Approximate selective inference via maximum likelihood

Abstract

This article considers a conditional approach to selective inference via approximate maximum likelihood for data described by Gaussian models. There are two important considerations in adopting a post-selection inferential perspective. While one of them concerns the effective use of information in data, the other aspect deals with the computational cost of adjusting for selection. Our approximate proposal serves both these purposes-- (i) exploits the use of randomness for efficient utilization of left-over information from selection; (ii) enables us to bypass potentially expensive MCMC sampling from conditional distributions. At the core of our method is the solution to a convex optimization problem which assumes a separable form across multiple selection queries. This allows us to address the problem of tractable and efficient inference in many practical scenarios, where more than one learning query is conducted to define and perhaps redefine models and their corresponding parameters. Through an in-depth analysis, we illustrate the potential of our proposal and provide extensive comparisons with other post-selective schemes in both randomized and non-randomized paradigms of inference