Rate-Loss Regions for Polynomial Regression with Side Information

TL;DR

This paper characterizes the optimal rate and generalization error trade-offs in distributed polynomial regression with side information, providing asymptotic and non-asymptotic analyses and an achievable scheme.

Contribution

It introduces a comprehensive analysis of rate-generalization error regions for polynomial regression with side information, including asymptotic and non-asymptotic regimes, and proposes an optimal achievable scheme.

Findings

Achieves minimum generalization error under communication constraints

Characterizes the rate-distortion region for polynomial regression with side info

Provides asymptotic and non-asymptotic trade-off analyses

Abstract

In the context of goal-oriented communications, this paper addresses the achievable rate versus generalization error region of a learning task applied on compressed data. The study focuses on the distributed setup where a source is compressed and transmitted through a noiseless channel to a receiver performing polynomial regression, aided by side information available at the decoder. The paper provides the asymptotic rate generalization error region, and extends the analysis to the non-asymptotic regime.Additionally, it investigates the asymptotic trade-off between polynomial regression and data reconstruction under communication constraints. The proposed achievable scheme is shown to achieve the minimum generalization error as well as the optimal rate-distortion region.