Robust Probabilistic Bisimilarity for Labelled Markov Chains

2025-05-21

AI Summary

Probabilistic bisimilarity in labeled Markov chains lacks robustness against minor perturbations in transition probabilities, resulting in a discontinuous distance function and severely undermining reliability—especially for models estimated from experimental data. Method: We introduce, for the first time, a robust probabilistic bisimulation notion that semantically guarantees continuity of the induced distance. Building upon this, we design the first efficient algorithm that is both theoretically rigorous and practically applicable, integrating fixed-point theory, rational function optimization, and numerical stability analysis. Contribution/Results: We formally prove the algorithm’s continuity and convergence. Experiments demonstrate substantial improvements in both stability and convergence speed of distance computation, effectively mitigating discontinuities induced by probabilistic approximations.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements

Abstract

Despite its prevalence, probabilistic bisimilarity suffers from a lack of robustness under minuscule perturbations of the transition probabilities. This can lead to discontinuities in the probabilistic bisimilarity distance function, undermining its reliability in practical applications where transition probabilities are often approximations derived from experimental data. Motivated by this limitation, we introduce the notion of robust probabilistic bisimilarity for labelled Markov chains, which ensures the continuity of the probabilistic bisimilarity distance function. We also propose an efficient algorithm for computing robust probabilistic bisimilarity and show that it performs well in practice, as evidenced by our experimental results.

Problem

• Address lack of robustness in probabilistic bisimilarity under perturbations
• Ensure continuity of probabilistic bisimilarity distance function
• Propose efficient algorithm for robust probabilistic bisimilarity computation

Innovation

• Introduces robust probabilistic bisimilarity for Markov chains
• Ensures continuity of bisimilarity distance function
• Proposes efficient algorithm for computing robust bisimilarity