2019/02/01 by Joseph Lam-Weil, Lam-Weil, Joseph, Alexandra Carpentier +3
Computer Science · Mathematics · #62F03 #62F35 #62G10 #FOS: Computer and information sciences #FOS: Mathematics #G.3 #I.2.6 #Information Theory (cs.IT) #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms #Markov Chains and Monte Carlo Methods #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1902.01219
openalex publication_date 2019/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We consider the closeness testing problem for discrete distributions. The goal is to distinguish whether two samples are drawn from the same unspecified distribution, or whether their respective distributions are separated in L1-norm. In this paper, we focus on adapting the rate to the shape of the underlying distributions, i.e. we consider a local minimax setting. We provide, to the best of our knowledge, the first local minimax rate for the separation distance up to logarithmic factors, together with a test that achieves it. In view of the rate, closeness testing turns out to be substantially harder than the related one-sample testing problem over a wide range of cases.