We examine an extension of the usual two-party communication mannequin through which Alice and Bob maintain likelihood distributions and over domains and , respectively. Their purpose is to estimate
to inside additive error for a bounded operate , recognized to each events. We discuss with this because the distributed estimation drawback. Particular instances of this drawback come up in a wide range of areas together with sketching, databases and studying. Our purpose is to know how the required communication scales with the communication complexity of and the error parameter .
The random sampling method — estimating the imply by averaging over random samples — requires complete communication, the place is the randomized communication complexity of . We design a brand new debiasing protocol which improves the dependence on to be linear as an alternative of quadratic. Moreover we present higher higher bounds for a number of particular lessons of capabilities, together with the Equality and Better-than capabilities. We introduce decrease certain strategies based mostly on spectral strategies and discrepancy, and present the optimality of a lot of our protocols: the debiasing protocol is tight for normal capabilities, and that our protocols for the equality and greater-than capabilities are additionally optimum. Moreover, we present that amongst full-rank Boolean capabilities, Equality is actually the best.
- †College of California, Los Angeles
- ‡ College of California, Berkeley
- § Institute for Superior Research (IAS)
