相关论文: Onsager-Machlup Posterior Transport for Deep Gauss…

Deep Gaussian Process (DGP) models offer a powerful nonparametric approach for Bayesian inference, but exact inference is typically intractable, motivating the use of various approximations. However, existing approaches, such as mean-field…

Optimal paths for the classical Onsager-Machlup function determining most probable paths between points on a manifold are only explicitly identified for specific processes, for example the Riemannian Brownian motion. This leaves out large…

Deep Gaussian processes (DGPs) are increasingly popular as predictive models in machine learning (ML) for their non-stationary flexibility and ability to cope with abrupt regime changes in training data. Here we explore DGPs as surrogates…

Sparse variational Gaussian process (GP) approximations based on inducing points have become the de facto standard for scaling GPs to large datasets, owing to their theoretical elegance, computational efficiency, and ease of implementation.…

Token reduction accelerates Multimodal Large Language Models (MLLMs) by reducing excessive tokens, but overlooks structural redundancy differences, where critical and redundant modules process identical token loads. For fine-grained…

The most probable transition paths of a stochastic dynamical system are the global minimizers of the Onsager-Machlup action functional and can be described by a necessary but not sufficient condition, the Euler-Lagrange equation (a…

Logistic Gaussian process (LGP) priors provide a flexible alternative for modelling unknown densities. The smoothness properties of the density estimates can be controlled through the prior covariance structure of the LGP, but the challenge…

Thanks to the reparameterization trick, deep latent Gaussian models have shown tremendous success recently in learning latent representations. The ability to couple them however with nonparamet-ric priors such as the Dirichlet Process (DP)…

We present two approximate Bayesian inference methods for parameter estimation in partial differential equation (PDE) models with space-dependent and state-dependent parameters. We demonstrate that these methods provide accurate and…

Variational inference is a powerful tool for approximate inference, and it has been recently applied for representation learning with deep generative models. We develop the variational Gaussian process (VGP), a Bayesian nonparametric…

Making predictions and quantifying their uncertainty when the input data is sequential is a fundamental learning challenge, recently attracting increasing attention. We develop SigGPDE, a new scalable sparse variational inference framework…

The use of Gaussian processes (GPs) is supported by efficient sampling algorithms, a rich methodological literature, and strong theoretical grounding. However, due to their prohibitive computation and storage demands, the use of exact GPs…

Deep Gaussian Processes (DGPs) compose GP layers to warp inputs, enabling improved emulation of computer models with nonstationary input-output behavior compared with ordinary GPs. In contrast to GPs, the predictive uncertainty for DGP…

The use of non-differentiable priors in Bayesian statistics has become increasingly popular, in particular in Bayesian imaging analysis. Current state of the art methods are approximate in the sense that they replace the posterior with a…

Parameter retrieval and model inversion are key problems in remote sensing and Earth observation. Currently, different approximations exist: a direct, yet costly, inversion of radiative transfer models (RTMs); the statistical inversion with…

When testing data and training data come from different distributions, deep neural networks (DNNs) will face significant safety risks in practical applications. Therefore, out-of-distribution (OOD) detection techniques, which can identify…

Deep Gaussian Processes (DGPs) combine the expressiveness of Deep Neural Networks (DNNs) with quantified uncertainty of Gaussian Processes (GPs). Expressive power and intractable inference both result from the non-Gaussian distribution over…

Turbulence transition often arises from a subcritical transition between bistable states characterized by invariant sets of deterministic dynamical systems, and such transitions can be triggered by system noise as rare events. In this…

Gaussian Process (GP) regression is a flexible modeling technique used to predict outputs and to capture uncertainty in the predictions. However, the GP regression process becomes computationally intensive when the training spatial dataset…

Macroscopic traffic flow is stochastic, but the physics-informed deep learning methods currently used in transportation literature embed deterministic PDEs and produce point-valued outputs; the stochasticity of the governing dynamics plays…