Fundamental Limits of Distributed Covariance Matrix Estimation Under Communication Constraints
Authors: Mohammad Reza Rahmani, Mohammad Hossein Yassaee, Mohammad Ali Maddah-Ali, Mohammad Reza Aref
ICML 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | 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. |
| Researcher Affiliation | Academia | 1Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran 2Sharif Center for Information Systems and Data Science, Sharif Institute for Convergence Science & Technology, Tehran, Iran 3Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, USA. |
| Pseudocode | No | The paper describes the proposed scheme and its components mathematically and conceptually (e.g., 'Quantization of estimated self-covariance matrices', 'Quantization of Data for approximating the cross covariance'), but it does not provide formal pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain any explicit statements about releasing source code or links to a code repository. |
| Open Datasets | No | The paper works with theoretical 'm i.i.d. samples of a random vector Z' and 'Gaussian distributions' for its proofs and scheme derivation. It does not use or make publicly available any specific real-world dataset. |
| Dataset Splits | No | The paper focuses on theoretical bounds and an achievable scheme for covariance matrix estimation. It does not involve empirical experiments with training, validation, or test splits of data. |
| Hardware Specification | No | The paper is theoretical and does not describe any specific hardware used for experiments. |
| Software Dependencies | No | The paper is theoretical and does not describe specific software dependencies with version numbers. |
| Experiment Setup | No | The paper is theoretical and focuses on mathematical derivations and an achievable scheme. It does not detail an experimental setup or hyperparameters for empirical validation. |