Distributed Simulation and Distributed Inference

04/19/2018

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by   Jayadev Acharya, et al.

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Independent samples from an unknown probability distribution p on a domain of size k are distributed across n players, with each player holding one sample. Each player can communicate ℓ bits to a central referee in a simultaneous message passing (SMP) model of communication to help the referee infer a property of the unknown p. When ℓ≥ k bits, the problem reduces to the well-studied collocated case where all the samples are available in one place. In this work, we focus on the communication-starved setting of ℓ < k, in which the landscape may change drastically. We propose a general formulation for inference problems in this distributed setting, and instantiate it to two prototypical inference questions: learning and uniformity testing.