{"id":3956,"date":"2025-05-20T07:03:13","date_gmt":"2025-05-20T07:03:13","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/05\/20\/2505-11622\/"},"modified":"2025-05-20T07:03:13","modified_gmt":"2025-05-20T07:03:13","slug":"2505-11622","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/05\/20\/2505-11622\/","title":{"rendered":"The Stochastic Occupation Kernel (SOCK) Method for Learning Stochastic Differential Equations"},"content":{"rendered":"

The Stochastic Occupation Kernel (SOCK) Method for Learning Stochastic Differential Equations
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arXiv:2505.11622v1 Announce Type: new
\nAbstract: We present a novel kernel-based method for learning multivariate stochastic differential equations (SDEs). The method follows a two-step procedure: we first estimate the drift term function, then the (matrix-valued) diffusion function given the drift. Occupation kernels are integral functionals on a reproducing kernel Hilbert space (RKHS) that aggregate information over a trajectory. Our approach leverages vector-valued occupation kernels for estimating the drift component of the stochastic process. For diffusion estimation, we extend this framework by introducing operator-valued occupation kernels, enabling the estimation of an auxiliary matrix-valued function as a positive semi-definite operator, from which we readily derive the diffusion estimate. This enables us to avoid common challenges in SDE learning, such as intractable likelihoods, by optimizing a reconstruction-error-based objective. We propose a simple learning procedure that retains strong predictive accuracy while using Fenchel duality to promote efficiency. We validate the method on simulated benchmarks and a real-world dataset of Amyloid imaging in healthy and Alzheimer’s disease (AD) subjects.<\/div>\n

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\n Michael L. Wells, Kamel Lahouel, Bruno Jedynak
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The Stochastic Occupation Kernel (SOCK) Method for Learning Stochastic Differential Equations arXiv:2505.11622v1 Announce Type: new Abstract: We present a novel kernel-based method for learning multivariate stochastic differential equations (SDEs). The method follows a two-step procedure: we first estimate the drift term function, then the (matrix-valued) diffusion function given the drift. Occupation kernels are integral functionals […]<\/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":[198,2058,606],"class_list":["post-3956","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-stat-ml","tag-method","tag-occupation","tag-stochastic"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/3956"}],"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=3956"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/3956\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=3956"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=3956"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=3956"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}