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We develop a framework for generalized variational inference in infinite-dimensional function spaces and use it to construct a method termed Gaussian Wasserstein inference (GWI). GWI leverages the Wasserstein distance between Gaussian…

Machine Learning · Statistics 2022-10-18 Veit D. Wild , Robert Hu , Dino Sejdinovic

A Bayesian pseudocoreset is a compact synthetic dataset summarizing essential information of a large-scale dataset and thus can be used as a proxy dataset for scalable Bayesian inference. Typically, a Bayesian pseudocoreset is constructed…

Machine Learning · Computer Science 2023-10-30 Balhae Kim , Hyungi Lee , Juho Lee

Due to developments in instruments and computers, functional observations are increasingly popular. However, effective methodologies for flexibly estimating the underlying trends with valid uncertainty quantification for a sequence of…

Methodology · Statistics 2022-09-22 Tomoya Wakayama , Shonosuke Sugasawa

In this paper we present a novel inference methodology to perform Bayesian inference for spatiotemporal Cox processes where the intensity function depends on a multivariate Gaussian process. Dynamic Gaussian processes are introduced to…

Methodology · Statistics 2019-03-12 Flávio B. Gonçalves , Dani Gamerman

Functional data analysis deals with data recorded densely over time (or any other continuum) with one or more observed curves per subject. Conceptually, functional data are continuously defined, but in practice, they are usually observed at…

Methodology · Statistics 2023-01-20 Chengqian Xian , Camila de Souza , John Jewell , Ronaldo Dias

We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often…

Numerical Analysis · Mathematics 2018-08-01 Qingping Zhou , Wenqing Liu , Jinglai Li , Youssef M. Marzouk

As high-dimensional and high-frequency data are being collected on a large scale, the development of new statistical models is being pushed forward. Functional data analysis provides the required statistical methods to deal with large-scale…

Statistics Theory · Mathematics 2020-07-08 Israel Martínez-Hernández , Marc G. Genton

We propose an algorithm for Bayesian functional optimisation - that is, finding the function to optimise a process - guided by experimenter beliefs and intuitions regarding the expected characteristics (length-scale, smoothness, cyclicity…

Machine Learning · Computer Science 2020-09-09 Alistair Shilton , Sunil Gupta , Santu Rana , Svetha Venkatesh

In this paper, we consider high-dimensional Gaussian graphical models where the true underlying graph is decomposable. A hierarchical $G$-Wishart prior is proposed to conduct a Bayesian inference for the precision matrix and its graph…

Statistics Theory · Mathematics 2021-02-18 Kyoungjae Lee , Xuan Cao

Considering the context of functional data analysis, we developed and applied a new Bayesian approach via Gibbs sampler to select basis functions for a finite representation of functional data. The proposed methodology uses Bernoulli latent…

Methodology · Statistics 2023-02-13 Pedro Henrique T. O. Sousa , Camila P. E. de Souza , Ronaldo Dias

Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an…

Data Analysis, Statistics and Probability · Physics 2008-02-03 Radford M. Neal

Functional data are typically modeled as sample paths of smooth stochastic processes in order to mitigate the fact that they are often observed discretely and noisily, occasionally irregularly and sparsely. The smoothness assumption is…

Methodology · Statistics 2021-12-23 Neda Mohammadi , Victor M. Panaretos

Many real world problems exhibit patterns that have periodic behavior. For example, in astrophysics, periodic variable stars play a pivotal role in understanding our universe. An important step when analyzing data from such processes is the…

Machine Learning · Computer Science 2012-08-20 Yuyang Wang , Roni Khardon , Pavlos Protopapas

We study a problem of estimation of smooth functionals of parameter $\theta $ of Gaussian shift model $$ X=\theta +\xi,\ \theta \in E, $$ where $E$ is a separable Banach space and $X$ is an observation of unknown vector $\theta$ in Gaussian…

Statistics Theory · Mathematics 2019-11-19 Vladimir Koltchinskii , Mayya Zhilova

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.…

Methodology · Statistics 2026-03-10 Adam Gorm Hoffmann , Claus Thorn Ekstrøm , Andreas Kryger Jensen

Collected data, which is used for analysis or prediction tasks, often have a hierarchical structure, for example, data from various people performing the same task. Modeling the data's structure can improve the reliability of the derived…

Applications · Statistics 2018-11-12 Dennis Becker

Biological data objects often have both of the following features: (i) they are functions rather than single numbers or vectors, and (ii) they are correlated due to phylogenetic relationships. In this paper we give a flexible statistical…

Quantitative Methods · Quantitative Biology 2012-12-20 Nick S. Jones , John Moriarty

Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…

Methodology · Statistics 2023-08-08 Sagnik Bhadury , Riten Mitra , Jeremy T. Gaskins

Motivated by distinct walking patterns in real-world free-living gait data, this paper proposes an innovative curve-based sampling scheme for the analysis of functional data characterized by a mixture of covariance structures. Traditional…

Methodology · Statistics 2025-04-10 Yian Yu , Bo Wang , Jian Qing Shi

Varying coefficient models are popular for estimating nonlinear regression functions in functional data models. Their Bayesian variants have received limited attention in large data applications, primarily due to prohibitively slow…

Machine Learning · Statistics 2025-06-03 Rajarshi Guhaniyogi , Laura Baracaldo , Sudipto Banerjee