Bayesian data selection

TL;DR

This paper introduces the Stein volume criterion, a Bayesian method for data and model selection that efficiently identifies relevant data features without complex nonparametric modeling, validated through simulations and biological data analysis.

Contribution

It proposes the Stein volume criterion, a novel Bayesian score for data and model selection that avoids fitting complex background models, with proven consistency and asymptotic properties.

Findings

The Stein volume criterion is computationally straightforward and effective.

It is consistent for data and model selection tasks.

Validated on single-cell RNA sequencing datasets.

Abstract

Insights into complex, high-dimensional data can be obtained by discovering features of the data that match or do not match a model of interest. To formalize this task, we introduce the "data selection" problem: finding a lower-dimensional statistic - such as a subset of variables - that is well fit by a given parametric model of interest. A fully Bayesian approach to data selection would be to parametrically model the value of the statistic, nonparametrically model the remaining "background" components of the data, and perform standard Bayesian model selection for the choice of statistic. However, fitting a nonparametric model to high-dimensional data tends to be highly inefficient, statistically and computationally. We propose a novel score for performing both data selection and model selection, the "Stein volume criterion", that takes the form of a generalized marginal likelihood with a kernelized Stein discrepancy in place of the Kullback-Leibler divergence. The Stein volume criterion does not require one to fit or even specify a nonparametric background model, making it straightforward to compute - in many cases it is as simple as fitting the parametric model of interest with an alternative objective function. We prove that the Stein volume criterion is consistent for both data selection and model selection, and we establish consistency and asymptotic normality (Bernstein-von Mises) of the corresponding generalized posterior on parameters. We validate our method in simulation and apply it to the analysis of single-cell RNA sequencing datasets using probabilistic principal components analysis and a spin glass model of gene regulation.