On the rate of convergence of a deep recurrent neural network estimate in a regression problem with dependent data

TL;DR

This paper investigates how deep recurrent neural networks can efficiently estimate regression functions with dependent data, under certain regularity conditions, overcoming the curse of dimensionality.

Contribution

It introduces regularity assumptions on data dependency and shows that deep recurrent neural networks can effectively handle high-dimensional regression problems with dependent data.

Findings

Deep recurrent neural networks can circumvent the curse of dimensionality under specific conditions.

Regularity assumptions on data dependency are crucial for the convergence analysis.

Theoretical results demonstrate the effectiveness of RNNs in dependent data regression tasks.

Abstract

A regression problem with dependent data is considered. Regularity assumptions on the dependency of the data are introduced, and it is shown that under suitable structural assumptions on the regression function a deep recurrent neural network estimate is able to circumvent the curse of dimensionality.