# Joint Causal Structure and Cluster Discovery Using Variational Inference

arXiv: https://arxiv.org/abs/2608.22212 · HTML: https://mlsanity.com/paper/2608.22212/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 26 references that are in the map.
- First posted on arXiv 23 Aug 2026.

## Builds on (most cited first, 15 of 15)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Learning Sparse Nonparametric DAGs](https://mlsanity.com/paper/1909.13189/) (2019)
- [Bayesian Structure Learning with Generative Flow Networks](https://mlsanity.com/paper/2202.13903/) (2022)
- [Causal Consistency of Structural Equation Models](https://mlsanity.com/paper/1707.00819/) (2017)
- [DiBS: Differentiable Bayesian Structure Learning](https://mlsanity.com/paper/2105.11839/) (2021)
- [Variational Causal Networks: Approximate Bayesian Inference over Causal Structures](https://mlsanity.com/paper/2106.07635/) (2021)
- [Parameter Priors for Directed Acyclic Graphical Models and the Characterization of Several Probability Distributions](https://mlsanity.com/paper/1301.6697/) (2013)
- [Causal Effect Identification in Cluster DAGs](https://mlsanity.com/paper/2202.12263/) (2022)
- [Data Analysis with Bayesian Networks: A Bootstrap Approach](https://mlsanity.com/paper/1301.6695/) (2013)
- [Multi-Level Cause-Effect Systems](https://mlsanity.com/paper/1512.07942/) (2015)
- [Foundations of Causal Discovery on Groups of Variables](https://mlsanity.com/paper/2306.07047/) (2023)
- [Learning Structures of Bayesian Networks for Variable Groups](https://mlsanity.com/paper/1508.07753/) (2015)
- [Vector causal inference between two groups of variables](https://mlsanity.com/paper/2209.14283/) (2022)
- [Optimal Variance Control of the Score Function Gradient Estimator for Importance Weighted Bounds](https://mlsanity.com/paper/2008.01998/) (2020)

## Built on by (most cited first, 1 of 1)

- [GO-Based Clustering for Learning Cluster-Level Causal Gene Regulatory Networks](https://mlsanity.com/paper/2610.06042/) (2026)

## Abstract (arXiv)

Causal discovery aims to understand the relationships between individual random variables. In many applications, such as brain imaging and climate modeling, it is more meaningful to consider interactions among groups of variables. Existing methods assume that knowledge of such groups or clusters is explicitly available when modeling interactions. However, in practice, these clusters as well as the causal relationships among them, are latent. In this paper, we present a novel approach based on variational inference to simultaneously infer both the latent clusters and causal structures. We learn an approximate posterior over clusters and graph-structure by considering variational distributions based on categorical and Bernoulli models respectively. We derive variational lower bounds and estimation techniques to learn variational and model parameters. The effectiveness of our proposed methods for cluster and causal discovery are demonstrated on both synthetic and real data sets.