{"ID":2893398,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.12878","arxiv_id":"2507.12878","title":"Bayesian Modeling and Estimation of Linear Time-Varying Systems using Neural Networks and Gaussian Processes","abstract":"The identification of Linear Time-Varying (LTV) systems from input-output data is a fundamental yet challenging ill-posed inverse problem. This work introduces a unified Bayesian framework that models the system's impulse response, $h(t, τ)$, as a stochastic process. We decompose the response into a posterior mean and a random fluctuation term, a formulation that provides a principled approach for quantifying uncertainty, unifies intrinsic channel variability and epistemic uncertainty through a common posterior representation, and naturally defines a new, useful system class we term Linear Time-Invariant in Expectation (LTIE). To perform inference, we leverage modern machine learning techniques, including Bayesian neural networks and Gaussian Processes, using scalable variational inference. We demonstrate through a series of experiments that our framework can infer the properties of an LTI system from a single noisy input-output pair, including under deliberate additive-noise misspecification, achieve a lower overall error floor than the classical CCF stacking baseline in a simulated ambient noise tomography setting, and track a continuously varying LTV impulse response by using a structured Gaussian Process prior. This work provides a flexible and robust methodology for uncertainty-aware system identification in dynamic environments.","short_abstract":"The identification of Linear Time-Varying (LTV) systems from input-output data is a fundamental yet challenging ill-posed inverse problem. This work introduces a unified Bayesian framework that models the system's impulse response, $h(t, τ)$, as a stochastic process. We decompose the response into a posterior mean and...","url_abs":"https://arxiv.org/abs/2507.12878","url_pdf":"https://arxiv.org/pdf/2507.12878v2","authors":"[\"Yaniv Shulman\"]","published":"2025-07-17T07:55:34Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\"]","methods":"[]","has_code":false}