# On learning parametric distributions from quantized samples

arXiv: https://arxiv.org/abs/2105.12019 · HTML: https://mlsanity.com/paper/2105.12019/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 17 references that are in the map.
- First posted on arXiv 25 May 2021.

## Builds on (most cited first, 1 of 1)

- [Geometric Lower Bounds for Distributed Parameter Estimation under Communication Constraints](https://mlsanity.com/paper/1802.08417/) (2018)

## Abstract (arXiv)

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 Lp-norms, with p > 1, in terms of Generalized Fisher information. Then, we develop minimax lower bounds on the estimation error for two losses: general Lp-norms and the related Wasserstein loss from optimal transport.