Related papers: Discrete Gaussian Vector Fields On Meshes

Real world-datasets characterized by discrete features are ubiquitous: from categorical surveys to clinical questionnaires, from unweighted networks to DNA sequences. Nevertheless, the most common unsupervised dimensional reduction methods…

Physical processes that manifest as tangential vector fields on a sphere are common in geophysical and environmental sciences. These naturally occurring vector fields are often subject to physical constraints, such as being curl-free or…

Diffusion models are generative models that have recently demonstrated impressive performances in terms of sampling quality and density estimation in high dimensions. They rely on a forward continuous diffusion process and a backward…

Complex multivariate time series arise in many fields, ranging from computer vision to robotics or medicine. Often we are interested in the independent underlying factors that give rise to the high-dimensional data we are observing. While…

Machine learning methods based on statistical principles have proven highly successful in dealing with a wide variety of data analysis and analytics tasks. Traditional data models are mostly concerned with independent identically…

The emergence of organized multiscale patterns resulting from convection is ubiquitous, observed throughout different cloud types. The reproduction of such patterns by general circulation models remains a challenge due to the complex nature…

Recent advances in learning techniques have enabled the modelling of dynamical systems for scientific and engineering applications directly from data. However, in many contexts explicit data collection is expensive and learning algorithms…

Understanding the temporal evolution of sets of vectors is a fundamental challenge across various domains, including ecology, crime analysis, and linguistics. For instance, ecosystem structures evolve due to interactions among plants,…

Gaussian processes (GPs) are popular nonparametric statistical models for learning unknown functions and quantifying the spatiotemporal uncertainty in data. Recent works have extended GPs to model scalar and vector quantities distributed…

General Circulation Models (GCMs) are widely used for future climate projections, but their coarse spatial resolution and systematic biases limit their direct use for impact studies. This limitation is particularly critical for wind-related…

We present a framework for inference for spatial processes that have actual values imperfectly represented by data. Environmental processes represented as spatial fields, either at fixed time points, or aggregated over fixed time periods,…

We propose a class of intrinsic Gaussian processes (in-GPs) for interpolation, regression and classification on manifolds with a primary focus on complex constrained domains or irregular shaped spaces arising as subsets or submanifolds of…

Topological abstractions offer a method to summarize the behavior of vector fields but computing them robustly can be challenging due to numerical precision issues. One alternative is to represent the vector field using a discrete approach,…

In this paper we introduce deep Gaussian process (GP) models. Deep GPs are a deep belief network based on Gaussian process mappings. The data is modeled as the output of a multivariate GP. The inputs to that Gaussian process are then…

We propose a novel discretization of tangent vector fields for triangle meshes. Starting with a Phong map continuously assigning normals to all points on the mesh, we define an extrinsic bases for continuous tangent vector fields by using…

We define a new class of Gaussian processes on compact metric graphs such as street or river networks. The proposed models, the Whittle--Mat\'ern fields, are defined via a fractional stochastic differential equation on the compact metric…

We propose a Bayesian model for mixed ordinal and continuous multivariate data to evaluate a latent spatial Gaussian process. Our proposed model can be used in many contexts where mixed continuous and discrete multivariate responses are…

A line field on a manifold is a smooth map which assigns a tangent line to all but a finite number of points of the manifold. As such, it can be seen as a generalization of vector fields. They model a number of geometric and physical…

Earth observation (EO) by airborne and satellite remote sensing and in-situ observations play a fundamental role in monitoring our planet. In the last decade, machine learning and Gaussian processes (GPs) in particular has attained…

We introduce a class of scalable Bayesian hierarchical models for the analysis of massive geostatistical datasets. The underlying idea combines ideas on high-dimensional geostatistics by partitioning the spatial domain and modeling the…