|| On Learning Parametric Distributions from Quantized Samples
||Septimia Sarbu, Huawei Technologies France, France; Abdellatif Zaidi, Universite Paris-Est, France|
||D3-S2-T3: Inference & Learning
||Wednesday, 14 July, 22:20 - 22:40
||Wednesday, 14 July, 22:40 - 23:00
We consider the problem of learning parametric distributions from their quantized samples in a network. Specifically, N agents or sensors observe independent samples of an unknown parametric distribution; and they use each k bits to describe the observed sample to a central processor whose goal is to estimate the unknown parameter. First, we establish a generalization of the well-known van Trees inequality to general p-norms in terms of Generalized Fisher information. Then, we develop minimax lower bounds on the estimation error for two losses: general p-norms and the related Wasserstein loss from optimal transport.