Better together? Statistical learning in models made of modules

TL;DR

This paper explores the advantages of modular statistical models over full models in situations with heterogeneous data and potential misspecification, providing criteria to guide the choice between them.

Contribution

It introduces principled criteria for selecting modular versus full-model approaches in complex, misspecified settings across various applied fields.

Findings

Modular approaches can prevent contamination from misspecified modules.

Criteria for choosing between modular and full models are proposed.

Modular methods are advantageous in many applied statistical contexts.

Abstract

In modern applications, statisticians are faced with integrating heterogeneous data modalities relevant for an inference, prediction, or decision problem. In such circumstances, it is convenient to use a graphical model to represent the statistical dependencies, via a set of connected "modules", each relating to a specific data modality, and drawing on specific domain expertise in their development. In principle, given data, the conventional statistical update then allows for coherent uncertainty quantification and information propagation through and across the modules. However, misspecification of any module can contaminate the estimate and update of others, often in unpredictable ways. In various settings, particularly when certain modules are trusted more than others, practitioners have preferred to avoid learning with the full model in favor of approaches that restrict the information propagation between modules, for example by restricting propagation to only particular directions along the edges of the graph. In this article, we investigate why these modular approaches might be preferable to the full model in misspecified settings. We propose principled criteria to choose between modular and full-model approaches. The question arises in many applied settings, including large stochastic dynamical systems, meta-analysis, epidemiological models, air pollution models, pharmacokinetics-pharmacodynamics, and causal inference with propensity scores.