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Machine learning methods on graphs have proven useful in many applications due to their ability to handle generally structured data. The framework of Gaussian Markov Random Fields (GMRFs) provides a principled way to define Gaussian models…

Probabilistic graphical models (PGMs) are powerful tools for representing statistical dependencies through graphs in high-dimensional systems. However, they are limited to pairwise interactions. In this work, we propose the simplicial…

We introduce Gaussian orthogonal latent factor processes for modeling and predicting large correlated data. To handle the computational challenge, we first decompose the likelihood function of the Gaussian random field with a…

We present GP-4DGS, a novel framework that integrates Gaussian Processes (GPs) into 4D Gaussian Splatting (4DGS) for principled probabilistic modeling of dynamic scenes. While existing 4DGS methods focus on deterministic reconstruction,…

We investigate two options for performing Bayesian inference on spatial log-Gaussian Cox processes assuming a spatially continuous latent field: Markov chain Monte Carlo (MCMC) and the integrated nested Laplace approximation (INLA). We…

Logic-Geometric Programming (LGP) is a powerful motion and manipulation planning framework, which represents hierarchical structure using logic rules that describe discrete aspects of problems, e.g., touch, grasp, hit, or push, and solves…

Gaussian process regression is a frequently used statistical method for flexible yet fully probabilistic non-linear regression modeling. A common obstacle is its computational complexity which scales poorly with the number of observations.…

Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…

Heterogeneous nature of the vehicular networks, which results from the co-existence of human-driven, semi-automated, and fully autonomous vehicles, is a challenging phenomenon toward the realization of the intelligent transportation systems…

A key challenge in spatial statistics is the analysis for massive spatially-referenced data sets. Such analyses often proceed from Gaussian process specifications that can produce rich and robust inference, but involve dense covariance…

Gaussian processes (GPs) are commonly used for geospatial analysis, but they suffer from high computational complexity when dealing with massive data. For instance, the log-likelihood function required in estimating the statistical model…

We present a framework for transfer learning based on modular variational Gaussian processes (GP). We develop a module-based method that having a dictionary of well fitted GPs, one could build ensemble GP models without revisiting any data.…

Gaussian processes are an effective model class for learning unknown functions, particularly in settings where accurately representing predictive uncertainty is of key importance. Motivated by applications in the physical sciences, the…

Gaussian processes (GPs) are frequently used in machine learning and statistics to construct powerful models. However, when employing GPs in practice, important considerations must be made, regarding the high computational burden,…

We present a novel approach for the analysis of multivariate case-control georeferenced data using Bayesian inference in the context of disease mapping, where the spatial distribution of different types of cancers is analyzed. Extending…

In spite of the diverse literature on nonstationary spatial modeling and approximate Gaussian process (GP) methods, there are no general approaches for conducting fully Bayesian inference for moderately sized nonstationary spatial data sets…

We propose a new framework to systematically incorporate data uncertainty in Gaussian Splatting. Being the new paradigm of neural rendering, Gaussian Splatting has been investigated in many applications, with the main effort in extending…

Gaussian processes (GPs) are commonly used as models for functions, time series, and spatial fields, but they are computationally infeasible for large datasets. Focusing on the typical setting of modeling data as a GP plus an additive noise…

Gaussian Processes (GPs) are widely used to model dependencies in spatial statistics and machine learning. However, exact inference is computationally intractable for GP regression, with a time complexity of $O(n^3)$. The Vecchia…

We study maximum likelihood estimation for spatial generalized linear mixed models with Gaussian process approximations using a stochastic Newton-Raphson algorithm. We consider two Gaussian Process approximations in this context: spectral…