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

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