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[2602.13098] Barron-Wiener-Laguerre models
Summary
The paper presents a probabilistic extension of Wiener-Laguerre models for causal operator learning, integrating Bayesian inference for enhanced uncertainty quantification in time-series modeling.
Why It Matters
This work bridges classical system identification with modern probabilistic approaches, offering a structured method for modeling nonlinear systems. It enhances predictive capabilities in machine learning by addressing uncertainty, which is crucial for applications in various fields such as finance, engineering, and AI.
Key Takeaways
- Introduces a probabilistic framework for Wiener-Laguerre models.
- Combines causal dynamics with Barron-type nonlinear approximators.
- Enhances uncertainty quantification in time-series modeling.
- Bridges classical and modern methodologies in system identification.
- Offers a principled approach to nonlinear systems identification.
Statistics > Methodology arXiv:2602.13098 (stat) [Submitted on 13 Feb 2026] Title:Barron-Wiener-Laguerre models Authors:Rahul Manavalan, Filip Tronarp View a PDF of the paper titled Barron-Wiener-Laguerre models, by Rahul Manavalan and 1 other authors View PDF HTML (experimental) Abstract:We propose a probabilistic extension of Wiener-Laguerre models for causal operator learning. Classical Wiener-Laguerre models parameterize stable linear dynamics using orthonormal Laguerre bases and apply a static nonlinear map to the resulting features. While structurally efficient and interpretable, they provide only deterministic point estimates. We reinterpret the nonlinear component through the lens of Barron function approximation, viewing two-layer networks, random Fourier features, and extreme learning machines as discretizations of integral representations over parameter measures. This perspective naturally admits Bayesian inference on the nonlinear map and yields posterior predictive uncertainty. By combining Laguerre-parameterized causal dynamics with probabilistic Barron-type nonlinear approximators, we obtain a structured yet expressive class of causal operators equipped with uncertainty quantification. The resulting framework bridges classical system identification and modern measure-based function approximation, providing a principled approach to time-series modeling and nonlinear systems identification. Subjects: Methodology (stat.ME); Machine Learning (cs.LG) Cite as: arX...