Efficient Learning of Stationary Diffusions with Stein-type Discrepancies
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911406696169472 |
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| author | Bleile, Fabian Lumpp, Sarah Drton, Mathias |
| author_facet | Bleile, Fabian Lumpp, Sarah Drton, Mathias |
| contents | Learning a stationary diffusion amounts to estimating the parameters of a stochastic differential equation whose stationary distribution matches a target distribution. We build on the recently introduced kernel deviation from stationarity (KDS), which enforces stationarity by evaluating expectations of the diffusion's generator in a reproducing kernel Hilbert space. Leveraging the connection between KDS and Stein discrepancies, we introduce the Stein-type KDS (SKDS) as an alternative formulation. We prove that a vanishing SKDS guarantees alignment of the learned diffusion's stationary distribution with the target. Furthermore, under broad parametrizations, SKDS is convex with an empirical version that is $ε$-quasiconvex with high probability. Empirically, learning with SKDS attains comparable accuracy to KDS while substantially reducing computational cost and yields improvements over the majority of competitive baselines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16597 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Efficient Learning of Stationary Diffusions with Stein-type Discrepancies Bleile, Fabian Lumpp, Sarah Drton, Mathias Machine Learning Statistics Theory 60H10, 60J60, 62M99 60H10, 60J60, 62M05 I.2.6; G.3 Learning a stationary diffusion amounts to estimating the parameters of a stochastic differential equation whose stationary distribution matches a target distribution. We build on the recently introduced kernel deviation from stationarity (KDS), which enforces stationarity by evaluating expectations of the diffusion's generator in a reproducing kernel Hilbert space. Leveraging the connection between KDS and Stein discrepancies, we introduce the Stein-type KDS (SKDS) as an alternative formulation. We prove that a vanishing SKDS guarantees alignment of the learned diffusion's stationary distribution with the target. Furthermore, under broad parametrizations, SKDS is convex with an empirical version that is $ε$-quasiconvex with high probability. Empirically, learning with SKDS attains comparable accuracy to KDS while substantially reducing computational cost and yields improvements over the majority of competitive baselines. |
| title | Efficient Learning of Stationary Diffusions with Stein-type Discrepancies |
| topic | Machine Learning Statistics Theory 60H10, 60J60, 62M99 60H10, 60J60, 62M05 I.2.6; G.3 |
| url | https://arxiv.org/abs/2601.16597 |