mlsanityData to 14 Oct 2026

Bit Efficient Toeplitz Covariance Estimation

arXiv 2412.12678 ↗First posted 17 Dec 2024eess.SPcited by 1

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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.

Key facts. Cited by 1 paper 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

18 of 72 references.

References · 18

  1. 2020UVeQFed: Universal Vector Quantization for Federated Learningcited by 107
  2. 2020Differentially Private Assouad, Fano, and Le Camcited by 55
  3. 2021On the Properties of Kullback-Leibler Divergence Between Multivariate Gaussian Distributionscited by 23
  4. 2018User-Friendly Covariance Estimation for Heavy-Tailed Distributionscited by 16
  5. 2022High Dimensional Statistical Estimation under Uniformly Dithered One-bit Quantizationcited by 13
  6. 2022Quantizing Heavy-tailed Data in Statistical Estimation: (Near) Minimax Rates, Covariate Quantization, and Uniform Recoverycited by 9
  7. 2016Fourier-sparse interpolation without a frequency gapcited by 6
  8. 2021Structured Covariance Matrix Estimation with Missing-Data for Radar Applications via Expectation-Maximizationcited by 6
  9. 2023Quantized Low-Rank Multivariate Regression with Random Ditheringcited by 5
  10. 2019Sample Efficient Toeplitz Covariance Estimationcited by 4
  11. 2023Plug-in Channel Estimation with Dithered Quantized Signals in Spatially Non-Stationary Massive MIMO Systemscited by 4
  12. 2023New Methods for MLE of Toeplitz Structured Covariance Matrices with Applications to RADAR Problemscited by 4
6 more
  1. 2023A Parameter-Free Two-Bit Covariance Estimator with Improved Operator Norm Error Ratecited by 4
  2. 2014Subspace Learning with Partial Informationcited by 3
  3. 2022A Robust and Statistically Efficient Maximum-Likelihood Method for DOA Estimation Using Sparse Linear Arrayscited by 3
  4. 2021On the asymptotic distribution of the maximum sample spectral coherence of Gaussian time series in the high dimensional regimecited by 1
  5. 2023Nonasymptotic Performance Analysis of Direct-Augmentation and Spatial-Smoothing ESPRIT for Localization of More Sources Than Sensors Using Sparse Arrayscited by 1
  6. 2023Efficient nonparametric estimation of Toeplitz covariance matricescited by 1

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Cited by year

Citing papers per year: 2025: 1.

1 paper.

  1. 2025Compressive Toeplitz Covariance Estimation From Few-Bit Quantized Measurements With Applications to DOA Estimationcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025The Optimization Landscape of Carath'eodory Decomposition of Toeplitz Covariances
  2. 2024Linear and Nonlinear MMSE Estimation in One-Bit Quantized Systems under a Gaussian Mixture Prior
  3. 2026High-Rate Quantized Matrix Multiplication II
  4. 2025MCRB for Parameter Estimation from One-Bit Quantized and Oversampled Measurements
  5. 2022On the Mean Square Error Optimal Estimator in One-Bit Quantized Systems
  6. 2026Quantization Error Is Spectrally Flat: A Single Random Probe Is a Calibrated, Data-Free Sensitivity Estimator, with Application to Budget-Targeted Mixed-Precision Quantization
  7. 2026Information-Theoretic Bounds for Sparse Covariance Estimation in the Vertical-Split Distributed Model
  8. 2026KBBQ: A Predictive Noise Law and the Limits of Spectrum Flattening in FP4 Quantization