Distributed Simulation and Distributed Inference

Understand

Independent samples from an unknown probability distribution $\bf p$ on a domain of size $k$ are distributed across $n$ players, with each player holding one sample.

• Each player can communicate $\ell$ bits to a central referee in a simultaneous message passing model of communication to help the referee infer a property of the unknown $\bf p$.
• What is the least number of players for inference required in the communication-starved setting of $\ell<\log k$? We begin by exploring a general &#34;simulate-and-infer&#34; strategy for such inference problems where the center simulates the desired number of samples from the unknown distribution and applies standard inference algorithms for the collocated setting.
• Our first result shows that for $\ell<\log k$ perfect simulation of even a single sample is not possible.