 has emerged as a paradigm for collaborative model estimation across multiple clients%2C 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%2C which scales with the number of observations and clients%2C 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%2C multilevel regression%2C and a novel hierarchical Bayesian split neural net model. Our work paves the way for privacy-preserving%2C decentralized Bayesian inference in vertically partitioned data scenarios%2C opening up new avenues for research and applications in various domains.?quality=80&w=1200)
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- GitHub - Pa-wan/Vertical-Federated-Learning
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