Adaptation and Learning Over Networks for Nonlinear System Modeling

Abstract

In this chapter, we analyze nonlinear filtering problems in distributed environments, e.g., sensor networks or peer-to-peer protocols. In these scenarios, the agents in the environment receive measurements in a streaming fashion, and they are required to estimate a common (nonlinear) model by alternating local computations and communications with their neighbors. We focus on the important distinction between single-task problems, where the underlying model is common to all agents, and multitask problems, where each agent might converge to a different model due to, e.g., spatial dependencies or other factors. Currently, most of the literature on distributed learning in the nonlinear case has focused on the single-task case, which may be a strong limitation in real-world scenarios. After introducing the problem and reviewing the existing approaches, we describe a simple kernel-based algorithm tailored for the multitask case. We evaluate the proposal on a simulated benchmark task, and we conclude by detailing currently open problems and lines of research.

Um algoritmo kernel baseado na ortogonalização de Gram-Schmidt para redes de difusão adaptativas

“…Para um dicionário fixo de cardinalidade N , a extensão do GS-KLMS para redes de difusão adaptativas segue os mesmos passos da do KLMS [9], [10]. Para uma configuração ATC, as equações do GS-KLMS distribuído (dGS-KLMS) são dadas para o nó k por (6).…”

“…Para reduzir o custo computacional, considerase um dicionário D fixo com N elementos, comum a todos os nós. Assim, seguindo uma configuração do tipo ATC (adaptthen-combine) 1 [8], as etapas de adaptação e de combinação do KLMS distribuído (dKLMS) são respectivamente dadas por [9], [10]…”

Diffusion Hammerstein Spline Adaptive Filtering Based on Orthogonal Gradient Adaptive Algorithm

“…According to the multitask case in the real world application [6]- [8], the authors in [6] has described the adaptation and learning of nonlinear filtering over the distributed network. A distributed with sparsity-aware adaptive algorithm [7] has been proposed to verify the Voterra system that can provide a good performance in the wireless sensor network (WSN).…”