Related papers: Macrofacet Theory for Gaussian Process Statistical…
Gaussian processes (GPs) defined through intrinsic random fields provide a flexible framework for modeling spatial phenomena, and have been advocated in a variety of applications over the past several decades. Nevertheless, their adoption…
We provide a new approach to approximate emulation of large computer experiments. By focusing expressly on desirable properties of the predictive equations, we derive a family of local sequential design schemes that dynamically define the…
Gaussian graphical models are used throughout the natural sciences, social sciences, and economics to model the statistical relationships between variables of interest in the form of a graph. We here provide a pedagogic introduction to…
Principal Component Analysis (PCA), a classical dimensionality reduction technique, and 2D Gaussian representation, an adaptation of 3D Gaussian Splatting for image representation, offer distinct approaches to modeling visual data. We…
When learning simulations for modeling physical phenomena in industrial designs, geometrical variabilities are of prime interest. While classical regression techniques prove effective for parameterized geometries, practical scenarios often…
We study the performance of nonparametric Bayes procedures for one-dimensional diffusions with periodic drift. We improve existing convergence rate results for Gaussian process (GP) priors with fixed hyper parameters. Moreover, we exhibit…
Gaussian processes are widely employed as versatile modelling and predictive tools in spatial statistics, functional data analysis, computer modelling and diverse applications of machine learning. They have been widely studied over…
Explainable machine learning has attracted much interest in the community where the stakes are high. Counterfactual explanations methods have become an important tool in explaining a black-box model. The recent advances have leveraged the…
Surface roughness plays a critical role and has effects in, e.g. fluid dynamics or contact mechanics. For example, to evaluate fluid behavior at different roughness properties, real-world or numerical experiments are performed. Numerical…
Nonparametric Bayesian models are used routinely as flexible and powerful models of complex data. Many times, a statistician may have additional informative beliefs about data distribution of interest, e.g., its mean or subset components,…
As Gaussian processes are used to answer increasingly complex questions, analytic solutions become scarcer and scarcer. Monte Carlo methods act as a convenient bridge for connecting intractable mathematical expressions with actionable…
Computer models are used as a way to explore complex physical systems. Stationary Gaussian process emulators, with their accompanying uncertainty quantification, are popular surrogates for computer models. However, many computer models are…
Predictive models for binary data are fundamental in various fields, and the growing complexity of modern applications has motivated several flexible specifications for modeling the relationship between the observed predictors and the…
Gaussian processes are the gold standard for many real-world modeling problems, especially in cases where a model's success hinges upon its ability to faithfully represent predictive uncertainty. These problems typically exist as parts of…
This paper presents the beginnings of an automatic statistician, focusing on regression problems. Our system explores an open-ended space of statistical models to discover a good explanation of a data set, and then produces a detailed…
We propose a novel Bayesian nonparametric method to learn translation-invariant relationships on non-Euclidean domains. The resulting graph convolutional Gaussian processes can be applied to problems in machine learning for which the input…
There is increasing interest in the problem of nonparametric regression with high-dimensional predictors. When the number of predictors $D$ is large, one encounters a daunting problem in attempting to estimate a $D$-dimensional surface…
Gaussian Processes face two primary challenges: constructing models for large datasets and selecting the optimal model. This master's thesis tackles these challenges in the low-dimensional case. We examine recent convergence results to…
We propose a probabilistic model for refining coarse-grained spatial data by utilizing auxiliary spatial data sets. Existing methods require that the spatial granularities of the auxiliary data sets are the same as the desired granularity…
Gaussian graphical models represent the backbone of the statistical toolbox for analyzing continuous multivariate systems. However, due to the intrinsic properties of the multivariate normal distribution, use of this model family may hide…