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Over the past decade, a number of algorithms for full-field elastic strain estimation from neutron and X-ray measurements have been published. Many of the recently published algorithms rely on modelling the unknown strain field as a…
In this paper we consider the problem of approximating Euclidean distances by the infinite integer grid graph. Although the topology of the graph is fixed, we have control over the edge-weight assignment $w:E\to \mathbb{R}_{\ge 0}$, and…
We introduce a probabilistic splat-based radiance field framework that retains the fast rasterization and test-time efficiency of 3D Gaussian Splatting (3DGS) while replacing heuristic primitive manipulation with gradient-based optimization…
Random fields are mathematical structures used to model the spatial interaction of random variables along time, with applications ranging from statistical physics and thermodynamics to system's biology and the simulation of complex systems.…
Consider a quite arbitrary (semi)parametric model with a Euclidean parameter of interest and assume that an asymptotically (semi)parametrically efficient estimator of it is given. If the parameter of interest is known to lie on a general…
Interest has been rising lately towards methods representing data in non-Euclidean spaces, e.g. hyperbolic or spherical, that provide specific inductive biases useful for certain real-world data properties, e.g. scale-free, hierarchical or…
Gaussian random fields play an important role in many areas of science and engineering. In practice, they are often simulated by sampling from a high-dimensional multivariate normal distribution, which arises from the discretisation of a…
We consider the problem of recovering an unknown matching between a set of $n$ randomly placed points in $\mathbb{R}^d$ and random perturbations of these points. This can be seen as a model for particle tracking and more generally, entity…
Gaussian random fields (GRF) are a fundamental stochastic model for spatiotemporal data analysis. An essential ingredient of GRF is the covariance function that characterizes the joint Gaussian distribution of the field. Commonly used…
We propose a method for the description and simulation of the nonlinear dynamics of slender structures modeled as Cosserat rods. It is based on interpreting the strains and the generalized velocities of the cross sections as basic variables…
Gaussian random fields are a powerful tool for modeling environmental processes. For high dimensional samples, classical approaches for estimating the covariance parameters require highly challenging and massive computations, such as the…
Gaussian Markov random fields (GMRFs) are useful in a broad range of applications. In this paper we tackle the problem of learning a sparse GMRF in a high-dimensional space. Our approach uses the l1-norm as a regularization on the inverse…
Graph representation learning resurges as a trending research subject owing to the widespread use of deep learning for Euclidean data, which inspire various creative designs of neural networks in the non-Euclidean domain, particularly…
Undirected graphical models are powerful tools for uncovering complex relationships among high-dimensional variables. This paper aims to fully recover the structure of an undirected graphical model when the data naturally take matrix form,…
In the last decade or so, we have witnessed deep learning reinvigorating the machine learning field. It has solved many problems in the domains of computer vision, speech recognition, natural language processing, and various other tasks…
In the last years, an increasing number of learning-based approaches have been proposed to tackle combinatorial optimization problems such as routing problems. Many of these approaches are based on graph neural networks (GNNs) or related…
Spatial models for areal data are often constructed such that all pairs of adjacent regions are assumed to have near-identical spatial autocorrelation. In practice, data can exhibit dependence structures more complicated than can be…
Large or very large spatial (and spatio-temporal) datasets have become common place in many environmental and climate studies. These data are often collected in non-Euclidean spaces (such as the planet Earth) and they often present…
This paper studies the formulation, well-posedness, and numerical solution of Bayesian inverse problems on metric graphs, in which the edges represent one-dimensional wires connecting vertices. We focus on the inverse problem of recovering…
Probabilistic analysis for metric optimization problems has mostly been conducted on random Euclidean instances, but little is known about metric instances drawn from distributions other than the Euclidean. This motivates our study of…