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Watson, Thomas

doi:10.4086/toc.2015.v011a001

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2018

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“…(For results about the complexity of other problems where the inputs are succinctly represented distributions, see [12,13,3,14,30,29].) [2,27,9] studied the complexity of statistical distance estimation when an algorithm is only given black-box access to oracles that produce samples from the distributions specified by x and y.…”

Section: Introductionmentioning

confidence: 99%

Communication Complexity of Statistical Distance

Watson

2018

ACM Trans. Comput. Theory

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We prove nearly matching upper and lower bounds on the randomized communication complexity of the following problem: Alice and Bob are each given a probability distribution over n elements, and they wish to estimate within ±ε the statistical (total variation) distance between their distributions. For some range of parameters, there is up to a log n factor gap between the upper and lower bounds, and we identify a barrier to using information complexity techniques to improve the lower bound in this case. We also prove a side result that we discovered along the way: the randomized communication complexity of n -bit Majority composed with n -bit Greater Than is Θ ( n log n ).

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