ECOD + COPOD novelty discriminator (single-sample, frozen-ECDF)

Single-sample-deployable novelty/outlier-detection-as-discriminator scorer (family NC) that bundles the two empirical-cumulative-distribution outlier detectors ECOD (Li et al., 2022) and COPOD (Li et al., 2020) from the Python pyod library. Both detectors flag a specimen as anomalous when its per-feature values fall in the extreme tails of an in-distribution reference, which here is the training CONTROL cohort (mirroring the healthy-reference convention of fit_conformal_anomaly).

Why the per-feature ECDF state is frozen rather than re-fitted at score time. pyod's ECOD$decision_function() / COPOD$decision_function() are transductive: they re-fit each per-feature empirical CDF on whatever batch is passed, so the score of one specimen depends on which other specimens are scored alongside it (measured batch-vs-row-by-row max difference \(\approx 0.68\) for ECOD). That is a batch-coupled scorer and would fail the single-sample deployability gate (singlesample_assert_row_equivariant). This implementation therefore NEVER calls pyod at score time. At fit it freezes the training-control per-feature order statistics and the per-feature skewness signs that ECOD uses; at score it evaluates each specimen's ECOD and COPOD aggregates against those frozen reference ECDFs in pure R, one specimen at a time. On the training-control rows the frozen reference ECDF equals the fit-time ECDF, so the pure-R aggregates reproduce pyod's decision_scores_ to machine precision (asserted by the test suite).

Single-sample transform. Each specimen is mapped to the self-contained per-sample robust CLR over its OWN strictly-positive support (geometric-mean centring on v > 0); this is exactly invariant to per-specimen scaling and uses no cross-row statistic. Missing universe features are absent from a specimen's rCLR support and contribute no tail term (documented single-sample-safe rule); the per-feature reference ECDF is simply skipped for an absent feature, exactly as if that coordinate carried the neutral aggregate 0.

Combining the two detectors and orientation. ECOD and COPOD live on different (feature-count-dependent) scales, so each per-specimen aggregate is z-standardized against the frozen control-aggregate mean / sd captured at fit, and the two z-scores are averaged. A single frozen orientation scalar (\(+1\) or \(-1\)), chosen at fit so that larger = more case-like (training AUC of the combined anomaly score against y_train; flipped if anomaly is anti-correlated with case), is applied at score. Orientation and standardization are frozen constants, so the score of a specimen depends only on that specimen and the frozen model.

Degenerate inputs (no present features, an all-zero specimen, or an empty control reference) return the neutral score 0.

References

Li Z, Zhao Y, Botta N, Ionescu C, Hu X. (2020) COPOD: Copula-Based Outlier Detection. ICDM.

Li Z, Zhao Y, Hu X, Botta N, Ionescu C, Chen G. (2022) ECOD: Unsupervised Outlier Detection Using Empirical Cumulative Distribution Functions. IEEE TKDE.

Vovk V, Gammerman A, Shafer G. (2005) Algorithmic Learning in a Random World. Springer.