{"id":5409,"date":"2025-07-18T07:02:25","date_gmt":"2025-07-18T07:02:25","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/07\/18\/2507-12878\/"},"modified":"2025-07-18T07:02:25","modified_gmt":"2025-07-18T07:02:25","slug":"2507-12878","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/07\/18\/2507-12878\/","title":{"rendered":"Bayesian Modeling and Estimation of Linear Time-Variant Systems using Neural Networks and Gaussian Processes"},"content":{"rendered":"

Bayesian Modeling and Estimation of Linear Time-Variant Systems using Neural Networks and Gaussian Processes
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arXiv:2507.12878v1 Announce Type: new
\nAbstract: The identification of Linear Time-Variant (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, $h(t, tau)$, 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 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 robustly infer the properties of an LTI system from a single noisy observation, show superior data efficiency compared to classical methods in a simulated ambient noise tomography problem, and successfully 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.<\/div>\n

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\n Yaniv Shulman
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Bayesian Modeling and Estimation of Linear Time-Variant Systems using Neural Networks and Gaussian Processes arXiv:2507.12878v1 Announce Type: new Abstract: The identification of Linear Time-Variant (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, $h(t, tau)$, as a stochastic […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,112],"tags":[557,496,15],"class_list":["post-5409","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-stat-ml","tag-bayesian","tag-linear","tag-time"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/5409"}],"collection":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/comments?post=5409"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/5409\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=5409"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=5409"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=5409"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}