Barron-Wiener-Laguerre models
This work provides a principled approach for time-series modeling and nonlinear systems identification, bridging classical system identification and modern function approximation, but it is incremental as it builds on existing Wiener-Laguerre models.
The paper tackled the problem of extending Wiener-Laguerre models for causal operator learning to include probabilistic uncertainty quantification by reinterpreting the nonlinear component using Barron function approximation, resulting in a structured class of causal operators with posterior predictive uncertainty.
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.