Post-selection inference via algorithmic stability

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.