Online-to-PAC generalization bounds under graph-mixing dependencies

Baptiste Abélès, Gergely Neu, Eugenio Clerico
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:3376-3384, 2025.

Abstract

Traditional generalization results in statistical learning require a training data set made of independently drawn examples. Most of the recent efforts to relax this independence assumption have considered either purely temporal (mixing) dependencies, or graph-dependencies, where non-adjacent vertices correspond to independent random variables. Both approaches have their own limitations, the former requiring a temporal ordered structure, and the latter lacking a way to quantify the strength of inter-dependencies. In this work, we bridge these two lines of work by proposing a framework where dependencies decay with graph distance. We derive generalization bounds leveraging the online-to-PAC framework, by deriving a novel concentration result and introducing an online learning framework incorporating the graph structure. The resulting high-probability generalization guarantees depend on both the mixing rate and the graph’s chromatic number.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-abeles25a, title = {Online-to-PAC generalization bounds under graph-mixing dependencies}, author = {Ab{\'e}l{\`e}s, Baptiste and Neu, Gergely and Clerico, Eugenio}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {3376--3384}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/abeles25a/abeles25a.pdf}, url = {https://proceedings.mlr.press/v258/abeles25a.html}, abstract = {Traditional generalization results in statistical learning require a training data set made of independently drawn examples. Most of the recent efforts to relax this independence assumption have considered either purely temporal (mixing) dependencies, or graph-dependencies, where non-adjacent vertices correspond to independent random variables. Both approaches have their own limitations, the former requiring a temporal ordered structure, and the latter lacking a way to quantify the strength of inter-dependencies. In this work, we bridge these two lines of work by proposing a framework where dependencies decay with graph distance. We derive generalization bounds leveraging the online-to-PAC framework, by deriving a novel concentration result and introducing an online learning framework incorporating the graph structure. The resulting high-probability generalization guarantees depend on both the mixing rate and the graph’s chromatic number.} }
Endnote
%0 Conference Paper %T Online-to-PAC generalization bounds under graph-mixing dependencies %A Baptiste Abélès %A Gergely Neu %A Eugenio Clerico %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-abeles25a %I PMLR %P 3376--3384 %U https://proceedings.mlr.press/v258/abeles25a.html %V 258 %X Traditional generalization results in statistical learning require a training data set made of independently drawn examples. Most of the recent efforts to relax this independence assumption have considered either purely temporal (mixing) dependencies, or graph-dependencies, where non-adjacent vertices correspond to independent random variables. Both approaches have their own limitations, the former requiring a temporal ordered structure, and the latter lacking a way to quantify the strength of inter-dependencies. In this work, we bridge these two lines of work by proposing a framework where dependencies decay with graph distance. We derive generalization bounds leveraging the online-to-PAC framework, by deriving a novel concentration result and introducing an online learning framework incorporating the graph structure. The resulting high-probability generalization guarantees depend on both the mixing rate and the graph’s chromatic number.
APA
Abélès, B., Neu, G. & Clerico, E.. (2025). Online-to-PAC generalization bounds under graph-mixing dependencies. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:3376-3384 Available from https://proceedings.mlr.press/v258/abeles25a.html.

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