Post-Selection Inference via Algorithmic Stability

TL;DR

This paper introduces a method for valid statistical inference after data-driven selection by leveraging algorithmic stability, particularly from differential privacy, enabling efficient corrections without complex sampling.

Contribution

It develops a novel post-selection inference approach based on algorithmic stability, providing computationally efficient corrections that do not require MCMC sampling.

Findings

Provides a stability-based correction method for post-selection inference

Achieves computational efficiency through simple corrections

Ensures valid inference after data-driven model selection

Abstract

When the target of statistical inference is chosen in a data-driven manner, the guarantees provided by classical theories vanish. We propose a solution to the problem of inference after selection by building on the framework of algorithmic stability, in particular its branch with origins in the field of differential privacy. Stability is achieved via randomization of selection and it serves as a quantitative measure that is sufficient to obtain non-trivial post-selection corrections for classical confidence intervals. Importantly, the underpinnings of algorithmic stability translate directly into computational efficiency -- our method computes simple corrections for selective inference without recourse to Markov chain Monte Carlo sampling.