We extend the celebrated sliced inverse regression to address the challenges of decentralized data, prioritizing privacy and communication efficiency. Our approach, federated sliced inverse regression (FSIR), facilitates collaborative estimation of the sufficient dimension reduction subspace among multiple clients, solely sharing local estimates to protect sensitive datasets from exposure. To guard against potential adversary attacks, FSIR further employs diverse perturbation strategies, including a novel multivariate Gaussian mechanism that guarantees differential privacy at a low cost of statistical accuracy. Additionally, FSIR naturally incorporates a collaborative variable screening step, enabling effective handling of high-dimensional client data. Theoretical properties of FSIR are established for both low-dimensional and high-dimensional settings, supported by extensive numerical experiments and real data analysis.

翻译：我们将经典的切片逆回归方法扩展至去中心化数据场景，着重解决隐私保护与通信效率问题。所提出的联邦切片逆回归（FSIR）框架支持多客户端协同估计充分降维子空间，各客户端仅共享局部估计值以保护敏感数据免于泄露。为抵御潜在对手攻击，FSIR进一步采用多种扰动策略，包括一种新颖的多变量高斯机制，在牺牲较低统计精度的前提下实现差分隐私保护。此外，FSIR自然融合协同变量筛选步骤，可有效处理高维客户端数据。本文建立了FSIR在低维与高维场景下的理论性质，并通过大量数值实验与真实数据分析验证其有效性。