Open Access
August 2023 Post-selection inference via algorithmic stability
Tijana Zrnic, Michael I. Jordan
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Ann. Statist. 51(4): 1666-1691 (August 2023). DOI: 10.1214/23-AOS2303


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 nontrivial 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.

Funding Statement

This work was supported by the Army Research Office (ARO) under contract W911NF-17-1-0304 as part of the collaboration between US DOD, UK MOD and UK Engineering and Physical Research Council (EPSRC) under the Multidisciplinary University Research Initiative (MURI).


We are grateful to Vitaly Feldman, Will Fithian, Moritz Hardt, Arun Kumar Kuchibhotla, and Adam Sealfon for many helpful discussions and feedback which has lead to improvements of this work. In particular, we thank Will Fithian for pointing out the advantages of the oracle definition of stability.


Download Citation

Tijana Zrnic. Michael I. Jordan. "Post-selection inference via algorithmic stability." Ann. Statist. 51 (4) 1666 - 1691, August 2023.


Received: 1 March 2022; Revised: 1 May 2023; Published: August 2023
First available in Project Euclid: 19 October 2023

Digital Object Identifier: 10.1214/23-AOS2303

Primary: 62J15
Secondary: 62F07 , 62J05

Keywords: differential privacy , Linear regression , Model selection , Post-selection inference , selective inference , stability

Rights: Copyright © 2023 Institute of Mathematical Statistics

Vol.51 • No. 4 • August 2023
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