P-value combinations and application to Conformal Prediction

Speaker: Matteo Gasparin, University of Padova, Italy

Abstract: The problem of combining p-values is an old and fundamental one, and the classic assumption of independence is often violated or unverifiable in many applications. There are many well-known rules that can combine a set of arbitrarily dependent p-values (for the same hypothesis) into a single p-value. We show that essentially all these existing rules can be strictly improved when the p-values are exchangeable, or when external randomization is allowed (or both). For example, we derive randomized and/or exchangeable improvements of well known rules like "twice the median" and "twice the average'", as well as geometric and harmonic means. Our work also improves rules for combining arbitrarily dependent p-values, since the latter becomes exchangeable if they are presented to the analyst in a random order. The main technical advance is to show that all existing combination rules can be obtained by calibrating the p-values to e-values (using an α-dependent calibrator), averaging those e-values, converting to a level-α test using Markov's inequality, and finally obtaining p-values by combining this family of tests; the improvements are delivered via recent randomized and exchangeable variants of Markov's inequality. In the final part, I will explain how these results can be used to improve the statistical efficiency of cross-conformal prediction.

Biography: Matteo is a PhD student in Statistical Sciences at the University of Padova, advised by Professor Bruno Scarpa. He spent a year as a visiting research scholar at the Department of Statistics and Data Science at Carnegie Mellon University, working with Aaditya Ramdas and his research group. He obtained both his Bachelor's and Master's degrees in Statistical Science from the University of Padova.

Host: Prof.ssa Antonietta Mira

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