Closed-form moment-matching fit

Implements regime (i) of Hoek and Elliott (2024). When N == 1, this is the exact moment match: mu is the target mean and Sigma is the target covariance. When N > 1, the function returns the deterministic moment-seed of init_moment_seed() wrapped as a gmm_fit, without iterative refinement — useful as a starting point for the iterative regimes.

Usage

fit_moment_match(target, N = 1L, ridge_eps = 1e-06, canonicalise = TRUE)

Arguments

target

A gmm_target.

N

Number of components. N >= 2 returns a moment-seeded mixture without iterative refinement.

ridge_eps

Ridge added to the empirical covariance for numerical stability.

canonicalise

Logical. If TRUE (the default), the fitted mixture is post-processed by gmm_canonicalise() so that components are sorted by descending weight and (as a tiebreaker) by descending ||mu||. Set FALSE to retain the raw component order.

Value

A gmm_fit with regime = "moment".

Details

Either the target must carry an n by p samples matrix, or its metadata slot must contain pre-computed moments of the form list(mean = <p-vec>, cov = <p-by-p>).

See also

Other fitting: fit_em_samples(), fit_kld_em(), from_kde(), from_objective(), select_N()

Examples

x <- matrix(stats::rnorm(200), ncol = 2)
tgt <- gmm_target_from_samples(x)
fit_moment_match(tgt, N = 1L)
#> <gmm_fit>: regime = "moment", K = 1, p = 2
#>   target     : target_from_samples
#>   iterations : 0
#>   converged  : TRUE
#>   [1] w = 1.0000, |mu| = 0.0897, tr(Sigma) = 2.0274