Yaohui Lin | Searcharxiv

arXiv2026

Exact grid-free confidence-region computation from dependent p-value functions under arbitrary dependence

Repeated sample splitting, cross-fitting, conformal ensembling, and related randomized workflows often produce multiple dependent valid p-value functions for the same target. Existing p-merging theory guarantees pointwise validity under arbitrary dependence, but turning the merged output into a confidence region typically requires repeated evaluation on a grid over the parameter space. This inversion step can be computationally costly, approximation-dependent, and increasingly difficult to scale. We study when confidence regions can instead be computed exactly from split-wise regions without gridding the parameter space. Our main structural result shows that mergers induced by step calibrators form a broad exactly executable class at the region level, and a partial converse within the calibrator-induced family indicates that exact executability is closely tied to step structure. Within this class, we develop exact voting algorithms, including an adaptive multi-quantile contour aggregator that avoids pre-specifying a single order-statistic threshold while preserving finite-sample validity under arbitrary dependence. Simulation studies on repeated-split regression and conformal prediction, together with real-data regression examples, show that the proposed methods provide stable, robustness-oriented exact inference with substantial runtime gains over grid-inversion comparators. A grid-resolution benchmark shows that fixed-k voting and adaptive multi-quantile voting are essentially insensitive to inversion-grid refinement, while a multidimensional single-threshold stress test illustrates the dimensional blow-up faced by grid-inversion baselines in a simple box-geometry setting. Taken together, the results show that arbitrary-dependence contour merging can be turned into an exactly executable region-computation framework rather than merely a pointwise validity device.

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arXiv2025

Possibilistic Inferential Models for Post-Selection Inference in High-Dimensional Linear Regression

Valid uncertainty quantification after model selection remains challenging in high-dimensional linear regression, especially within the possibilistic inferential model (PIM) framework. We develop possibilistic inferential models for post-selection inference based on a regularized split possibilistic construction (RSPIM) that combines generic high-dimensional selectors with PIM validification through sample splitting. A first subsample is used to select a sparse model; ordinary least-squares refits on an independent inference subsample yield classical t/F pivots, which are then turned into consonant plausibility contours. In Gaussian linear models this leads to coor-dinatewise intervals with exact finite-sample strong validity conditional on the split and selected model, uniformly over all selectors that use only the selection data. We further analyze RSPIM in a sparse p >> n regime under high-level screening conditions, develop orthogonalized and bootstrap-based extensions for low-dimensional targets with high-dimensional nuisance, and study a maxitive multi-split aggregation that stabilizes inference across random splits while preserving strong validity. Simulations and a riboflavin gene-expression example show that calibrated RSPIM intervals are well behaved under both Gaussian and heteroskedastic errors and are competitive with state-of-the-art post-selection methods, while plausibility contours provide transparent diagnostics of post-selection uncertainty.

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