A1426
Title: Conformalized method for empirical bayes normal mean inference problem with heteroscedastic variance
Authors: Kwangok Seo - Inha University (Korea, South) [presenting]
Abstract: The normal mean inference problem is studied, which involves simultaneous testing of the means of many normal distributions. This problem has been extensively studied within the empirical Bayes (EB) framework. However, the reliability of most EB methods heavily depends on two key conditions: (i) the prior distribution is correctly specified, and (ii) it can be accurately estimated. In practice, both conditions are difficult to satisfy, and it is often unclear whether they hold in a given application. To overcome these limitations, a new algorithm is proposed, called COIN (conformal inference for normal mean inference problem). Unlike traditional empirical Bayes approaches, COIN produces decision rules whose validity does not depend on the correct specification or accurate estimation of the prior. It is theoretically proven that COIN asymptotically controls the false discovery rate at the nominal level, even in the presence of prior misspecification or estimation errors. Since the COIN algorithm requires an external training dataset to estimate the prior distribution and conformity score function, two data-splitting strategies are introduced---sample-splitting and feature-splitting---for the case where such external data are unavailable. Theoretical guarantees are provided for the data-splitting strategies and their effectiveness is demonstrated through extensive numerical studies and three real data examples.
