Open Access
2022 Concentration inequalities for non-causal random fields
Rémy Garnier, Raphaël Langhendries
Author Affiliations +
Electron. J. Statist. 16(1): 1681-1725 (2022). DOI: 10.1214/22-EJS1992


Concentration inequalities are widely used for analyzing machine learning algorithms. However, the current concentration inequalities cannot be applied to some non-causal processes which appear for instance in Natural Language Processing (NLP). This is mainly due to the non-causal nature of such involved data, in the sense that each data point depends on other neighboring data points. In this paper, we establish a framework for modeling non-causal random fields and prove a Hoeffding-type concentration inequality. The proof of this result is based on a local approximation of the non-causal random field by a function of a finite number of i.i.d. random variables.

Funding Statement

This work was partly involved in the CY Initiative of Excellence(grant “Investissements d’Avenir” ANR-16-IDEX-0008), Project “EcoDep” PSI-AAP2020-0000000013.


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Rémy Garnier. Raphaël Langhendries. "Concentration inequalities for non-causal random fields." Electron. J. Statist. 16 (1) 1681 - 1725, 2022.


Received: 1 January 2021; Published: 2022
First available in Project Euclid: 15 March 2022

MathSciNet: MR4393791
zbMATH: 1490.60129
Digital Object Identifier: 10.1214/22-EJS1992

Primary: 60E15 , 60G48 , 60G60
Secondary: 62M45 , 68Q32

Keywords: Hoeffding’s inequality , learning in non-i.i.d scenarios , Learning theory , local dependence , Non-causal random fields

Vol.16 • No. 1 • 2022
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