Fit the deep-feature class-conditional Mahalanobis LRT discriminator

Trains a BatchNorm-free MLP embedding on the per-sample-rCLR, universe-aligned TRAINING matrix (via reticulate-python torch; Adam, cross-entropy), EXPORTS the weights up to the penultimate embedding layer to R as plain numeric matrices/vectors, DISCARDS the python module and the 2-logit head, then estimates the frozen per-class Gaussian means and a single TIED ridge-regularised covariance in the embedding space using the PURE-R forward the scorer evaluates (guaranteeing fit/score consistency despite float32 training). The fitted model holds no external pointer.

Usage

fit_lrt_deepmaha(X_train, y_train, meta_train = NULL, hp = list())

Arguments

X_train: Numeric matrix (samples $\times$ features) of non-negative abundances with unique, non-empty feature names (colnames).
y_train: Numeric / integer 0/1 labels (1 = case), length nrow(X_train), with at least one case and one control.
meta_train: Optional per-sample metadata. Accepted for interface uniformity and otherwise ignored.
hp: Optional list of hyperparameters. Allowed fields: hidden (positive-integer vector of layer widths up to the embedding; the LAST entry is the embedding dim $d$; default c(64L, 32L)), activation ("relu" (default) or "tanh"), epochs (positive integer; default 200L), lr (positive Adam learning rate; default 1e-3), weight_decay (non-negative Adam L2; default 1e-4), batch_size (positive integer minibatch; default 32L), ridge (positive covariance ridge factor; default 1e-3), min_features (feature-overlap floor at scoring, positive integer; default 3L), device ("cpu" (default), "cuda", or "auto"; "cuda"/"auto" fall back to CPU with no GPU), and seed (integer; default 42L).

Value

Object of class lrt_deepmaha_model: a list with feature_universe, weights (exported per-layer list(W, b) up to the embedding), activation, mu_case, mu_ctrl, Sigma_reg_inv (inverse of the ridge-regularised tied covariance), embedding_dim, device (resolved), seed, and hp.

Details

The score is the class-conditional Gaussian log-likelihood ratio with a shared covariance: $s(z) = -\tfrac12 (z-\mu_{\mathrm{case}})^\top \Sigma^{-1} (z-\mu_{\mathrm{case}}) + \tfrac12 (z-\mu_{\mathrm{ctrl}})^\top \Sigma^{-1} (z-\mu_{\mathrm{ctrl}})$, exactly linear in the embedding $z$ (LDA in embedding space). The tied covariance is the pooled within-class estimator $\Sigma = ((n_1-1)S_1 + (n_0-1)S_0)/(n_1+n_0-2)$, ridge-regularised as $\Sigma + \lambda\,\overline{\mathrm{diag}(\Sigma)}\,I$ with $\lambda = $ hp$ridge, with a positive-definite floor if needed. This uses the unbiased pooled denominator; Lee 2018 displays the $1/N$ MLE form, which differs only by a constant scaling of the tied covariance and so leaves the per-specimen score ranking (and AUC) unchanged.

References

Lee K, Lee K, Lee H, Shin J. (2018) A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks. NeurIPS 31. arXiv:1807.03888.

Examples

if (FALSE) { # \dontrun{
set.seed(1)
n <- 80; p <- 30; k <- 8
L <- matrix(stats::rnorm(n * p, 4, 0.5), nrow = n,
            dimnames = list(NULL, paste0("miR-", seq_len(p))))
y <- rep(c(0, 1), each = n / 2)
L[y == 1, seq_len(k)] <- L[y == 1, seq_len(k)] + 1.2
X <- exp(L)
model <- fit_lrt_deepmaha(X, y)
score_lrt_deepmaha(model, X[1, , drop = FALSE])
} # }