proxymix

proxymix fits multivariate Gaussian-mixture proxies that are Kullback–Leibler optimal to user-supplied target densities on $\mathbb{R}^p$. Three regimes from Hoek and Elliott (2024) are unified under one verb:

Regime	When it applies	Method
(i) moment	$N = 1$ component	Closed-form moment matching
(ii) sample	i.i.d. samples from the target are available	Classical EM
(iii) kld	target density f(x) can be evaluated but not (cheaply) sampled	KLD-EM with importance sampling — the wedge

No other CRAN package implements regime (iii) for arbitrary parametric $f$. mclust, mixtools, flexmix all assume samples.

Installation

Local install from the source tree:

R CMD build proxymix
R CMD INSTALL proxymix_*.tar.gz

Quick start

library(proxymix)

## A target you can evaluate but not sample from — a 2D "banana".
banana <- banana_target()

## Fit a 3-component Gaussian mixture proxy via KLD-EM with importance sampling.
fit <- fit_proxymix(banana, N = 3L, regime = "kld",
                    proposal = is_mvt(n_dim = 2L, df = 5),
                    is_size = 2000L, max_iter = 25L)

print(fit)
#> <gmm_fit>: regime = "kld", K = 3, p = 2
#>   target     : banana
#>   iterations : 25
#>   converged  : FALSE
#>   [1] w = 0.5185, |mu| = 0.3203, tr(Sigma) = 1.4429
#>   [2] w = 0.2664, |mu| = 1.0130, tr(Sigma) = 2.4879
#>   [3] w = 0.2151, |mu| = 1.1665, tr(Sigma) = 2.4686

## Closed-form operations on the fitted mixture.
gmm_marginalise(fit, keep = 1L)
#> <marginal[1] of kld_em[N=3] on banana>: K = 3 components in p = 1 dimensions
#>   [1] w = 0.5185, |mu| = 0.0075, tr(Sigma) = 0.4566
#>   [2] w = 0.2664, |mu| = 0.9980, tr(Sigma) = 0.5020
#>   [3] w = 0.2151, |mu| = 1.0880, tr(Sigma) = 0.5608
gmm_conditionalise(fit, given = c(NA, 0.5))
#> <conditional of kld_em[N=3] on banana>: K = 3 components in p = 1 dimensions
#>   [1] w = 0.5223, |mu| = 0.0245, tr(Sigma) = 0.4551
#>   [2] w = 0.2590, |mu| = 1.1247, tr(Sigma) = 0.2020
#>   [3] w = 0.2188, |mu| = 1.1205, tr(Sigma) = 0.2423

The unified fitting verb

fit_proxymix(
  target,
  N        = 1L,
  regime   = c("auto", "moment", "sample", "kld"),
  ...
)

• target is an S7 gmm_target produced by gmm_target() (from a log-density), gmm_target_from_samples() (from samples), or one of the built-in factories (banana_target(), donut_target(), mixture_target()).
• regime = "auto" picks the cheapest applicable regime from the target’s contents.

Closed-form mixture operators

dgmm(x, fit)              # density evaluation
rgmm(n, fit)              # exact sampling
gmm_marginalise(fit, keep)
gmm_conditionalise(fit, given)
gmm_kld(fit_p, fit_q)     # Monte Carlo + variational bounds

Vignettes

The package ships with four educational vignettes:

• quickstart — one-page tour.
• three_regimes — a walk-through of regimes (i)–(iii) on toy 2-D targets, including the agreement of (i) and (iii) at $N = 1$.
• density_shapes — the wedge demonstration: banana, donut, three-mixture targets fit by importance-sampled KLD-EM.
• roadmap — the Tier-2 stubs and the research directions they support.

Interactive tutorial

A standalone, single-file HTML primer for proxymix is hosted at

https://max578.github.io/proxymix-tutorial/

The page is targeted at Adelaide University Mathematics and Statistics undergraduates (Guided depth, default) and postgraduate / PhD readers (Technical depth, via the in-page dial). It runs in the browser with no R install required, and works the same way offline by double-click. Source at max578/proxymix-tutorial.

Reference

Hoek, J. van der and Elliott, R. J. (2024). Mixtures of multivariate Gaussians. Stochastic Analysis and Applications. doi:10.1080/07362994.2024.2372605.

Licence

MIT © Max Moldovan.