ZI‑PLN-PCA with missing data using log(S) parametrization

Fits a zero‑inflated Poisson log‑normal (ZI‑PLN-PCA) latent factor model to a count matrix with missing values, using a variational objective and an alternative parametrization on the variational scales: $$ \code{log(S)} \text{ instead of } S. $$ This guarantees positivity of \(S\) and allows simple box constraints on \(log(S) \) via tolLogS.

Usage

Miss.ZIPLNPCA.logS(
  Y,
  X,
  q,
  params = NULL,
  config = NULL,
  tolxi = NULL,
  tolLogS = 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, they are initialized by Init_ZIP. If provided, it must include a positive S; the function internally adds logS <- log(S).

config

Optional list of optimizer controls. If NULL, defaults to PLNPCA_param()$config_optim.

tolxi

Numeric tolerance for the Jaakkola‑type \(\xi\) updates in the logistic bound (default 1e-4).

tolLogS

Numeric upper bound applied to logS (box constraint). Defaults to Inf. Use this to avoid excessively large variational scales when needed.

Value

A list with components:

mStep

Model parameters: gamma (d x 1), beta (d x 1), and loadings C (p x q).

eStep

Variational parameters: means M (n x q), scales S (n x q), and logistic bound parameters xi (n x p).

pred

List with predictors and expected counts: mu (n x p), nu (n x p), backend Poisson mean A (n x p), and predicted recomputed in R: $$\exp\!\big( X B + M C^\top + 0.5\,(S\odot S)\,(C\odot C)^\top \big).$$

imputed

n x p matrix equal to xi * A at missing entries of Y, and Y elsewhere.

iter

Number of iterations; elboPath (trajectory of ELBO); elbo (final ELBO).

params.init

Initial parameters passed to the backend (with logS added).

monitoring

Optimizer diagnostics/logs.

gradB, gradD, gradC, gradM, gradS

ELBO gradients w.r.t. corresponding parameters (via Elbo_grad).

Details

Missing entries are handled by a mask R = 1_{observed}(Y); a working matrix Y.na sets missings to 0 for the objective evaluation. Box constraints are set on logS via config$upper_bounds, using tolLogS. Make sure X matches vec(Y).

See also

Miss.ZIPLNPCA for the S parametrization, Init_ZIP, Elbo_grad

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.logS(Y = Y, X = X, q = q, tolLogS = 2)  # cap logS
fit$elbo
str(fit$eStep$S)
} # }