Interpretability by design with Formal Concept Analysis

The decision: expose co-occurrence as structure

Formal Concept Analysis starts with objects, attributes, and an incidence relation. A closure identifies the attributes shared by every object matching a selection. In the site’s invented eight-record context, selecting HighBP matches four records; all four also contain HighChol, so the closure adds that attribute.

This is a precise statement about the context, not a causal statement about blood pressure and cholesterol. The published study uses concept structure to constrain logistic regression. Keeping the context and the statistical model separate makes it easier to see what each contributes.

The consequence: interpretability becomes an objective term

The method adds a within-concept coefficient-variance penalty to logistic loss. Related coefficients are encouraged toward coherence rather than being explained only after an unconstrained model has been fitted. This is a structural modeling choice, with a trade-off that belongs in evaluation.

The lab illustrates the direction of that pull using chosen starting coefficients and a closure-strength slider. It does not solve the published optimization problem. Only coefficients belonging to the selected closed concept move; a change in the toy variance must not be mistaken for an improvement in held-out performance.

The table does not have one universal winner

The reported held-out table makes the trade-off concrete. FCA has precision 0.7094 and F1 0.5564. Logistic regression and gradient boosting each have AUC 0.8462, compared with FCA’s 0.8095. Gradient boosting has the lowest reported Brier score, 0.0715, compared with FCA’s 0.0780.

Those measurements answer different questions. A threshold-sensitive precision result is not an AUC result, and a discrimination result is not by itself a calibration or decision-utility result. The lab keeps this table fixed even while the illustrative coefficients move.

• Read precision together with recall and the thresholding protocol.
• Inspect calibration-sensitive scores alongside ranking performance.
• Treat structural readability as a property to examine, not proof of clinical readiness.

What the table check can verify

The downloadable Python check validates the reported metric ranges, finds the best value for each metric, and re-renders all four models on common 0-to-1 scales. It is useful for checking transcription and comparison logic. It is not an independent fit on patient-level data.

The study’s retrospective, survey-derived setting remains a limitation. A readable coefficient structure does not remove sampling bias, establish causality, or demonstrate prospective clinical benefit. Full reproduction requires the archived implementation and the original data and evaluation procedures.