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, q, O = NULL, w = NULL, 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)).

q

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

O

Optional numeric n x p matrix of offsets (default: zeros).

w

Optional numeric vector of length n with observation weights (default: all ones).

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:

1. Rowwise design (nrow(X) == n): one row per sample.

2. Vectorized design (nrow(X) == n*p): X aligns with vec(Y) (vectorization by columns).

See also

Init, PLNPCA_param MatrixToVector, VectorToMatrix, Elbo_grad

Examples

set.seed(1)
n <- 30; p <- 5; q <- 2
Y <- matrix(rpois(n * p, 2), n, p)
Y[sample(n * p, 20)] <- NA                        # missing entries
X <- cbind(1, rnorm(n))                           # rowwise design, n x d

fit <- Miss.PLNPCA(Y = Y, X = X, q = q)
fit$elbo
#> [1] -71.26403
str(fit$pred$A)
#>  num [1:30, 1:5] 2 2.01 1.57 2.69 2.54 ...