Conformalized Deep Splines for Optimal and Efficient Prediction Sets
Nathaniel Diamant, Ehsan Hajiramezanali, Tommaso Biancalani, Gabriele Scalia
Abstract
Uncertainty estimation is critical in high-stakes machine learning applications. One effective way to estimate uncertainty is conformal prediction, which can provide predictive inference with statistical coverage guarantees. We present a new conformal regression method, Spline Prediction Intervals via Conformal Estimation (SPICE), that estimates the conditional density using neural- network-parameterized splines. We prove universal approximation and optimality results for SPICE, which are empirically reflected by our experiments. SPICE is compatible with two different efficient-to- compute conformal scores, one designed for size-efficient marginal coverage (SPICE-ND) and the other for size-efficient conditional coverage (SPICE-HPD). Results on benchmark datasets demonstrate SPICE-ND models achieve the smallest average prediction set sizes, including average size reductions of nearly 50% for some datasets compared to the next best baseline. SPICE-HPD models achieve the best conditional coverage compared to baselines. The SPICE implementation is made available.
BibTeX
@InProceedings{pmlr-v238-diamant24a,
title = {Conformalized Deep Splines for Optimal and Efficient Prediction Sets},
author = {Diamant, Nathaniel and Hajiramezanali, Ehsan and Biancalani, Tommaso and Scalia, Gabriele},
booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics},
pages = {1657--1665},
year = {2024},
editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen},
volume = {238},
series = {Proceedings of Machine Learning Research},
month = {02--04 May},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v238/diamant24a/diamant24a.pdf},
url = {https://proceedings.mlr.press/v238/diamant24a.html},
abstract = {Uncertainty estimation is critical in high-stakes machine learning applications. One effective way to estimate uncertainty is conformal prediction, which can provide predictive inference with statistical coverage guarantees. We present a new conformal regression method, Spline Prediction Intervals via Conformal Estimation (SPICE), that estimates the conditional density using neural- network-parameterized splines. We prove universal approximation and optimality results for SPICE, which are empirically reflected by our experiments. SPICE is compatible with two different efficient-to- compute conformal scores, one designed for size-efficient marginal coverage (SPICE-ND) and the other for size-efficient conditional coverage (SPICE-HPD). Results on benchmark datasets demonstrate SPICE-ND models achieve the smallest average prediction set sizes, including average size reductions of nearly 50% for some datasets compared to the next best baseline. SPICE-HPD models achieve the best conditional coverage compared to baselines. The SPICE implementation is made available.}
}