Distribution-Free Prediction Sets for Two-Layer Hierarchical Models

We consider the problem of constructing distribution-free prediction sets for data from two-layer hierarchical distributions. For iid data, can be constructed using method conformal prediction. The validity hinges on exchangeability which does not hold when groups observations come distinct distributions, such as multiple each patient in a medical database. extend methods to setting. develop CDF pooling, single subsampling, and repeated subsampling approaches construct unsupervised supervised settings. compare these terms coverage average set size. If asymptotic is acceptable, we recommend pooling its balance between empirical desire guarantees, then approach. Supplementary materials this article are available online.