Score a linearized-optimal-transport (CDT tangent) LRT discriminator

Scores each row of X independently with the frozen model learned by fit_ot_lot. For one specimen the abundances are mapped to the self-contained per-sample rCLR representation, its present coordinates \(z_{\mathrm{pos}}\) are taken, and its CDT quantile function \(Q = \mathrm{quantile}(z_{\mathrm{pos}}, t_k, \mathrm{type}=1)\) (the empirical inverse-CDF) is formed on the frozen grid. The score is the frozen linear functional of the CDT tangent embedding $$S(Q) = w^\top (Q - Q_{\mathrm{ref}}) + b,$$ larger meaning more case-like.

At scoring time the present feature set is intersect(model$feature_universe, colnames(X)); the per-sample rCLR is formed over exactly that set. The reference \(Q_{\mathrm{ref}}\), the grid \(t_k\) and the head \((w,b)\) are frozen from training and live in the fixed-dimension CDT tangent space, so no present-subset re-derivation is needed and no scored-batch statistic is used. 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 feature-universe columns are present, the documented neutral score 0 is returned for every row; a specimen whose own present rCLR coordinates number fewer than model$hp$min_features (e.g. a near-empty profile) also scores the neutral 0.

Usage

score_ot_lot(model, X, meta = NULL)

Arguments

model

An ot_lot_model object returned by fit_ot_lot.

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 reference, grid and head.

References

Park S.R., Kolouri S., Kundu S., Rohde G.K. (2018) The cumulative distribution transform and linear pattern classification. Applied and Computational Harmonic Analysis 45(3): 616-641.

Examples

if (FALSE) { # \dontrun{
set.seed(1)
n <- 200; p <- 40
y <- rep(c(0, 1), each = n / 2)
E <- matrix(0, n, p, dimnames = list(NULL, paste0("miR-", seq_len(p))))
E[y == 0, ] <- stats::rnorm(sum(y == 0) * p, 0, 0.30)
E[y == 1, ] <- stats::rnorm(sum(y == 1) * p, 0, 0.60)
X <- exp(6 + E)
model <- fit_ot_lot(X, y)
score_ot_lot(model, X[1, , drop = FALSE])
} # }