# Better together? Statistical learning in models made of modules

arXiv: https://arxiv.org/abs/1708.08719 · HTML: https://mlsanity.com/paper/1708.08719/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Aug 2017.

## Built on by (most cited first, 6 of 6)

- [EdgeBench: Unveiling Scaling Laws of Learning from Real-World Environments](https://mlsanity.com/paper/2607.05155/) (2026)
- [Shrinkage Bayesian Causal Forests for Heterogeneous Treatment Effects Estimation](https://mlsanity.com/paper/2102.06573/) (2021)
- [Uncertainty Quantification and Propagation in Surrogate-based Bayesian Inference](https://mlsanity.com/paper/2312.05153/) (2023)
- [Scalable Semi-Modular Inference with Variational Meta-Posteriors](https://mlsanity.com/paper/2204.00296/) (2022)
- [Bayesian Estimation of Causal Effects Using Proxies of a Latent Interference Network](https://mlsanity.com/paper/2505.08395/) (2025)
- [Bayesian X-Learner: Calibrated Posterior Inference for Heterogeneous Treatment Effects under Heavy-Tailed Outcomes](https://mlsanity.com/paper/2604.27394/) (2026)

## Abstract (arXiv)

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.