ELBO and parameter gradients (ZIP‑PLN variational objective)

Computes the Evidence Lower Bound (ELBO) and its gradients with respect to the model and variational parameters for a zero‑inflated Poisson log‑normal (ZIP‑PLN) latent factor model. This is a thin R wrapper around a fast C++ implementation, with a small preprocessing step that replaces NA values in Y by zeros before delegation.

Usage

Elbo_grad(data, params, tolxi)

Arguments

data

A list with elements:

Y

Numeric n x p count matrix (may contain NA).

X

Numeric n x d design matrix for the abundance/log‑mean part.

R

Numeric/binary design matrix for the zero‑inflation (logit) part (same number of rows as Y); can be NULL if not used.

params

A list with elements:

B

Matrix of regression coefficients for X (abundance).

D

Matrix of regression coefficients for X (zero‑inflation).

C

Loadings matrix for the latent factors (rank q).

M

Variational means of the latent factors.

S

Variational standard deviations (or log‑SDs) of the latent factors.

tolxi

Numeric, convergence tolerance used for the variational bound on the logistic term.

Value

A list containing at least:

elbo

Scalar numeric, the ELBO value.

grad_B, grad_D, grad_C, grad_M, grad_S

Gradients w.r.t. the corresponding parameters.

Details

This function sets NA entries of data$Y to 0 internally (they are not dropped) before calling the C++ backend Elbo_grad_Rcpp. Ensure the dimensions of X, R and the parameter matrices are compatible with Y.

See also

Elbo_grad_Rcpp (backend C++).