Rate-Loss Regions for Polynomial Regression with Side Information

Jiahui Wei (1, 2, 3, 4, 5) , Philippe Mary (1, 2, 3) , Elsa Dupraz (5, 4)

1 INSA Rennes - Institut National des Sciences Appliquées - Rennes
2 UR - Université de Rennes
3 IETR - Institut d'Électronique et des Technologies du numéRique
4 Lab-STICC_CODES - Equipe CODES
5 IMT Atlantique - MEE - Département Mathematical and Electrical Engineering

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.

Mots clés: Information theory; source coding; statistical learning; rate-distortion theory; generalization error

Domaines: Théorie de l'information et codage [math.IT]

Jiahui Wei, Philippe Mary, Elsa Dupraz. Rate-Loss Regions for Polynomial Regression with Side Information. International Zurich Seminar on Information and Communication (IZS), Mar 2024, Zurich, Switzerland. ⟨hal-04578256⟩