Conformal Inference for Random Objects

Music City Center 

An inferential toolkit for analyzing object-valued responses, i.e., data situated in general metric spaces, paired with Euclidean predictors, is of interest for many statistical applications. We develop a conformal approach that utilizes conditional optimal transport costs for distance profiles. Distance profiles correspond to one-dimensional distributions of probability mass falling into balls of increasing radius. The average transport cost to transport a given distance profile to all other distance profiles is the basis for the proposed conditional profile scores. The distribution of conditional profile average transport costs serves as conformity score for general metric space-valued responses, facilitating the construction of prediction sets by the split conformal algorithm. We derive the uniform convergence rate of the proposed conformity score estimators and establish asymptotic conditional validity for the resulting prediction sets. The utility of the proposed conditional profile score is demonstrated through its finite sample performance in various metric spaces, with network data from New York taxi trips and compositional data on energy sourcing of U.S. states. This talk is based on joint work with Hang Zhou, UC Davis.

Conformity Score

Metric Statistics

Random Objects

Distance Profiles

Optimal Transport

Networks