A Novel Bias-Variance Decomposition of the LMS Algorithm Learning Behavior

Authors

DOI:

https://doi.org/10.14209/jcis.2026.5

Keywords:

Adaptive Filtering, Stochastic Model, Least Mean Squares, Bias-variance

Abstract

This paper revisits the learning dynamics of the least-mean-squares (LMS) algorithm through a new bias–variance decomposition of the mean-square deviation that remains valid for colored and non-Gaussian inputs. Building on the radial-angular input model of Slock, which separates a continuous radial component from a discrete angular distribution, novel closed-form, modewise expressions for the transient and steady-state behavior are derived. Our framework unifies and extends recent results on bias-variance decomposition of the mean-square deviation of the LMS algorithm. The analysis clarifies when classical Gaussian-based predictions fail and offers a tractable pathway to performance prediction and parameter tuning of LMS under realistic, non-ideal input models.

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Author Biographies

João Pedro Costa e Silva Mayworm, CEFET/RJ

Joao Pedro C. e S. Mayworm is currently studying at the Federal Center for Technological Education (CEFET/RJ) in the Telecommunications Technical High School program.

Flavio Henrique Origuela Meira, CEFET/RJ

Flavio H. O. Meira (Member, IEEE) received the B.Sc. degree in Electrical Engineering from Anhanguera University of Niterói, Brazil, in 2018. He holds postgraduate degrees in Mechatronic Engineering (UCP, 2019), Industrial Automation and Control Engineering (UCAM, 2022), Maintenance Engineering (Unyleya, 2023), Industrial Networks Engineering (Unyleya, 2024), and Teaching in Professional and Technological Education (Ítalo Brasileiro, 2024). His research interests include signal processing, machine learning, fault diagnosis in electric machines, and intelligent systems for automation.

Luis Tarrataca, CEFET/RJ

Luís Tarrataca is a Professor and the Program Coordinator in Computer Engineering at the Federal Center for Technological Education Celso Suckow da Fonseca (CEFET/RJ), Brazil. He received his B.Sc., M.Sc., and Ph.D. degrees in Information Systems and Computer Engineering from Instituto Superior Técnico, University of Lisbon, Portugal. His most recent research focused on applied artificial intelligence, machine learning, and optimization problems relevant to engineering and industrial systems.

Diego Barreto Haddad, CEFET/RJ

Diego B. Haddad (Member, IEEE) was born in Niterói, RJ, Brazil, in 1983. He received the B.Sc. degree in
Electrical Engineering in 2005, and the M.Sc. and D.Sc. degrees in Electrical Engineering from the Federal University of Rio de Janeiro, Brazil, in 2008 and 2013, respectively. He is with the Federal Center for Technological Education (CEFET/RJ). Dr. Haddad has authored more than 70 journal papers and over 70 conference papers. His research interests include signal processing, symbolic regression, machine learning, computer vision and adaptive filtering algorithms.

The paper introduces a novel bias–variance decomposition of the LMS algorithm that remains valid for colored and non-Gaussian inputs, revealing mode-dependent learning dynamics and transient variance peaks.

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Published

2026-03-18

How to Cite

Costa e Silva Mayworm, J. P., Origuela Meira, F. H., Tarrataca, L., & Barreto Haddad, D. (2026). A Novel Bias-Variance Decomposition of the LMS Algorithm Learning Behavior. Journal of Communication and Information Systems, 41(1), 44–48. https://doi.org/10.14209/jcis.2026.5

Issue

Vol. 41 No. 1 (2026)

Section

Letters

License

Copyright (c) 2026 João Pedro Costa e Silva Mayworm, Flavio Henrique Origuela Meira, Luis Tarrataca, Diego Barreto Haddad (Author)

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Received 2025-11-29
Accepted 2026-03-03
Published 2026-03-18