arXiv research

This paper introduces Bayes Hilbert spaces for efficient posterior approximation.

FHBI enhances generalization in Bayesian inference with iterative steps in functional spaces.

The article analyzes LCE in Hilbert space, deriving new formulas and regularisation methods.

Kernel-based Bayesian filter for nonlinear systems using infinite-dimensional operators.

Bayesian nonparametric models get better posterior estimates via SPDE methods.

New variational inference approach using Hilbert space for robotic state estimation.

The paper revisits and improves on a Bayesian relevance vector machine method for small sample sizes.

Quantum Graphical Models (QGMs) generalize classical graphical models by adopting the formalism for reasoning about uncertainty from quantum mechanics. Unlike classical graphical models, QGMs represent uncertainty with density matrices in complex Hilbert spaces. Hilbert space embeddings (HSEs) also generalize Bayesian …

Unified analysis for nonlinear parametric models in Bayesian optimization.

The paper studies estimating the normalizing constant using queries to a black-box function in RKHS.

BayesIMP combines multiple causal graphs to estimate average treatment effects with uncertainty.

Improves DRO with Bayesian Ambiguity Sets for model misspecification.

Random exploration optimizes Bayesian optimization with optimal error rates and computational efficiency.

The paper improves error bounds for Bayesian quadrature in noisy settings.

fCBO optimizes interventions in causal graphs using Gaussian processes.

This paper proposes a Hilbert space embedding for Dirichlet Process mixture models via a stick-breaking construction of Sethuraman. Although Bayesian nonparametrics offers a powerful approach to construct a prior that avoids the need to specify the model size/complexity explicitly, an exact inference is often intractab…

Bayesian approach learns linear operators from noisy data.

The automation of posterior inference in Bayesian data analysis has enabled experts and nonexperts alike to use more sophisticated models, engage in faster exploratory modeling and analysis, and ensure experimental reproducibility. However, standard automated posterior inference algorithms are not tractable at the scal…

Bayesian optimization algorithm reduces regret with efficient region pruning.

DeltaBO accelerates Bayesian optimization with theoretical guarantees.

Bayesian kernel regression improves functional output prediction.

Modeling functional data, this study uncovers the size-and-shape of functions under noisy observations.

A new method improves inference for complex Bayesian models.

CEI achieves convergence rates for constrained Bayesian optimization.

We focus on kernel methods for set-valued inputs and their application to Bayesian set optimization, notably combinatorial optimization. We investigate two classes of set kernels that both rely on Reproducing Kernel Hilbert Space embeddings, namely the ``Double Sum'' (DS) kernels recently considered in Bayesian set opt…

We propose a vector-valued regression problem whose solution is equivalent to the reproducing kernel Hilbert space (RKHS) embedding of the Bayesian posterior distribution. This equivalence provides a new understanding of kernel Bayesian inference. Moreover, the optimization problem induces a new regularization for the …

Bayesian deconditioning improves downscaling of spatial fields.

Study optimizes learning rates for conditional mean embedding estimates.

Kernel Bayes' rule has been proposed as a nonparametric kernel-based method to realize Bayesian inference in reproducing kernel Hilbert spaces. However, we demonstrate both theoretically and experimentally that the prediction result by kernel Bayes' rule is in some cases unnatural. We consider that this phenomenon is i…

SOBER framework optimizes Bayesian optimization tasks efficiently.

We extend the herding algorithm to continuous spaces by using the kernel trick. The resulting "kernel herding" algorithm is an infinite memory deterministic process that learns to approximate a PDF with a collection of samples. We show that kernel herding decreases the error of expectations of functions in the Hilbert …

Paper tackles infinite-dimensional optimization and Bayesian learning for stochastic differential equations.

Metric spaces uniquely split into Hilbert and non-line-split parts.

New Hilbert bundles with ends defined from indexed bases.

Study geometry of tetrahedra in complex hyperbolic space and Hilbert spaces.

We give first examples of finitely generated groups having an intermediate, with values in (0,1), Hilbert space compression (which is a numerical parameter measuring the distortion required to embed a metric space into Hilbert space). These groups include certain diagram groups. In particular, we show that the Hilbert …

GWI combines deep neural networks with Gaussian processes for better predictive performance and uncertainty quantification.

Theory developed for Hilbert geometry over valued fields, linking real and non-Archimedean geometries.

Measuring conditional independence is one of the important tasks in statistical inference and is fundamental in causal discovery, feature selection, dimensionality reduction, Bayesian network learning, and others. In this work, we explore the connection between conditional independence measures induced by distances on …

Study Markov chain gradient descent in Hilbert spaces for quadratic loss.

No exceptional orbits found in Hilbert spaces actions.

In the paper "Direct Images, Fields of Hilbert Spaces, and Geometric Quantization", Lempert and Szőke proved that any flat analytic Hilbert field will induce a hermitian Hilbert bundle and gave an example of a flat Hilbert field that does not induce any Hilbert bundle. In this paper, we will provide an example of an an…

Bayesian optimization tackles uncertainty in context variables.

New GP-based method improves uncertainty quantification for causal functions.

We introduce a notion of fibred coarse embedding into Hilbert space for metric spaces, which is a generalization of Gromov's notion of coarse embedding into Hilbert space. It turns out that a large class of expander graphs admit such an embedding. We show that the maximal coarse Baum-Connes conjecture holds for metric …

When there is a family of complex structures on the phase space, parametrized by a set $S$, the prequantum Hilbert spaces produced by geometric quantization, using the half-form correction, also depends on these parameters. This way we obtain a field of Hilbert spaces $p:H^{pr Q}\rightarrow S$. We show that this field …

This study describes the Fisher-Rao metric on Gaussian measures in infinite-dimensional spaces.

Paper analyzes convergence rate of noisy Bayesian Optimization with Expected Improvement.