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.
This work was partly involved in the CY Initiative of Excellence(grant “Investissements d’Avenir” ANR-16-IDEX-0008), Project “EcoDep” PSI-AAP2020-0000000013.
"Concentration inequalities for non-causal random fields." Electron. J. Statist. 16 (1) 1681 - 1725, 2022. https://doi.org/10.1214/22-EJS1992