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Basque Center for Applied Mathematics

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Representative Papers

Efficient Exploration Is Enough

Sep 07, 2026

本文研究在无外部奖励情况下,通过优先生成可泛化的经验来实现高效探索,理论上和实证上展示了该方法能自动产生复杂行为。

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SPDE Methods for Nonparametric Bayesian Posterior Contraction and Laplace Approximation

Mar 23, 2026

This work investigates the non-asymptotic characterization of posterior contraction rates and finite-sample Bernstein–von Mises (BvM) behavior in nonparametric Bayesian models. By interpreting the posterior distribution as the invariant measure of a Langevin stochastic partial differential equation (SPDE) on a separable Hilbert space, the study extends diffusion-based analytical frameworks to infinite-dimensional settings for the first time. This approach enables precise control over posterior moments and yields sharp non-asymptotic concentration rates in Hilbert norm, along with a quantitative Laplace approximation of the posterior. In the context of nonparametric linear Gaussian inverse problems, the theory elucidates how likelihood curvature and prior regularity jointly govern posterior contraction rates and finite-sample BvM phenomena.

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Latest Papers

Efficient Exploration Is Enough

Sep 07, 2026

本文研究在无外部奖励情况下,通过优先生成可泛化的经验来实现高效探索,理论上和实证上展示了该方法能自动产生复杂行为。

0 citationsRead paper

SPDE Methods for Nonparametric Bayesian Posterior Contraction and Laplace Approximation

Mar 23, 2026

This work investigates the non-asymptotic characterization of posterior contraction rates and finite-sample Bernstein–von Mises (BvM) behavior in nonparametric Bayesian models. By interpreting the posterior distribution as the invariant measure of a Langevin stochastic partial differential equation (SPDE) on a separable Hilbert space, the study extends diffusion-based analytical frameworks to infinite-dimensional settings for the first time. This approach enables precise control over posterior moments and yields sharp non-asymptotic concentration rates in Hilbert norm, along with a quantitative Laplace approximation of the posterior. In the context of nonparametric linear Gaussian inverse problems, the theory elucidates how likelihood curvature and prior regularity jointly govern posterior contraction rates and finite-sample BvM phenomena.

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