Auditable unit-aware thresholds in symbolic regression via logistic-gated operators

Area of Science:

• Computational biology
• Machine learning
• Medical informatics

Background:

• Symbolic regression (SR) traditionally struggles with unit-aware thresholds crucial for clinical decisions.
• Existing SR methods lack explicit, auditable cut-points for medical applications.

Purpose of the Study:

• To introduce logistic-gated operators (LGOs) as differentiable primitives within a genetic programming SR engine.
• To enable SR to generate clinically relevant, unit-aware thresholds for decision-making.

Main Methods:

• Embedding LGOs—differentiable gates with learnable parameters—into a genetic programming SR framework.
• Training models in standardized space and mapping thresholds back to physical units for auditability.
• Evaluating LGO performance on public health (MIMIC-IV ICU, eICU, NHANES) and UCI benchmark datasets.

Main Results:

• LGOs identified clinically plausible cut-points on public health datasets, with many falling within 10-20% of guideline anchors.
• On high-risk classification tasks, LGOs achieved comparable or improved Area Under the Receiver Operating Characteristic Curve (AUROC) and calibration versus AutoScore.
• LGOs provided explicit, auditable thresholds, unlike AutoScore's point tables, and gates were pruned on smooth benchmarks, enhancing parsimony.

Conclusions:

• The proposed LGO approach enhances symbolic regression by incorporating auditable, unit-aware thresholds.
• This method yields compact, interpretable equations that can support clinical decision-making.
• LGOs offer a promising advancement for applying symbolic regression in healthcare and other domains requiring explicit thresholds.