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  1. Fundamental Limits of Distributed Covariance Matrix Estimation Under Communication Constraints
Fundamental Limits of Distributed Covariance Matrix Estimation Under Communication Constraints
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Fundamental Limits of Distributed Covariance Matrix Estimation Under Communication Constraints

Rahmani, M. R

Fundamental Limits of Distributed Covariance Matrix Estimation Under Communication Constraints

Rahmani, M. R ; Sharif University of Technology | 2024

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  1. Type of Document: Article
  2. Publisher: 2024
  3. Abstract:
  4. Estimating high-dimensional covariance matrices is crucial in various domains. This work considers a scenario where two collaborating agents access disjoint dimensions of m samples from a high-dimensional random vector, and they can only communicate a limited number of bits to a central server, which wants to accurately approximate the covariance matrix. We analyze the fundamental trade-off between communication cost, number of samples, and estimation accuracy. We prove a lower bound on the error achievable by any estimator, highlighting the impact of dimensions, number of samples, and communication budget. Furthermore, we present an algorithm that achieves this lower bound up to a logarithmic factor, demonstrating its near-optimality in practical settings. Copyright 2024 by the author(s)
  5. Keywords:
  6. Cost estimating ; Covariance matrix ; Central servers ; Collaborating agents ; Communication constraints ; Covariance matrices ; Covariance matrix estimation ; High-dimensional ; Higher-dimensional ; Low bound ; Number of samples ; Random vectors ; Budget control
  7. Source: Proceedings of Machine Learning Research ; Volume 235 , 2024 , Pages 41927-41958 ; 26403498 (ISSN)
  8. URL: https://proceedings.mlr.press/v235/rahmani24a.html