AMDCP: Adaptive Mixture Density for Conformal Prediction

Sriram Tolety

Keywords: mixture density networks, adaptive non-conformity score, uncertainty quantification, prediction intervals, multimodal distributions, Mahalanobis distance, coverage efficiency, regression calibration, heteroskedasticity, multimodal distributions, coverage guarantees

TL;DR: Our "glass-box" method uses a novel score on a model's internal structure for analytic, non-contiguous regions. This robust approach yields sharper sets with 10x faster inference than SOTA generative methods, as confirmed by extensive ablations.

Abstract: We present Adaptive Mixture Density for Conformal Prediction (AMDCP), a "glass-box" component-aware framework that co-designs the non-conformity scoring framework with a mixture-density head. Our weight-aware score yields analytic non-contiguous unions of ellipsoids with constant-time membership tests, preserving classical coverage guarantees while improving efficiency. A comprehensive empirical evaluation on real-world datasets from demand forecasting to protein property prediction demonstrates that AMDCP's regions are sharper than existing generative methods, while also being an order of magnitude faster at inference time and 2-3x faster in training. We complement these results with theory (finite-sample marginal validity; an asymptotic optimality guarantee; and approximate group-conditional coverage) and extensive ablations under extreme distributions, model misspecification, model backbones, and more. AMDCP turns CP into a practical tool for real-world implementation: it is valid by construction, produces shape-adaptive sharp predictive sets, and is systems-efficient for modern pipelines.

Primary Area: generative models

Submission Number: 6300