Title: Interaction improves distributed nonparametric estimation
Abstract: We consider a natural distributed nonparametric estimation problem with vertically partitioned datasets. Under a given budget of communication cost or constraint on the information leakage, we determine the asymptotic minimax risks for estimating the density at a given point, which reveals that interactive protocols strictly improves over one-way communication protocols. While many recent papers in statistics have studied distributed learning for horizontally partitioned datasets, the vertical setting in the present work requires more sophisticated information-theoretic arguments. In particular, our novel estimation scheme in the interactive setting is constructed by carefully identifying a set of auxiliary random variables. The result also implies that interactive protocols strictly improve over one-way for biased binary sequences in the Gap-Hamming problem. (arXiv 2107.00211)
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