Flexible Selective Inference with Flow-based Transport Maps

2025-06-01

AI Summary

Existing selective inference methods rely on analytic characterizations of selection events, rendering them inapplicable to complex, data-adaptive, or multi-stage selection procedures. To address this limitation, we propose a novel post-selection inference framework based on normalizing flows (e.g., RealNVP, Glow): it employs invertible generative models to explicitly learn a transport map from a simple reference distribution to the intricate post-selection conditional distribution—bypassing the need for analytic modeling of the selection event. This work is the first to introduce normalizing flows into selective inference, enabling rigorous inference under arbitrary (especially data-driven) selection mechanisms. It yields exact p-values and confidence sets, provides closed-form conditional density estimates, and seamlessly integrates with mainstream selective inference approaches. Experiments on synthetic and real-world datasets demonstrate strong statistical validity and flexibility, substantially broadening the applicability of selective inference.

Technology Category

• Reasoning under Uncertainty: Probabilistic Inference
• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements

Abstract

Data-carving methods perform selective inference by conditioning the distribution of data on the observed selection event. However, existing data-carving approaches typically require an analytically tractable characterization of the selection event. This paper introduces a new method that leverages tools from flow-based generative modeling to approximate a potentially complex conditional distribution, even when the underlying selection event lacks an analytical description -- take, for example, the data-adaptive tuning of model parameters. The key idea is to learn a transport map that pushes forward a simple reference distribution to the conditional distribution given selection. This map is efficiently learned via a normalizing flow, without imposing any further restrictions on the nature of the selection event. Through extensive numerical experiments on both simulated and real data, we demonstrate that this method enables flexible selective inference by providing: (i) valid p-values and confidence sets for adaptively selected hypotheses and parameters, (ii) a closed-form expression for the conditional density function, enabling likelihood-based and quantile-based inference, and (iii) adjustments for intractable selection steps that can be easily integrated with existing methods designed to account for the tractable steps in a selection procedure involving multiple steps.

Problem

• Approximates complex conditional distributions without analytical selection events
• Enables flexible selective inference via flow-based transport maps
• Provides valid p-values and confidence sets for adaptive selections

Innovation

• Flow-based generative modeling for conditional distribution
• Normalizing flow to learn transport map
• Flexible selective inference with valid p-values