PLN-PCA with missing data (variational fit + imputation)

Fits a Poisson log-normal PCA model (PLN-PCA) to a count matrix with missing values, using a variational objective optimized by NLOpt-based routines. The function estimates model/variational parameters and returns expected counts to impute missing entries.

Usage

Miss.PLNPCA(Y, X, O = NULL, w = NULL, q, params = NULL, config = NULL)

Arguments

Y: Numeric n x p count matrix. May contain NA.
X: Numeric design matrix of covariates: either n x d (rowwise) or (n*p) x d (vectorized to match MatrixToVector(Y)).
O: Optional numeric n x p matrix of offsets (default: zeros).
w: Optional numeric vector of length n with observation weights (default: all ones).
q: Integer, latent rank (dimension of the latent space).
params: Optional initial parameters (list) typically produced by Init; if NULL, they are initialized internally.
config: Optional optimizer configuration; if NULL, defaults to PLNPCA_param()$config_optim.

Value

A list with components:

mStep: List with beta (1 x d) and C (p x q).
eStep: List with M (n x q) and S (n x q).
pred: List with A and predicted, both equal to the n x p matrix of expected counts used for imputation: $$ A = \exp\!\big(O + X B + M C^\top + 0.5\,(S\odot S)\,(C\odot C)^\top\big), $$ where $\odot$ denotes the Hadamard product and X B is reshaped to n x p when X is vectorized.
iter: Integer, number of iterations.
elboPath: Numeric vector of objective (ELBO) values over iterations.
elbo: Final ELBO value.
params.init: The initial parameters used.
monitoring: Optimizer log/diagnostics as returned by the backend.

Details

Two designs for X are supported:

Rowwise design (nrow(X) == n): one row per sample.
Vectorized design (nrow(X) == n*p): X aligns with vec(Y) (vectorization by columns).

Examples

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

fit <- Miss.PLNPCA(
  Y = Y, X = X, q = q,
  O = matrix(0, n, p),
  w = rep(1, n),
  params = NULL,
  config = NULL
)
str(fit$pred$A)     # expected counts (n x p)
fit$elbo            # final ELBO
} # }