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On learning parametric distributions from quantized samples
- Publication Year :
- 2021
-
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.<br />Comment: Short version accepted for publication at the IEEE Information Theory Symposium (ISIT) 2021; this version contains the detailed proofs with some minor corrections
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2105.12019
- Document Type :
- Working Paper