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arXiv · 2311.00774

Conformalized Deep Splines for Optimal and Efficient Prediction Sets

Nathaniel Diamant·Ehsan Hajiramezanali·Tommaso Biancalani·Gabriele Scalia
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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 validated by our experiments. SPICE is compatible with two different efficient-to-compute conformal scores, one oracle-optimal for marginal coverage (SPICE-ND) and the other asymptotically optimal for 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.

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Nathaniel Diamant, Ehsan Hajiramezanali, Tommaso Biancalani, Gabriele Scalia. 2023-11-01. Conformalized Deep Splines for Optimal and Efficient Prediction Sets. https://arxiv.org/abs/2311.00774

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