Related papers: Transformed Gaussian Markov Random Fields and Spat…
In genome-wide prediction, independence of marker allele substitution effects is typically assumed; however, since early stages of this technology it has been known that nature points to correlated effects. In statistics, graphical models…
We propose a novel probabilistic model to facilitate the learning of multivariate tail dependence of multiple financial assets. Our method allows one to construct from known random vectors, e.g., standard normal, sophisticated joint…
Over the last few decades, image-based building surface reconstruction has garnered substantial research interest and has been applied across various fields, such as heritage preservation, architectural planning, etc. Compared to the…
The manuscript develops new method and theory for non-linear regression for binary dependent data using random forests. Existing implementations of random forests for binary data cannot explicitly account for data correlation common in…
Wireless radiance field (WRF) reconstruction aims to learn a continuous, queryable representation of radio frequency characteristics over 3D space and direction, from which specific quantities, such as the spatial power spectrum (SPS) at a…
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…
Data derived from remote sensing or numerical simulations often have a regular gridded structure and are large in volume, making it challenging to find accurate spatial models that can fill in missing grid cells or simulate the process…
Geographical random forest (GRF) is a recently developed and spatially explicit machine learning model. With the ability to provide more accurate predictions and local interpretations, GRF has already been used in many studies. The current…
We study linear models under heavy-tailed priors from a probabilistic viewpoint. Instead of computing a single sparse most probable (MAP) solution as in standard deterministic approaches, the focus in the Bayesian compressed sensing…
Bayesian inference of Gibbs random fields (GRFs) is often referred to as a doubly intractable problem, since the likelihood function is intractable. The exploration of the posterior distribution of such models is typically carried out with…
Markov random fields (MRFs) are invaluable tools across diverse fields, and spatiotemporal MRFs (STMRFs) amplify their effectiveness by integrating spatial and temporal dimensions. However, modeling spatiotemporal data introduces additional…
A fundamental challenge in developing high-impact machine learning technologies is balancing the need to model rich, structured domains with the ability to scale to big data. Many important problem areas are both richly structured and large…
We establish a martingale-type characterisations for the continuum Gaussian free field (GFF) and for fractional Gaussian free fields (FGFs), using their connection to the stochastic heat equation and to fractional stochastic heat equations.…
Motivated by problems from neuroimaging in which existing approaches make use of "mass univariate" analysis which neglects spatial structure entirely, but the full joint modelling of all quantities of interest is computationally infeasible,…
This work addresses the problem of simulating Gaussian random fields that are continuously indexed over a class of metric graphs, termed graphs with Euclidean edges, being more general and flexible than linear networks. We introduce three…
Gaussian processes are valuable tools for non-parametric modelling, where typically an assumption of stationarity is employed. While removing this assumption can improve prediction, fitting such models is challenging. In this work,…
For marine biologists, ascertaining the dependence structures between marine species and marine environments, such as sea surface temperature and ocean depth, is imperative for defining ecosystem functioning and providing insights into the…
Flood extent mapping plays a crucial role in disaster management and national water forecasting. Unfortunately, traditional classification methods are often hampered by the existence of noise, obstacles and heterogeneity in spectral…
Random field models are mathematical structures used in the study of stochastic complex systems. In this paper, we compute the shape operator of Gaussian random field manifolds using the first and second fundamental forms (Fisher…
Hidden Markov models (HMMs) are powerful tools for analysing time series data that depend on discrete underlying but unobserved states. As such, they have gained prominence across numerous empirical disciplines, in particular ecology,…