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This review article focuses on regularised estimation procedures applicable to geostatistical and spatial econometric models. These methods are particularly relevant in the case of big geospatial data for dimensionality reduction or model…
The declining response rates in probability surveys along with the widespread availability of unstructured data has led to growing research into non-probability samples. Existing robust approaches are not well-developed for non-Gaussian…
Weak gravitational lensing surveys are rapidly becoming important tools to probe directly the mass density fluctuations in the universe and its background dynamics. Earlier studies have shown that it is possible to model the statistics of…
Gaussian processes (GPs) are widely used as distributions of random effects in linear mixed models, which are fit using the restricted likelihood or the closely-related Bayesian analysis. This article addresses two problems. First, we…
A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…
3D Gaussian Splatting (3D-GS) has emerged as an efficient 3D representation and a promising foundation for semantic tasks like segmentation. However, existing 3D-GS-based segmentation methods typically rely on high-dimensional category…
We consider the problem of learning a Gaussian variational approximation to the posterior distribution for a high-dimensional parameter, where we impose sparsity in the precision matrix to reflect appropriate conditional independence…
This paper proposes novel noise-free Bayesian optimization strategies that rely on a random exploration step to enhance the accuracy of Gaussian process surrogate models. The new algorithms retain the ease of implementation of the classical…
In this work, we employ the Bayesian inference framework to solve the problem of estimating the solution and particularly, its derivatives, which satisfy a known differential equation, from the given noisy and scarce observations of the…
We introduce a scalable approach to Gaussian process inference that combines spatio-temporal filtering with natural gradient variational inference, resulting in a non-conjugate GP method for multivariate data that scales linearly with…
Gaussian processes (GPs) are commonplace in spatial statistics. Although many non-stationary models have been developed, there is arguably a lack of flexibility compared to equipping each location with its own parameters. However, the…
The primary objective of this work is to develop coarse-graining schemes for stochastic many-body microscopic models and quantify their effectiveness in terms of a priori and a posteriori error analysis. In this paper we focus on stochastic…
We introduce a novel edge tracing algorithm using Gaussian process regression. Our edge-based segmentation algorithm models an edge of interest using Gaussian process regression and iteratively searches the image for edge pixels in a…
The large time and length scales and, not least, the vast number of particles involved in industrial-scale simulations inflate the computational costs of the Discrete Element Method (DEM) excessively. Coarse grain models can help to lower…
We present an iterative framework to improve the amortized approximations of posterior distributions in the context of Bayesian inverse problems, which is inspired by loop-unrolled gradient descent methods and is theoretically grounded in…
This work introduces the concept of parametric Gaussian processes (PGPs), which is built upon the seemingly self-contradictory idea of making Gaussian processes parametric. Parametric Gaussian processes, by construction, are designed to…
Current approaches for fine-grained recognition do the following: First, recruit experts to annotate a dataset of images, optionally also collecting more structured data in the form of part annotations and bounding boxes. Second, train a…
We consider the problem of sequential estimation of the unknowns of state-space and deep state-space models that include estimation of functions and latent processes of the models. The proposed approach relies on Gaussian and deep Gaussian…
Spatio-temporal point process models play a central role in the analysis of spatially distributed systems in several disciplines. Yet, scalable inference remains computa- tionally challenging both due to the high resolution modelling…
Coarse-Graining (CG) models are low resolution approximation of high resolution models, such as all-atomic (AA) models. An effective CG model is expected to reproduce equilibrium values of sufficient physical quantities of its AA model,…