Výsledky vyhledávání - "Williams, Bernardo"

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Stochastic variance-reduced Gaussian variational inference on the Bures-Wasserstein manifold

Autor: Luu, Hoang Phuc Hau, Yu, Hanlin, Williams, Bernardo, Hartmann, Marcelo, Klami, Arto

Optimization in the Bures-Wasserstein space has been gaining popularity in the machine learning community since it draws connections between variational inference and Wasserstein gradient flows. The variational inference objective function of Kullbac

Externí odkaz: http://arxiv.org/abs/2410.02490

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Non-geodesically-convex optimization in the Wasserstein space

Autor: Luu, Hoang Phuc Hau, Yu, Hanlin, Williams, Bernardo, Mikkola, Petrus, Hartmann, Marcelo, Puolamäki, Kai, Klami, Arto

We study a class of optimization problems in the Wasserstein space (the space of probability measures) where the objective function is nonconvex along generalized geodesics. Specifically, the objective exhibits some difference-of-convex structure alo

Externí odkaz: http://arxiv.org/abs/2406.00502

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Riemannian Laplace Approximation with the Fisher Metric

Autor: Yu, Hanlin, Hartmann, Marcelo, Williams, Bernardo, Girolami, Mark, Klami, Arto

Laplace's method approximates a target density with a Gaussian distribution at its mode. It is computationally efficient and asymptotically exact for Bayesian inference due to the Bernstein-von Mises theorem, but for complex targets and finite-data p

Externí odkaz: http://arxiv.org/abs/2311.02766

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Warped geometric information on the optimisation of Euclidean functions

Autor: Hartmann, Marcelo, Williams, Bernardo, Yu, Hanlin, Girolami, Mark, Barp, Alessandro, Klami, Arto

We consider the fundamental task of optimising a real-valued function defined in a potentially high-dimensional Euclidean space, such as the loss function in many machine-learning tasks or the logarithm of the probability distribution in statistical

Externí odkaz: http://arxiv.org/abs/2308.08305

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Scalable Stochastic Gradient Riemannian Langevin Dynamics in Non-Diagonal Metrics

Autor: Yu, Hanlin, Hartmann, Marcelo, Williams, Bernardo, Klami, Arto

Stochastic-gradient sampling methods are often used to perform Bayesian inference on neural networks. It has been observed that the methods in which notions of differential geometry are included tend to have better performances, with the Riemannian m

Externí odkaz: http://arxiv.org/abs/2303.05101

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