +334,7 @@ loo_moment_match_i <- function(i, } if (quantities_i$ki < ki) { uparsi <- trans$upars - total_shift <- total_shift + trans$shift - total_scaling <- total_scaling * trans$scaling + total <- add_step_to_total(total, trans, cov) lwi <- quantities_i$lwi lwfi <- quantities_i$lwfi @@ -365,8 +366,7 @@ loo_moment_match_i <- function(i, } if (quantities_i$ki < ki) { uparsi <- trans$upars - total_shift <- total_shift + trans$shift - total_mapping <- trans$mapping %*% total_mapping + total <- add_step_to_total(total, trans, cov) lwi <- quantities_i$lwi lwfi <- quantities_i$lwfi @@ -389,7 +389,7 @@ loo_moment_match_i <- function(i, if (split && (iterind > 1)) { # compute split transformation split_obj <- loo_moment_match_split( - x, upars, cov, total_shift, total_scaling, total_mapping, i, + x, upars, cov, total$shift, total$scaling, total$mapping, i, log_prob_upars = log_prob_upars, log_lik_i_upars = log_lik_i_upars, cores = 1, r_eff_i = r_eff_i, is_method = is_method, ... ) @@ -486,6 +486,39 @@ update_quantities_i <- function(x, upars, i, orig_log_prob, +#' Add one accepted moment matching step to the total transformation +#' +#' Each step maps the current draws `u` to `L (u - mean(u)) + mean(u) + shift`, +#' where `L` is the identity, `diag(scaling)` or `mapping`. The shifts add up, +#' and the linear parts compose in the order in which the steps were accepted. +#' After any accepted step the loop in `loo_moment_match_i()` starts again with +#' the shift step, so a scaling step can follow a covariance step. With +#' `cov = TRUE` the scaling is therefore applied to the rows of `mapping` +#' (`diag(scaling) %*% mapping`), and `scaling` stays one. With `cov = FALSE` +#' there is no covariance step, and the scalings are kept in `scaling`. +#' +#' @noRd +#' @param total A list with `shift`, `scaling` and `mapping`. +#' @param trans The output of `shift()`, `shift_and_scale()` or +#' `shift_and_cov()`. +#' @param cov Logical; the `cov` argument of the moment matching. +#' @return The updated `total`. +#' +add_step_to_total <- function(total, trans, cov) { + total$shift <- total$shift + trans$shift + if (!is.null(trans$scaling)) { + if (cov) { + total$mapping <- trans$scaling * total$mapping + } else { + total$scaling <- total$scaling * trans$scaling + } + } + if (!is.null(trans$mapping)) { + total$mapping <- trans$mapping %*% total$mapping + } + total +} + #' Shift a matrix of parameters to their weighted mean. #' Also calls update_quantities_i which updates the importance weights based on #' the supplied model object. diff --git a/R/split_moment_matching.R b/R/split_moment_matching.R index 383aeb05..e44dba39 100644 --- a/R/split_moment_matching.R +++ b/R/split_moment_matching.R @@ -13,9 +13,15 @@ #' @param total_shift A vector representing the total shift made by the moment #' matching algorithm. #' @param total_scaling A vector representing the total scaling of marginal -#' variance made by the moment matching algorithm. -#' @param total_mapping A vector representing the total covariance -#' transformation made by the moment matching algorithm. +#' variance made by the moment matching algorithm. With `cov = TRUE`, +#' [loo_moment_match()] includes the scaling in `total_mapping` instead, and +#' this vector is all ones. +#' @param total_mapping A square matrix representing the total linear +#' transformation made by the moment matching algorithm: the product of the +#' linear parts of the accepted steps, in the order in which they were +#' accepted. Used only when `cov = TRUE`. The transformation is +#' `T(theta) = total_mapping %*% diag(total_scaling) %*% (theta - m) + m + +#' total_shift`, where `m` is the mean of `upars`. #' @param i Observation index. #' @param log_prob_upars A function that takes arguments `x` and `upars` and #' returns a matrix of log-posterior density values of the unconstrained @@ -85,9 +91,14 @@ loo_moment_match_split <- function(x, upars, cov, total_shift, total_scaling, log_liki_half <- log_lik_i_upars(x, upars = upars_trans_half, i = i, ...) # compute weights - log_prob_half_trans_inv <- (log_prob_half_trans_inv - - log(prod(total_scaling)) - - log(det(total_mapping))) + # log of the absolute Jacobian determinant of T; the mapping is part of T + # only when cov = TRUE + log_det_jacobian <- sum(log(total_scaling)) + if (cov) { + log_det_jacobian <- log_det_jacobian + + as.numeric(determinant(total_mapping, logarithm = TRUE)$modulus) + } + log_prob_half_trans_inv <- log_prob_half_trans_inv - log_det_jacobian stable_S <- log_prob_half_trans > log_prob_half_trans_inv lwi_half <- -log_liki_half + log_prob_half_trans @@ -125,7 +136,7 @@ loo_moment_match_split <- function(x, upars, cov, total_shift, total_scaling, # currently ignores chain information # since we have two proposal distributions # compute S_eff separately from both and take the smaller - take <- seq_len(S)[-seq_len(S_half)] + take <- seq_len(S_half) log_liki_half_1 <- log_liki_half[take, drop = FALSE] dim(log_liki_half_1) <- c(length(take), 1, 1) take <- seq_len(S)[-seq_len(S_half)] diff --git a/man/loo_moment_match_split.Rd b/man/loo_moment_match_split.Rd index 91a6d826..176d3c43 100644 --- a/man/loo_moment_match_split.Rd +++ b/man/loo_moment_match_split.Rd @@ -34,10 +34,15 @@ matched.