# A Stable Distance Persistence Homology for Dynamic Bayesian Network Clustering

arXiv: https://arxiv.org/abs/2605.11226 · HTML: https://mlsanity.com/paper/2605.11226/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 24 references that are in the map.
- First posted on arXiv 11 May 2026.

## Builds on (most cited first, 2 of 2)

- [Exploiting Causality for Selective Belief Filtering in Dynamic Bayesian Networks (Extended Abstract)](https://mlsanity.com/paper/1907.05850/) (2019)
- [The diameter of a stochastic matrix: A new measure for sensitivity analysis in Bayesian networks](https://mlsanity.com/paper/2407.04667/) (2024)

## Abstract (arXiv)

Dynamic Bayesian networks (DBNs) are a widely used framework for modeling systems whose probabilistic structure evolves over time. Standard inference methods focus on local conditional distributions and can miss larger-scale patterns in how dependencies between variables organize and change over time. We introduce a topological approach to this problem. To each DBN we associate a time-varying graph, called a Dynamic Bayesian Graph (DBG), by assigning to each edge a strength that measures variation in its conditional dependence across parent configurations, and retaining edges whose strength exceeds a chosen threshold. We show that this construction fits within the dynamic graph framework of Kim and M'emoli, enabling the use of tools from topological data analysis. Applying persistent homology to a DBG produces a barcode, which records the merging and disappearance of connected groups of strongly dependent variables over time. We prove that this barcode is stable: small perturbations in the conditional probability tables of the DBN lead to small changes in the resulting barcode. This yields a principled and noise-resistant summary of how dependency structure evolves in a dynamic Bayesian network.