Convergence Analysis of Distributed Inference with Vector-Valued Gaussian Belief Propagation
Authors: Jian Du, Shaodan Ma, Yik-Chung Wu, Soummya Kar, José M. F. Moura
JMLR 2017 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | This paper considers inference over distributed linear Gaussian models using factor graphs and Gaussian belief propagation (BP). The distributed inference algorithm involves only local computation of the information matrix and of the mean vector, and message passing between neighbors. Under broad conditions, it is shown that the message information matrix converges to a unique positive definite limit matrix for arbitrary positive semidefinite initialization, and it approaches an arbitrarily small neighborhood of this limit matrix at an exponential rate. A necessary and sufficient convergence condition for the belief mean vector to converge to the optimal centralized estimator is provided under the assumption that the message information matrix is initialized as a positive semidefinite matrix. Further, it is shown that Gaussian BP always converges when the underlying factor graph is given by the union of a forest and a single loop. The proposed convergence condition in the setup of distributed linear Gaussian models is shown to be strictly weaker than other existing convergence conditions and requirements, including the Gaussian Markov random field based walk-summability condition, and applicable to a large class of scenarios. |
| Researcher Affiliation | Academia | Jian Du EMAIL Department of Electrical and Computer Engineering Carnegie Mellon University Pittsburgh, PA 15213, USA Shaodan Ma EMAIL Department of Electrical and Computer Engineering University of Macau Avenida da Universidade, Taipa, Macau Yik-Chung Wu EMAIL Department of Electrical and Electronic Engineering The University of Hong Kong Pokfulam Road, Hong Kong Soummya Kar EMAIL Jos e M. F. Moura EMAIL Department of Electrical and Computer Engineering Carnegie Mellon University Pittsburgh, PA 15213, USA |
| Pseudocode | No | The paper describes the iterative algorithm in Section 3, stating, "The iterative algorithm based on Gaussian BP is summarized as follows." However, this summary is provided in descriptive paragraph form, not as a structured pseudocode block or clearly labeled algorithm. |
| Open Source Code | No | The paper does not provide any explicit statements about releasing source code, nor does it include links to a code repository. The paper focuses on theoretical analysis rather than empirical implementation. |
| Open Datasets | No | The paper is theoretical in nature, focusing on convergence analysis of Gaussian Belief Propagation for linear Gaussian models. It does not conduct experiments with specific datasets and therefore does not mention any publicly available or open datasets. |
| Dataset Splits | No | The paper does not involve experimental evaluation using datasets, as it is a theoretical work. Therefore, there is no mention of training/test/validation dataset splits. |
| Hardware Specification | No | The paper is a theoretical work focused on convergence analysis and does not involve experimental runs requiring specific hardware. Thus, no hardware specifications (like GPU/CPU models) are mentioned. |
| Software Dependencies | No | The paper is a theoretical study on Gaussian Belief Propagation convergence. It does not describe any specific implementation or experiments that would require detailing software dependencies with version numbers. |
| Experiment Setup | No | The paper is purely theoretical, presenting convergence analysis and conditions for Gaussian Belief Propagation. It does not describe any experimental setups, hyperparameters, or training configurations. |