Distributed Selective Inference for Quantile Regression

2026-08-13

AI Summary

This work addresses the computational and statistical challenges of post-selection inference in high-dimensional quantile regression by proposing the first distributed selective inference framework. The method innovatively integrates a response proxy strategy with randomized Lasso to transform the nonsmooth quantile loss into a penalized least squares problem. By precisely characterizing the selection event via KKT conditions, it enables efficient inference with only three rounds of communication. Under standard regularity conditions, the asymptotic validity of the proposed inference procedure is rigorously established. Extensive simulations and empirical analyses further demonstrate its superior finite-sample performance.

Abstract

We propose a distributed selective inference framework tailored for high-dimensional quantile regression. To enable valid post-selection inference in this context, we address the computational challenge posed by the non-smooth quantile loss via a response-surrogation strategy. This strategy transforms the problem into a penalized least-squares formulation, thereby facilitating the application of distributed selective inference. For valid post-selection inference, a randomized procedure is introduced, in which the Lasso selection event is characterized through the associated Karush-Kuhn-Tucker conditions and the conditional distribution of the aggregated estimator is derived given the selection event. The resulting algorithm requires only three rounds of communication between local machines and the central server. Under standard regularity conditions, we establish the asymptotic validity of the proposed procedure and develop a large-deviation approximation to the selective likelihood for computationally tractable implementation. Simulation studies and a real-data application demonstrate the satisfactory finite-sample performance of the proposed method.

Problem

• distributed inference
• selective inference
• quantile regression
• high-dimensional statistics
• post-selection inference

Innovation

• distributed selective inference
• quantile regression
• response surrogation
• post-selection inference
• randomized Lasso