ZI‑PLN-PCA (missing data) — variational E‑step solver

Fits a zero‑inflated Poisson log‑normal (ZI‑PLN-PCA) latent factor model on a count matrix with missing values using a single call to a variational optimization backend (VE). Returns model/variational parameters and expected Poisson means suitable for imputation and prediction.

Usage

Miss.ZIPLNPCA_VE(Y, X, q, params = NULL, config_vem = NULL, config = NULL)

Arguments

Y

Numeric n x p count matrix. May contain NA.

X

Numeric design matrix with n*p rows and d columns, aligned with vec(Y) (vectorization by columns).

q

Integer, latent rank (dimension of the latent space).

params

Optional list of initial parameters. If NULL, Init_ZIP is called.

config_vem

List of outer VE controls (stopping and bounds), with fields:

maxiter: Maximum iterations (not always used by this backend, default 10000).
ftol: ELBO tolerance (default 1e-08).
xtol: Parameter tolerance (default 1e-04).
tolS: List with lower, upper bounds for S (default list(lower = 1e-4, upper = 1)).
tolxi: Tolerance for the Jaakkola‑type $\xi$ updates (default 1e-04).

config

List of NLOpt controls for the backend (algorithm, tolerances, maxeval, etc.). If NULL, sensible defaults are provided.

Value

A list with components:

mStep: Model parameters: gamma (d x 1), beta (d x 1), loadings C (p x q).
eStep: Variational parameters: M (n x q), S (n x q), xi (n x p).
pred: List with predictors and expected counts: mu (n x p), nu (n x p), backend mean A (n x p), and predicted recomputed in R.
elbo: Final ELBO value.
params.init: Initial parameters used.
monitoring: Backend diagnostics (if provided).
elbo1, elbo2, elbo3, elbo4, elbo5: Decomposition terms of the ELBO (as returned by the backend).

Details

Missing entries are handled via a binary mask R = 1_{observed}(Y), and a working copy Y.na with zeros at missing locations for the objective evaluation. Box constraints on S are injected into config$lower_bounds and config$upper_bounds using config_vem$tolS.

Predicted mean: ici, la recomposition côté R utilise $$ \exp\!\big( X B + M C^\top + 0.5\, S \,(C\odot C)^\top \big). $$ D'autres fonctions du package emploient $0.5\,(S\odot S)\,(C\odot C)^\top$. Vérifie et harmonise selon la paramétrisation attendue par ton backend.

Examples

if (FALSE) { # \dontrun{
set.seed(1)
n <- 40; p <- 12; d <- 3; q <- 2
Y <- matrix(rpois(n*p, 2), n, p); Y[sample(length(Y), 20)] <- NA
X <- cbind(1, rnorm(n*p), rnorm(n*p))  # (n*p) x d

fit <- Miss.ZIPLNPCA_VE(Y = Y, X = X, q = q)
fit$elbo
str(fit$mStep); str(fit$eStep)
} # }