Title: AMDCP: Adaptive Mixture Density for Conformal Prediction
Primary area: generative models
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

Abstract: We present Adaptive Mixture Density for Conformal Prediction (AMDCP), a glass-box framework that co-designs the non-conformity scoring framework with a mixture-density head. Our weight-aware component 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 weather forecasting to protein property prediction demonstrates that AMDCP's regions are sharper than state-of-the-art generative methods, while also being an order of magnitude faster at inference time. We complement these results with theory (finite-sample marginal validity; an asymptotic efficiency guarantee; and approximate group-conditional coverage) and extensive ablations under extreme distributions, model misspecification, various model architectures, 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.

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.