Fit a Gaussian-mixture proxy to a target density

The unified front door of proxymix. Picks a fitting regime (or honours an explicit choice) and dispatches to the corresponding regime-specific fitter:

Usage

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

Arguments

target: A gmm_target.
N: Number of components.
regime: One of "auto", "moment", "sample", "kld".
...: Additional arguments forwarded to the regime-specific fitter. The most useful pass-throughs are canonicalise (whether to apply gmm_canonicalise() to the returned fit; default TRUE), validation_size and validation_proposal (held-out IS validation for regime "kld"), max_iter, tol, n_starts, and seed.

Value

A gmm_fit.

Details

"moment" - closed-form moment matching (fit_moment_match()).
"sample" - classical EM on i.i.d. samples (fit_em_samples()).
"kld" - importance-sampled KLD-EM (fit_kld_em()) for a target that can be evaluated but not sampled.

With regime = "auto" the choice is made from the shape of the supplied target:

N == 1 and the target carries samples or moments: "moment".
N >= 2 and the target carries samples: "sample".
The target carries log_density only (no samples): "kld".

Examples

## auto: samples + N=2 -> classical EM.
x <- matrix(stats::rnorm(200), ncol = 2)
tgt_s <- gmm_target_from_samples(x)
fit_proxymix(tgt_s, N = 2L, max_iter = 25L)
#> Auto-selected regime: "sample".
#> <gmm_fit>: regime = "sample", K = 2, p = 2
#>   target     : target_from_samples
#>   iterations : 25
#>   converged  : FALSE
#>   [1] w = 0.7928, |mu| = 0.3344, tr(Sigma) = 1.4380
#>   [2] w = 0.2072, |mu| = 1.5704, tr(Sigma) = 1.3301

## explicit "kld" on a log-density-only target.
fit_proxymix(banana_target(), N = 3L, regime = "kld",
             is_size = 1000L, max_iter = 20L, seed = 1L)
#> <gmm_fit>: regime = "kld", K = 3, p = 2
#>   target     : banana
#>   iterations : 20
#>   converged  : FALSE
#>   [1] w = 0.6103, |mu| = 0.3840, tr(Sigma) = 1.3456
#>   [2] w = 0.3228, |mu| = 0.8867, tr(Sigma) = 2.4049
#>   [3] w = 0.0670, |mu| = 2.4700, tr(Sigma) = 5.6889