Vertical federated learning (VFL) has emerged as a paradigm for collaborative
model estimation across multiple clients, each holding a distinct set of
covariates. This paper introduces the first comprehensive framework for fitting
Bayesian models in the VFL setting. We propose a novel approach that leverages
data augmentation techniques to transform VFL problems into a form compatible
with existing Bayesian federated learning algorithms. We present an innovative
model formulation for specific VFL scenarios where the joint likelihood
factorizes into a product of client-specific likelihoods. To mitigate the
dimensionality challenge posed by data augmentation, which scales with the
number of observations and clients, we develop a factorized amortized
variational approximation that achieves scalability independent of the number
of observations. We showcase the efficacy of our framework through extensive
numerical experiments on logistic regression, multilevel regression, and a
novel hierarchical Bayesian split neural net model. Our work paves the way for
privacy-preserving, decentralized Bayesian inference in vertically partitioned
data scenarios, opening up new avenues for research and applications in various
domains.

该研究提出了第一个用于垂直联合学习（VFL）中贝叶斯模型拟合的全面框架，通过数据增强技术将 VFL 问题转化为与现有贝叶斯联合学习算法兼容的形式，并开创了在垂直分区数据场景中进行隐私保护、去中心化贝叶斯推断的新研究方向与应用领域。

通过数据增强和摊销推理实现可扩展的垂直联邦学习

Scalable Vertical Federated Learning via Data Augmentation and Amortized  Inference

In this study, we explore the emergence of symbols during interactions
between individuals through an experimental semiotic study. Previous studies
investigate how humans organize symbol systems through communication using
artificially designed subjective experiments. In this study, we have focused on
a joint attention-naming game (JA-NG) in which participants independently
categorize objects and assign names while assuming their joint attention.
In the theory of the Metropolis-Hastings naming game (MHNG), listeners accept
provided names according to the acceptance probability computed using the
Metropolis-Hastings (MH) algorithm. The theory of MHNG suggests that symbols
emerge as an approximate decentralized Bayesian inference of signs, which is
represented as a shared prior variable if the conditions of MHNG are satisfied.
This study examines whether human participants exhibit behavior consistent
with MHNG theory when playing JA-NG. By comparing human acceptance decisions of
a partner's naming with acceptance probabilities computed in the MHNG, we
tested whether human behavior is consistent with the MHNG theory. The main
contributions of this study are twofold. First, we reject the null hypothesis
that humans make acceptance judgments with a constant probability, regardless
of the acceptance probability calculated by the MH algorithm. This result
suggests that people followed the acceptance probability computed by the MH
algorithm to some extent. Second, the MH-based model predicted human
acceptance/rejection behavior more accurately than the other four models:
Constant, Numerator, Subtraction, and Binary. This result indicates that symbol
emergence in JA-NG can be explained using MHNG and is considered an approximate
decentralized Bayesian inference.

研究人员通过实验符号学研究探索个体之间交互中符号的出现。该研究对主动注意并称呼游戏进行了研究，并比较了人类接受概率和通过 Metropolis-Hastings 算法计算的接受概率的差异。研究表明，在 JA-NG 下进行符号出现的 MHNG 模型可以解释人类的行为，并认为这是一种近似的分散式贝叶斯推断。