} matching algorithm.} \item{total_scaling}{A vector representing the total scaling of marginal -variance made by the moment matching algorithm.} +variance made by the moment matching algorithm. With \code{cov = TRUE}, +\code{\link[=loo_moment_match]{loo_moment_match()}} includes the scaling in \code{total_mapping} instead, and +this vector is all ones.} -\item{total_mapping}{A vector representing the total covariance -transformation made by the moment matching algorithm.} +\item{total_mapping}{A square matrix representing the total linear +transformation made by the moment matching algorithm: the product of the +linear parts of the accepted steps, in the order in which they were +accepted. Used only when \code{cov = TRUE}. The transformation is +\code{T(theta) = total_mapping \%*\% diag(total_scaling) \%*\% (theta - m) + m + total_shift}, where \code{m} is the mean of \code{upars}.} \item{i}{Observation index.} diff --git a/tests/testthat/_snaps/loo_moment_matching.md b/tests/testthat/_snaps/loo_moment_matching.md index 1a7be2f3..6d381b25 100644 --- a/tests/testthat/_snaps/loo_moment_matching.md +++ b/tests/testthat/_snaps/loo_moment_matching.md @@ -256,1489 +256,1489 @@ # loo_moment_match_split works - WAoAAAACAAQGAQACAwAAAAITAAAABAAAAA4AAA+gwCRQwPxkFVbAJL982dpWW8Alg7U+WIPR - wCG9Sha57abAIv30cjfFt8Ai2Bs/kTNAwCWDlPEsULDAI6o6yFoaz8AqLVWYQSqqwCXNfiym - bkzAIy5URlSPssAgYs9EiNj0wCf8HOgdFwXAJIrGh1EQfMAl2w9HXDE7wCFqfr4Sk5DAJrYM - msoM7cAl7woOvp4QwCRiJ+d17I7AKgLZuKQmzsArdUFdCRPMwCbfLdZe9JbAJQvooQtAWMAi - qN9wlN5AwCerIljb+XjAGjGmsazU0MApN1TFQVdGwCTbnwrB3T/AIujlMDS/ccAlrD+eX8dh - wBn9t61vZzjAFXwG98xl0MAmgPGkt/hnwCbt7opJnWvAIlRvMNWwaMAhZ1GiekS0wCZgS+ZJ - 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b7791dbb..c69f3401 100644 --- a/tests/testthat/test_loo_moment_matching.R +++ b/tests/testthat/test_loo_moment_matching.R @@ -502,13 +502,15 @@ test_that("loo_moment_match_split works", { expect_equal(lwi_1_ps, split$lwi) + # with cov = TRUE, loo_moment_match() includes the scaling in the mapping + # and leaves total_scaling at one split2 <- loo_moment_match_split( x, upars, - cov = FALSE, + cov = TRUE, total_shift = c(-0.1, -0.2), - total_scaling = c(0.7, 0.7), - total_mapping = matrix(c(1, 0.1, 0.1, 1), 2, 2), + total_scaling = c(1, 1), + total_mapping = 0.7 * matrix(c(1, 0.1, 0.1, 1), 2, 2), i = 1, log_prob_upars = log_prob_upars_test, log_lik_i_upars = log_lik_i_upars_test, @@ -570,6 +572,12 @@ test_that("loo_moment_match_split evaluates the inverse of its transformation", r_eff_i = 1, is_method = "psis" ) + expect_length(seen, 2) + first <- seq_len(as.integer(0.5 * S)) + # first call: second half untransformed; second call: first half + # untransformed + expect_equal(seen[[1]][second, , drop = FALSE], upars[second, , drop = FALSE]) + expect_equal(seen[[2]][first, , drop = FALSE], upars[first, , drop = FALSE]) # the second call evaluates the inverse-transformed draws inv <- seen[[2]][second, , drop = FALSE] fwd <- sweep(inv, 2, m, "-") @@ -582,6 +590,56 @@ test_that("loo_moment_match_split evaluates the inverse of its transformation", } }) +test_that("the total transformation composes the accepted steps in order", { + # The moment matching loop starts again with the shift step after every + # accepted step, so a scaling step can follow a covariance step. The + # transformation that loo_moment_match_split() rebuilds from the totals + # must map the original draws to the draws that the steps produced one + # after another. + first <- seq_len(as.integer(0.5 * S)) + sequences <- list( + list(cov = TRUE, steps = c("cov", "scale", "shift", "cov", "scale")), + list(cov = FALSE, steps = c("scale", "shift", "scale")) + ) + for (sq in sequences) { + total <- list(shift = c(0, 0), scaling = c(1, 1), mapping = diag(2)) + u <- upars + for (step in sq$steps) { + trans <- switch(step, + shift = shift(x, u, lwi_1), + scale = shift_and_scale(x, u, lwi_1), + cov = shift_and_cov(x, u, lwi_1) + ) + u <- trans$upars + total <- add_step_to_total(total, trans, sq$cov) + } + seen <- list() + log_prob_record <- function(x, upars, ...) { + seen[[length(seen) + 1]] <<- upars + log_prob_upars_test(x, upars, ...) + } + loo_moment_match_split( + x, + upars, + cov = sq$cov, + total_shift = total$shift, + total_scaling = total$scaling, + total_mapping = total$mapping, + i = 1, + log_prob_upars = log_prob_record, + log_lik_i_upars = log_lik_i_upars_test, + cores = 1, + r_eff_i = 1, + is_method = "psis" + ) + # the first call evaluates T(theta) for the first half of the draws + expect_equal( + unname(seen[[1]][first, , drop = FALSE]), + unname(u[first, , drop = FALSE]) + ) + } +}) + test_that("shift_and_scale is stable for large parameter values", { upars <- matrix(1e8 + c(-1, 0, 1), ncol = 1) result <- shift_and_scale(NULL, upars, rep(-log(3), 3))