# Bit Efficient Toeplitz Covariance Estimation

arXiv: https://arxiv.org/abs/2412.12678 · HTML: https://mlsanity.com/paper/2412.12678/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 72 references that are in the map.
- First posted on arXiv 17 Dec 2024.

## Builds on (most cited first, 18 of 18)

- [UVeQFed: Universal Vector Quantization for Federated Learning](https://mlsanity.com/paper/2006.03262/) (2020)
- [Differentially Private Assouad, Fano, and Le Cam](https://mlsanity.com/paper/2004.06830/) (2020)
- [On the Properties of Kullback-Leibler Divergence Between Multivariate Gaussian Distributions](https://mlsanity.com/paper/2102.05485/) (2021)
- [User-Friendly Covariance Estimation for Heavy-Tailed Distributions](https://mlsanity.com/paper/1811.01520/) (2018)
- [High Dimensional Statistical Estimation under Uniformly Dithered One-bit Quantization](https://mlsanity.com/paper/2202.13157/) (2022)
- [Quantizing Heavy-tailed Data in Statistical Estimation: (Near) Minimax Rates, Covariate Quantization, and Uniform Recovery](https://mlsanity.com/paper/2212.14562/) (2022)
- [Fourier-sparse interpolation without a frequency gap](https://mlsanity.com/paper/1609.01361/) (2016)
- [Structured Covariance Matrix Estimation with Missing-Data for Radar Applications via Expectation-Maximization](https://mlsanity.com/paper/2105.03738/) (2021)
- [Quantized Low-Rank Multivariate Regression with Random Dithering](https://mlsanity.com/paper/2302.11197/) (2023)
- [Sample Efficient Toeplitz Covariance Estimation](https://mlsanity.com/paper/1905.05643/) (2019)
- [Plug-in Channel Estimation with Dithered Quantized Signals in Spatially Non-Stationary Massive MIMO Systems](https://mlsanity.com/paper/2301.04641/) (2023)
- [New Methods for MLE of Toeplitz Structured Covariance Matrices with Applications to RADAR Problems](https://mlsanity.com/paper/2307.03923/) (2023)
- [A Parameter-Free Two-Bit Covariance Estimator with Improved Operator Norm Error Rate](https://mlsanity.com/paper/2308.16059/) (2023)
- [Subspace Learning with Partial Information](https://mlsanity.com/paper/1402.4844/) (2014)
- [A Robust and Statistically Efficient Maximum-Likelihood Method for DOA Estimation Using Sparse Linear Arrays](https://mlsanity.com/paper/2203.13433/) (2022)
- [On the asymptotic distribution of the maximum sample spectral coherence of Gaussian time series in the high dimensional regime](https://mlsanity.com/paper/2107.02891/) (2021)
- [Nonasymptotic Performance Analysis of Direct-Augmentation and Spatial-Smoothing ESPRIT for Localization of More Sources Than Sensors Using Sparse Arrays](https://mlsanity.com/paper/2302.11209/) (2023)
- [Efficient nonparametric estimation of Toeplitz covariance matrices](https://mlsanity.com/paper/2303.10018/) (2023)

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

- [Compressive Toeplitz Covariance Estimation From Few-Bit Quantized Measurements With Applications to DOA Estimation](https://mlsanity.com/paper/2512.22527/) (2025)

## Abstract (arXiv)

This paper addresses the challenge of Toeplitz covariance matrix estimation from partial entries of random quantized samples. To balance trade-offs among the number of samples, the number of entries observed per sample, and the data resolution, we propose a ruler-based quantized Toeplitz covariance estimator. We derive non-asymptotic error bounds and analyze the convergence rates of the proposed estimator. Our results show that the estimator is near-optimal and imply that reducing data resolution within a certain range has a limited impact on the estimation accuracy. Numerical experiments are provided that validate our theoretical findings and show effectiveness of the proposed estimator.