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.

通过神经网络参数化样条估计条件密度的SPICE方法是一种新的与可靠统计覆盖保证相容的一致性回归方法，具有普遍逼近和最优性结果，适用于两种高效计算的一致性评分，能够提供较小的平均预测区间并保证最佳条件覆盖。

优化和高效预测集的合规化深度样条