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This paper constructs bounds on the minimax risk under loss functions when statistical estimation is performed in a distributed environment and with communication constraints. We treat this problem using techniques from information theory and communication complexity. In many cases our bounds rely crucially on metric entropy conditions and the classical reduction from estimation to testing. A number of examples exhibit how bounds on the minimax risk play out in practice. We also study distributed statistical estimation problems in the context of PAC-learnability and derive explicit algorithms for solving classical problems. We study the communication complexity of these algorithms.
Senior Honors Thesis. Official advisor: Peter Winkler. De facto advisor: Peter Doyle.
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James A. Brofos, "Communication Complexity of Distributed Statistical Algorithms." Dartmouth Computer Science Technical Report TR2015-777, May 2015.
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