# Memory, Communication, and Statistical Queries

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Jacob Steinhardt,
Gregory Valiant,
Stefan Wager
;

29th Annual Conference on Learning Theory, PMLR 49:1490-1516, 2016.

#### Abstract

If a concept class can be represented with a certain amount of memory, can it be efficiently learned with the same amount of memory? What concepts can be efficiently learned by algorithms that extract only a few bits of information from each example? We introduce a formal framework for studying these questions, and investigate the relationship between the fundamental resources of memory or communication and the sample complexity of the learning task. We relate our memory-bounded and communication-bounded learning models to the well-studied statistical query model. This connection can be leveraged to obtain both upper and lower bounds: we show strong lower bounds on learning parity functions with bounded communication, as well as upper bounds on solving sparse linear regression problems with limited memory.

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