Empirical PAC-Bayes Bounds for Markov Chains

arXiv:2509.20985 · stat.ML, cs.LG · Submitted 2025-09-25 · Read on arXiv

stat.ML, cs.LG

Submitted: 2025-09-25

Updated: 2026-03-11

Comments: To appear in the proceedings of AISTATS 2026

Journal ref: Proceedings of the 29th International Conference on Artificial Intelligence and Statistics (AISTATS), Proceedings of Machine Learning Research, 2026, vol. 300, pp. 361-369

Code: https://github.com/v-ahe/empirical-pac-bayes-markov

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Spectral Gap — 3× in this paper · explained in 5 episodes
• Core — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 13 episodes

Sources

• Generalization bounds for mixing processes via delayed online-to-PAC conversions
• Minimax optimality of deep neural networks on dependent data via PAC-Bayes bounds
• Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data
• Estimating the Mixing Coefficients of Geometrically Ergodic Markov Processes
• Estimating the Spectral Gap of a Reversible Markov Chain from a Short Trajectory
• A Note on the PAC Bayesian Theorem
• Optimistic Estimation of Convergence in Markov Chains with the Average-Mixing Time

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