A Stable Distance Persistence Homology for Dynamic Bayesian Network Clustering

• URL: http://arxiv.org/abs/2605.11226v1
• Date: Mon, 11 May 2026 20:43:30 GMT
• Title: A Stable Distance Persistence Homology for Dynamic Bayesian Network Clustering
• Abstract summary: We introduce a topological approach to how variables organize and change over time in a dynamic Bayesian network.<n>Applying persistent homology to a DBG produces a barcode, which records the merging and disappearance of connected groups of strongly dependent variables.<n>This yields a principled and noise-resistant summary of how dependency structure evolves in a dynamic Bayesian network.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 Mémoli, 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.

Related papers

• Graph2TS: Structure-Controlled Time Series Generation via Quantile-Graph VAEs [1.0499611180329804]
  We propose a structure-residual perspective on time-series generation, viewing temporal data as the combination of a structural backbone and residual dynamics.<n>By conditioning generation on structure rather than labels or metadata, the model preserves global temporal organization while enabling controlled variation.<n> Experiments on diverse datasets, including sunspot, electricity load, ECG, and EEG signals, demonstrate improved distributional fidelity, temporal alignment, and representativeness compared to diffusion- and GAN-based baselines.
  arXiv  Detail & Related papers  (2026-03-20T14:12:11Z)
• Topology Identification and Inference over Graphs [61.06365536861156]
  Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks.<n>This chapter provides an overview of graph topology identification and statistical inference methods for multidimensional data.
  arXiv  Detail & Related papers  (2025-12-11T00:47:09Z)
• Unsupervised Online 3D Instance Segmentation with Synthetic Sequences and Dynamic Loss [52.28880405119483]
  Unsupervised online 3D instance segmentation is a fundamental yet challenging task.<n>Existing methods, such as UNIT, have made progress in this direction but remain constrained by limited training diversity.<n>We propose a new framework that enriches the training distribution through synthetic point cloud sequence generation.
  arXiv  Detail & Related papers  (2025-09-27T08:53:27Z)
• Learning Discrete Bayesian Networks with Hierarchical Dirichlet Shrinkage [52.914168158222765]
  We detail a comprehensive Bayesian framework for learning DBNs.<n>We give a novel Markov chain Monte Carlo (MCMC) algorithm utilizing parallel Langevin proposals to generate exact posterior samples.<n>We apply our methodology to uncover prognostic network structure from primary breast cancer samples.
  arXiv  Detail & Related papers  (2025-09-16T17:24:35Z)
• PowerGrow: Feasible Co-Growth of Structures and Dynamics for Power Grid Synthesis [75.14189839277928]
  We present PowerGrow, a co-generative framework that significantly reduces computational overhead while maintaining operational validity.<n> Experiments across benchmark settings show that PowerGrow outperforms prior diffusion models in fidelity and diversity.<n>This demonstrates its ability to generate operationally valid and realistic power grid scenarios.
  arXiv  Detail & Related papers  (2025-08-29T01:47:27Z)
• Time Series Domain Adaptation via Latent Invariant Causal Mechanism [28.329164754662354]
  Time series domain adaptation aims to transfer the complex temporal dependence from the labeled source domain to the unlabeled target domain.<n>Recent advances leverage the stable causal mechanism over observed variables to model the domain-invariant temporal dependence.<n>However, modeling precise causal structures in high-dimensional data, such as videos, remains challenging.
  arXiv  Detail & Related papers  (2025-02-23T16:25:58Z)
• Structural Entropy Guided Probabilistic Coding [52.01765333755793]
  We propose a novel structural entropy-guided probabilistic coding model, named SEPC.<n>We incorporate the relationship between latent variables into the optimization by proposing a structural entropy regularization loss.<n> Experimental results across 12 natural language understanding tasks, including both classification and regression tasks, demonstrate the superior performance of SEPC.
  arXiv  Detail & Related papers  (2024-12-12T00:37:53Z)
• SiBBlInGS: Similarity-driven Building-Block Inference using Graphs across States [9.827587981833053]
  We present a framework for Similarity-driven Building Block Inference using Graphs across States (SiBBlInGS) SiBBlInGS offers a graph-based dictionary learning approach for discovering sparse BBs along with their temporal traces. We demonstrate SiBBlInGS's ability to reveal insights into complex phenomena as well as its robustness to noise and missing samples.
  arXiv  Detail & Related papers  (2023-06-07T22:41:04Z)
• Bayesian Structure Learning with Generative Flow Networks [85.84396514570373]
  In Bayesian structure learning, we are interested in inferring a distribution over the directed acyclic graph (DAG) from data. Recently, a class of probabilistic models, called Generative Flow Networks (GFlowNets), have been introduced as a general framework for generative modeling. We show that our approach, called DAG-GFlowNet, provides an accurate approximation of the posterior over DAGs.
  arXiv  Detail & Related papers  (2022-02-28T15:53:10Z)
• Recursive Bayesian Networks: Generalising and Unifying Probabilistic Context-Free Grammars and Dynamic Bayesian Networks [0.0]
  Probabilistic context-free grammars (PCFGs) and dynamic Bayesian networks (DBNs) are widely used sequence models with complementary strengths and limitations. We present Recursive Bayesian Networks (RBNs), which generalise and unify PCFGs and DBNs, combining their strengths and containing both as special cases.
  arXiv  Detail & Related papers  (2021-11-02T19:21:15Z)
• Recurrent Dirichlet Belief Networks for Interpretable Dynamic Relational Data Modelling [29.138765941440145]
  Dirichlet Belief Network(DirBN) has been recently proposed as a promising approach in learning interpretable deep latent representations for objects. We propose a deep dynamic probabilistic framework -- the Recurrent Dirichlet Belief Network(Recurrent-DBN) -- to study interpretable hidden structures from dynamic relational data.
  arXiv  Detail & Related papers  (2020-02-24T13:40:24Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.