# Modelling Heterogeneity Using Bayesian Structured Sparsity

arXiv: https://arxiv.org/abs/2103.15919 · HTML: https://mlsanity.com/paper/2103.15919/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 112 references that are in the map.
- First posted on arXiv 29 Mar 2021.

## Builds on (most cited first, 12 of 12)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Recursive Partitioning for Heterogeneous Causal Effects](https://mlsanity.com/paper/1504.01132/) (2015)
- [Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC](https://mlsanity.com/paper/1507.04544/) (2015)
- [Understanding predictive information criteria for Bayesian models](https://mlsanity.com/paper/1307.5928/) (2013)
- [Trend Filtering on Graphs](https://mlsanity.com/paper/1410.7690/) (2014)
- [Algorithms for Fitting the Constrained Lasso](https://mlsanity.com/paper/1611.01511/) (2016)
- [A concave pairwise fusion approach to subgroup analysis](https://mlsanity.com/paper/1508.07045/) (2015)
- [Efficient Implementations of the Generalized Lasso Dual Path Algorithm](https://mlsanity.com/paper/1405.3222/) (2014)
- [Multiscale spatial density smoothing: an application to large-scale radiological survey and anomaly detection](https://mlsanity.com/paper/1507.07271/) (2015)
- [Locally adaptive smoothing with Markov random fields and shrinkage priors](https://mlsanity.com/paper/1512.06505/) (2015)
- [Estimation and Inference on Nonlinear and Heterogeneous Effects](https://mlsanity.com/paper/1703.05849/) (2017)
- [Bayesian Trend Filtering](https://mlsanity.com/paper/1505.07710/) (2015)

## Abstract (arXiv)

How to estimate heterogeneity, e.g. the effect of some variable differing across observations, is a key question in political science. Methods for doing so make simplifying assumptions about the underlying nature of the heterogeneity to draw reliable inferences. This paper allows a common way of simplifying complex phenomenon (placing observations with similar effects into discrete groups) to be integrated into regression analysis. The framework allows researchers to (i) use their prior knowledge to guide which groups are permissible and (ii) appropriately quantify uncertainty. The paper does this by extending work on "structured sparsity" from a traditional penalized likelihood approach to a Bayesian one by deriving new theoretical results and inferential techniques. It shows that this method outperforms state-of-the-art methods for estimating heterogeneous effects when the underlying heterogeneity is grouped and more effectively identifies groups of observations with different effects in observational data.