In this paper, we consider a wireless federated inference scenario in which devices and a server share a pre-trained machine learning model. The devices communicate statistical information about their local data to the server over a common wireless channel, aiming to enhance the quality of the inference decision at the server. Recent work has introduced federated conformal prediction (CP), which leverages devices-to-server communication to improve the reliability of the server's decision. With federated CP, devices communicate to the server information about the loss accrued by the shared pre-trained model on the local data, and the server leverages this information to calibrate a decision interval, or set, so that it is guaranteed to contain the correct answer with a pre-defined target reliability level. Previous work assumed noise-free communication, whereby devices can communicate a single real number to the server. In this paper, we study for the first time federated CP in a wireless setting. We introduce a novel protocol, termed wireless federated conformal prediction (WFCP), which builds on type-based multiple access (TBMA) and on a novel quantile correction strategy. WFCP is proved to provide formal reliability guarantees in terms of coverage of the predicted set produced by the server. Using numerical results, we demonstrate the significant advantages of WFCP against digital implementations of existing federated CP schemes, especially in regimes with limited communication resources and/or large number of devices.

翻译：本文考虑一种无线联邦推理场景，其中设备与服务器共享一个预训练机器学习模型。设备通过公共无线信道向服务器传递其本地数据的统计信息，旨在提升服务器推理决策的质量。近期研究引入了联邦共形预测（CP）方法，利用设备到服务器的通信来增强服务器决策的可靠性。在联邦CP中，设备向服务器传递共享预训练模型在本地数据上产生的损失信息，服务器利用这些信息校准决策区间（或集合），使其能够以预设的目标可靠度保证包含正确答案。此前研究假设无噪声通信，允许设备向服务器传输单个实数。本文首次在无线环境下研究联邦CP问题，提出一种名为无线联邦共形预测（WFCP）的新协议。该协议基于类型多址接入（TBMA）及一种新型分位数校正策略构建，被证明能为服务器生成的预测集合提供严格的覆盖可靠性保证。数值结果表明，相较于现有联邦CP方案的数字实现，WFCP在通信资源有限和/或设备数量庞大的场景中具有显著优势。