On learning parametric distributions from quantized samples

Septimia Sarbu; Abdellatif Zaidi

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arXiv · 2105.12019

On learning parametric distributions from quantized samples

Septimia Sarbu·Abdellatif Zaidi

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Abstract

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 each of them uses $k$ bits to describe its observed sample to a central processor whose goal is to estimate the unknown distribution. First, we establish a generalization of the well-known van Trees inequality to general $L_p$-norms, with $p > 1$, in terms of Generalized Fisher information. Then, we develop minimax lower bounds on the estimation error for two losses: general $L_p$-norms and the related Wasserstein loss from optimal transport.

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Septimia Sarbu, Abdellatif Zaidi. 2021-05-25. On learning parametric distributions from quantized samples. https://arxiv.org/abs/2105.12019

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