Conformalized Deep Splines for Optimal and Efficient Prediction Sets

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.