Score a Bures-Wasserstein Gaussian-OT class-conditional LRT discriminator

Scores each row of X independently with the frozen model learned by fit_lrt_bw. For one specimen the abundances are mapped to the self-contained per-sample rCLR representation \(z\), and the score is the Gaussian log-likelihood ratio of case vs control under the frozen BW-regularized class Gaussians $$S(z) = -\tfrac{1}{2}(z-\mu_{\mathrm{case}})^\top \Sigma_{\mathrm{case}}^{\mathrm{reg}\,-1}(z-\mu_{\mathrm{case}}) - \tfrac{1}{2}\log\det\Sigma_{\mathrm{case}}^{\mathrm{reg}} + \tfrac{1}{2}(z-\mu_{\mathrm{control}})^\top \Sigma_{\mathrm{control}}^{\mathrm{reg}\,-1} (z-\mu_{\mathrm{control}}) + \tfrac{1}{2}\log\det\Sigma_{\mathrm{control}}^{\mathrm{reg}}.$$

At scoring time the present feature set is intersect(model$feature_universe, colnames(X)). The class representation (per-class mean, BW-regularized precision and log determinant) is re-derived over exactly that present set from the frozen raw anchors – using only frozen training data, never a scored-batch statistic – which keeps partial-overlap scores consistent and equal to the fit-time representation at full overlap. The score of a row therefore depends only on that row and the frozen model, and is exactly (to numerical tolerance) invariant to per-sample scaling. If fewer than model$hp$min_features features are present, the documented neutral score 0 is returned for every row.

Usage

score_lrt_bw(model, X, meta = NULL)

Arguments

model

An lrt_bw_model object returned by fit_lrt_bw.

X

Numeric matrix (samples \(\times\) features) of non-negative abundance values. Columns must be named feature ids.

meta

Optional per-sample metadata. Accepted for interface uniformity and ignored by this method.

Value

Plain finite numeric vector of length nrow(X). Larger values are more case-like. Scoring uses only each row's own values plus the frozen anchors and hyperparameters.

References

Bhatia R., Jain T., Lim Y. (2019) On the Bures-Wasserstein distance between positive definite matrices. Expositiones Mathematicae 37(2): 165-191.

Takatsu A. (2011) Wasserstein geometry of Gaussian measures. Osaka Journal of Mathematics 48(4): 1005-1026.

Examples

if (FALSE) { # \dontrun{
set.seed(1)
n <- 160; p <- 30
L <- matrix(stats::rnorm(n * p, 4, 0.6), nrow = n,
            dimnames = list(NULL, paste0("miR-", seq_len(p))))
y <- rep(c(0, 1), each = n / 2)
shift <- rep(c(1.2, -1.2), length.out = 12)
L[y == 1, 1:12] <- L[y == 1, 1:12] + matrix(shift, sum(y == 1), 12, byrow = TRUE)
X <- exp(L)
model <- fit_lrt_bw(X, y)
score_lrt_bw(model, X[1, , drop = FALSE])
} # }