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Expectation Maximization (EM) is the standard method to learn Gaussianmixtures. Yet its classic, centralized form is often infeasible, due to privacyconcerns and computational and communication bottlenecks. Prior work dealt withdata distributed by examples, horizontal partitioning, but we lack acounterpart for data scattered by features, an increasingly common scheme (e.g.user profiling with data from multiple entities). To fill this gap, we providean EM-based algorithm to fit Gaussian mixtures to Vertically Partitioned data(VP-EM). In federated learning setups, our algorithm matches the centralized EMfitting of Gaussian mixtures constrained to a subspace. In arbitrarycommunication graphs, consensus averaging allows VP-EM to run on largepeer-to-peer networks as an EM approximation. This mismatch comes fromconsensus error only, which vanishes exponentially fast with the number ofconsensus rounds. We demonstrate VP-EM on various topologies for both syntheticand real data, evaluating its approximation of centralized EM and seeing thatit outperforms the available benchmark.

Decentralized EM to Learn Gaussian Mixtures from Datasets Distributed by Features