Model-free selective inference under covariate shift via weighted conformal p-values

TL;DR

This paper develops a model-free, covariate shift-aware method using weighted conformal p-values to control false positives and FDR in selective inference tasks without relying on modeling assumptions.

Contribution

It introduces weighted conformal p-values and the WCS procedure for model-free selective inference under covariate shift, controlling false discovery rate in finite samples.

Findings

WCS controls FDR in finite samples.

Method performs well in simulations and real datasets.

Applicable to causal inference, drug discovery, and outlier detection.

Abstract

This paper introduces novel weighted conformal p-values and methods for model-free selective inference. The problem is as follows: given test units with covariates $X$ and missing responses $Y$, how do we select units for which the responses $Y$ are larger than user-specified values while controlling the proportion of false positives? Can we achieve this without any modeling assumptions on the data and without any restriction on the model for predicting the responses? Last, methods should be applicable when there is a covariate shift between training and test data, which commonly occurs in practice. We answer these questions by first leveraging any prediction model to produce a class of well-calibrated weighted conformal p-values, which control the type-I error in detecting a large response. These p-values cannot be passed on to classical multiple testing procedures since they may not obey a well-known positive dependence property. Hence, we introduce weighted conformalized selection (WCS), a new procedure which controls false discovery rate (FDR) in finite samples. Besides prediction-assisted candidate selection, WCS (1) allows to infer multiple individual treatment effects, and (2) extends to outlier detection with inlier distributions shifts. We demonstrate performance via simulations and applications to causal inference, drug discovery, and outlier detection datasets.