Optimal Algorithms and Lower Bounds for Testing Closeness of Structured Distributions
IEEE Symposium on Foundations of Computer Science(2015)
摘要
We give a general unified method that can be used for L1 closeness testing of a wide range of university structured distribution families. More specifically, we design a sample optimal and computationally efficient algorithm for testing the equivalence of two unknown (potentially arbitrary) university distributions under the Ak-distance metric: Given sample access to distributions with density functions p, q: I → R, we want to distinguish between the cases that p=q and |p-q| Ak ≥ ε with probability at least 2/3. We show that for any k ≥2, >0, the optimal sample complexity of the Ak-closeness testing problem is Θ(max{k4/5/Θ6/5, k1/2/Θ2). This is the first o(k) sample algorithm for this problem, and yields new, simple L1 closeness testers, in most cases with optimal sample complexity, for broad classes of structured distributions.
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关键词
distribution testing,testing closeness,structured distributions
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