# Convex Quantization Preserves Logconcavity

arXiv: https://arxiv.org/abs/2206.05598 · HTML: https://mlsanity.com/paper/2206.05598/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 19 references that are in the map.
- First posted on arXiv 11 Jun 2022.

## Builds on (most cited first, 4 of 4)

- [Deep Signal Recovery with One-Bit Quantization](https://mlsanity.com/paper/1812.00797/) (2018)
- [Dictionary Learning for Blind One Bit Compressed Sensing](https://mlsanity.com/paper/1508.07648/) (2015)
- [Sinusoidal Parameter Estimation from Signed Measurements via Majorization-Minimization Based RELAX](https://mlsanity.com/paper/2103.11500/) (2021)
- [BER Performance Analysis of Coarse Quantized Uplink Massive MIMO](https://mlsanity.com/paper/1711.09309/) (2017)

## Built on by (most cited first, 1 of 1)

- [Sensitivity-Aware Density Estimation in Multiple Dimensions](https://mlsanity.com/paper/2506.02323/) (2025)

## Abstract (arXiv)

A logconcave likelihood is as important to proper statistical inference as a convex cost function is important to variational optimization. Quantization is often disregarded when writing likelihood models, ignoring the limitations of the physical detectors used to collect the data. These two facts call for the question: would including quantization in likelihood models preclude logconcavity? are the true data likelihoods logconcave? We provide a general proof that the same simple assumption that leads to logconcave continuous-data likelihoods also leads to logconcave quantized-data likelihoods, provided that convex quantization regions are used.