Distribution-Free Prediction Sets for Two-Layer Hierarchical Models
针对医疗数据等分层结构数据，扩展了无分布预测集方法，提出三种构建预测集的方法，并比较其覆盖率和平均集大小。
We consider the problem of constructing distribution-free prediction sets for data from two-layer hierarchical distributions. For iid data, prediction sets can be constructed using the method of conformal prediction. The validity of conformal prediction hinges on the exchangeability of the data, which does not hold when groups of observations come from distinct distributions, such as multiple observations on each patient in a medical database. We extend conformal methods to a hierarchical setting. We develop CDF pooling, single subsampling, and repeated subsampling approaches to construct prediction sets in unsupervised and supervised settings. We compare these approaches in terms of coverage and average set size. If asymptotic coverage is acceptable, we recommend CDF pooling for its balance between empirical coverage and average set size. If we desire coverage guarantees, then we recommend the repeated subsampling approach. Supplementary materials for this article are available online.