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In vertical federated learning (FL), the features of a data sample aredistributed across multiple agents. As such, inter-agent collaboration can bebeneficial not only during the learning phase, as is the case for standardhorizontal FL, but also during the inference phase. A fundamental theoreticalquestion in this setting is how to quantify the cost, or performance loss, ofdecentralization for learning and/or inference. In this paper, we considergeneral supervised learning problems with any number of agents, and provide anovel information-theoretic quantification of the cost of decentralization inthe presence of privacy constraints on inter-agent communication within aBayesian framework. The cost of decentralization for learning and/or inferenceis shown to be quantified in terms of conditional mutual information termsinvolving features and label variables.

An Information-Theoretic Analysis of The Cost of Decentralization for Learning and Inference Under Privacy Constraints