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We use hyperbolic wavelet regression for the fast reconstruction of high-dimensional functions having only low dimensional variable interactions. Compactly supported periodic Chui-Wang wavelets are used for the tensorized hyperbolic wavelet…

When statistical analyses consider multiple data sources, Markov melding provides a method for combining the source-specific Bayesian models. Markov melding joins together submodels that have a common quantity. One challenge is that the…

Bayesian regression remains a simple but effective tool based on Bayesian inference techniques. For large-scale applications, with complicated posterior distributions, Markov Chain Monte Carlo methods are applied. To improve the well-known…

We propose to use a simulation driven inverse inference approach to model the dynamics of tree branches under manipulation. Learning branch dynamics and gaining the ability to manipulate deformable vegetation can help with occlusion-prone…

In Bayesian inverse problems sampling the posterior distribution is often a challenging task when the underlying models are computationally intensive. To this end, surrogates or reduced models are often used to accelerate the computation.…

Variational inference approximates Bayesian posterior distributions by projecting onto a tractable family of distributions. While most theoretical analyses evaluate the quality of this approximation using global divergence measures, many…

Fast and Relaxed Vector Fitting (FRVF) is a frequency-domain system identification approach that has been widely adopted in electrical system modelling, while its application to mechanical systems has remained relatively unexplored. In this…

Varying coefficient models (VCMs) are widely used for estimating nonlinear regression functions for functional data. Their Bayesian variants using Gaussian process priors on the functional coefficients, however, have received limited…

Graph Neural Networks (GNNs) have received considerable attention since its introduction. It has been widely applied in various fields due to its ability to represent graph structured data. However, the application of GNNs is constrained by…

In recent years a number of methods have been developed for automatically learning the (sparse) connectivity structure of Markov Random Fields. These methods are mostly based on L1-regularized optimization which has a number of…

We study the numerical integration problem for functions with infinitely many variables. The function spaces of integrands we consider are weighted reproducing kernel Hilbert spaces with norms related to the ANOVA decomposition of the…

Graph Neural Networks (GNNs) have achieved promising performance in a variety of graph-focused tasks. Despite their success, however, existing GNNs suffer from two significant limitations: a lack of interpretability in their results due to…

Gravitational waves from compact binaries measured by the LIGO and Virgo detectors are routinely analyzed using Markov Chain Monte Carlo sampling algorithms. Because the evaluation of the likelihood function requires evaluating millions of…

Gaussian Mixture Models (GMMs) are a standard tool in data analysis. However, they face problems when applied to high-dimensional data (e.g., images) due to the size of the required full covariance matrices (CMs), whereas the use of…

Applications of machine learning techniques for materials modeling typically involve functions known to be equivariant or invariant to specific symmetries. While graph neural networks (GNNs) have proven successful in such tasks, they…

Matrix denoising is central to signal processing and machine learning. Its statistical analysis when the matrix to infer has a factorised structure with a rank growing proportionally to its dimension remains a challenge, except when it is…

Graph neural network simulators (GNS) have emerged as a computationally efficient tool for simulating granular flows. Previous efforts have been limited to simplified homogeneous geometries characterized only by the friction angle, which…

The simulation of microcirculatory blood flow in realistic vascular architectures poses significant challenges due to the multiscale nature of the problem and the topological complexity of capillary networks. In this work, we propose a…

We propose a Neural Hidden Markov Model (HMM) with Adaptive Granularity Attention (AGA) for high-frequency order flow modeling. The model addresses the challenge of capturing multi-scale temporal dynamics in financial markets, where…

Most applications of Bayesian Inference for parameter estimation and model selection in astrophysics involve the use of Monte Carlo techniques such as Markov Chain Monte Carlo (MCMC) and nested sampling. However, these techniques are time…