Statistical learning for $\psi$-weakly dependent processes

TL;DR

This paper studies statistical learning for $$-weakly dependent processes, establishing consistency, generalization bounds, and near-i.i.d. learning rates, with applications to time series prediction and causal models.

Contribution

It introduces a unified framework for weak dependence conditions and proves learning guarantees for empirical risk minimization in this setting.

Findings

Consistency of empirical risk minimization established.

Generalization bounds derived for $$-weakly dependent processes.

Learning rate close to $O(n^{-1/2})$ for certain hypothesis classes.

Abstract

We consider statistical learning question for $\psi$-weakly dependent processes, that unifies a large class of weak dependence conditions such as mixing, association,$\cdots$ The consistency of the empirical risk minimization algorithm is established. We derive the generalization bounds and provide the learning rate, which, on some H{\"o}lder class of hypothesis, is close to the usual $O(n^{-1/2})$ obtained in the {\it i.i.d.} case. Application to time series prediction is carried out with an example of causal models with exogenous covariates.