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.

翻译：在面向目标通信的背景下，本文研究了在压缩数据上执行学习任务时可实现的码率与泛化误差区域。该研究聚焦于分布式场景：信源经压缩后通过无噪信道传输至接收端，接收端在解码器可利用边信息的辅助下执行多项式回归。本文给出了渐近的码率-泛化误差区域，并将分析扩展至非渐近情形。此外，本文还探究了在通信约束下多项式回归与数据重构之间的渐近权衡。所提出的可实现方案被证明能够达到最小泛化误差以及最优的率-失真区域。