On the Convergence of DEM’s Linear Parameter Estimator

Ajith Anil Meera; Martijn Wisse

doi:10.1007/978-3-030-93736-2_49

On the Convergence of DEM’s Linear Parameter Estimator

Ajith Anil Meera^*, Martijn Wisse

^*Corresponding author for this work

Robot Dynamics

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

2 Citations (Scopus)

10 Downloads (Pure)

Abstract

The free energy principle from neuroscience provides an efficient data-driven framework called the Dynamic Expectation Maximization (DEM), to learn the generative model in the environment. DEM’s growing potential to be the brain-inspired learning algorithm for robots demands a mathematically rigorous analysis using the standard control system tools. Therefore, this paper derives the mathematical proof of convergence for its parameter estimator for linear state space systems, subjected to colored noise. We show that the free energy based parameter learning converges to a stable solution for linear systems. The paper concludes by providing a proof of concept through simulation for a wide range of spring damper systems.

Original language	English
Title of host publication	Machine Learning and Principles and Practice of Knowledge Discovery in Databases
Subtitle of host publication	Proceedings of the International Workshops of ECML PKDD 2021
Editors	Michael Kamp, Michael Kamp, Irena Koprinska, et. al.
Publisher	Springer
Pages	692-700
ISBN (Print)	978-3-030-93735-5
DOIs	https://doi.org/10.1007/978-3-030-93736-2_49
Publication status	Published - 2022
Event	21st European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, ECML PKDD 2021 - Virtual, Online Duration: 13 Sept 2021 → 17 Sept 2021

Publication series

Name	Communications in Computer and Information Science
Volume	1524 CCIS
ISSN (Print)	1865-0929
ISSN (Electronic)	1865-0937

Conference

Conference	21st European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, ECML PKDD 2021
City	Virtual, Online
Period	13/09/21 → 17/09/21

Bibliographical note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

Dynamic expectation maximization
Free energy principle
Linear state space systems
Parameter estimation

Access to Document

10.1007/978-3-030-93736-2_49

978-3-030-93736-2_49Final published version, 234 KB

Cite this

Meera, A. A., & Wisse, M. (2022). On the Convergence of DEM’s Linear Parameter Estimator. In M. Kamp, M. Kamp, I. Koprinska, & E. A. (Eds.), Machine Learning and Principles and Practice of Knowledge Discovery in Databases: Proceedings of the International Workshops of ECML PKDD 2021 (pp. 692-700). (Communications in Computer and Information Science; Vol. 1524 CCIS). Springer. https://doi.org/10.1007/978-3-030-93736-2_49

Meera, Ajith Anil ; Wisse, Martijn. / On the Convergence of DEM’s Linear Parameter Estimator. Machine Learning and Principles and Practice of Knowledge Discovery in Databases: Proceedings of the International Workshops of ECML PKDD 2021. editor / Michael Kamp ; Michael Kamp ; Irena Koprinska ; et. al. Springer, 2022. pp. 692-700 (Communications in Computer and Information Science).

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abstract = "The free energy principle from neuroscience provides an efficient data-driven framework called the Dynamic Expectation Maximization (DEM), to learn the generative model in the environment. DEM{\textquoteright}s growing potential to be the brain-inspired learning algorithm for robots demands a mathematically rigorous analysis using the standard control system tools. Therefore, this paper derives the mathematical proof of convergence for its parameter estimator for linear state space systems, subjected to colored noise. We show that the free energy based parameter learning converges to a stable solution for linear systems. The paper concludes by providing a proof of concept through simulation for a wide range of spring damper systems.",

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Meera, AA & Wisse, M 2022, On the Convergence of DEM’s Linear Parameter Estimator. in M Kamp, M Kamp, I Koprinska & EA (eds), Machine Learning and Principles and Practice of Knowledge Discovery in Databases: Proceedings of the International Workshops of ECML PKDD 2021. Communications in Computer and Information Science, vol. 1524 CCIS, Springer, pp. 692-700, 21st European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, ECML PKDD 2021, Virtual, Online, 13/09/21. https://doi.org/10.1007/978-3-030-93736-2_49

On the Convergence of DEM’s Linear Parameter Estimator. / Meera, Ajith Anil; Wisse, Martijn.
Machine Learning and Principles and Practice of Knowledge Discovery in Databases: Proceedings of the International Workshops of ECML PKDD 2021. ed. / Michael Kamp; Michael Kamp; Irena Koprinska; et. al. Springer, 2022. p. 692-700 (Communications in Computer and Information Science; Vol. 1524 CCIS).

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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Meera AA, Wisse M. On the Convergence of DEM’s Linear Parameter Estimator. In Kamp M, Kamp M, Koprinska I, EA, editors, Machine Learning and Principles and Practice of Knowledge Discovery in Databases: Proceedings of the International Workshops of ECML PKDD 2021. Springer. 2022. p. 692-700. (Communications in Computer and Information Science). doi: 10.1007/978-3-030-93736-2_49