Related papers: A Hierarchical Model for Aggregated Functional Dat…
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…
In order to scale standard Gaussian process (GP) regression to large-scale datasets, aggregation models employ factorized training process and then combine predictions from distributed experts. The state-of-the-art aggregation models,…
Spatial functional data arise in many settings, such as particulate matter curves observed at monitoring stations and age population curves at each areal unit. Most existing functional regression models have limited applicability because…
Gaussian processes (GPs) are ubiquitous tools for modeling and predicting continuous processes in physical and engineering sciences. This is partly due to the fact that one may employ a Gaussian process as an interpolator while facilitating…
Gaussian processes provide a compact representation for modeling and estimating an unknown function, that can be updated as new measurements of the function are obtained. This paper extends this powerful framework to the case where the…
We discuss the Gaussian graphical model (GGM; an undirected network of partial correlation coefficients) and detail its utility as an exploratory data analysis tool. The GGM shows which variables predict one-another, allows for sparse…
Deep Gaussian Processes learn probabilistic data representations for supervised learning by cascading multiple Gaussian Processes. While this model family promises flexible predictive distributions, exact inference is not tractable.…
Generalized additive models (GAMs) provide a way to blend parametric and non-parametric (function approximation) techniques together, making them flexible tools suitable for many modeling problems. For instance, GAMs can be used to…
Statistical analysis of high-dimensional functional times series arises in various applications. Under this scenario, in addition to the intrinsic infinite-dimensionality of functional data, the number of functional variables can grow with…
Multi-dimensional functional data arises in numerous modern scientific experimental and observational studies. In this paper we focus on longitudinal functional data, a structured form of multidimensional functional data. Operating within a…
Functional data describe a wide range of processes, such as growth curves and spectral absorption. In this study, we analyze air pollution data from the In-service Aircraft for a Global Observing System, focusing on the spatial interactions…
In many applications, smooth processes generate data that is recorded under a variety of observation regimes, such as dense, sparse or fragmented observations that are often contaminated with error. The statistical goal of registering and…
The analytic inference, e.g. predictive distribution being in closed form, may be an appealing benefit for machine learning practitioners when they treat wide neural networks as Gaussian process in Bayesian setting. The realistic widths,…
Estimation of the mean and covariance parameters for functional data is a critical task, with local linear smoothing being a popular choice. In recent years, many scientific domains are producing multivariate functional data for which $p$,…
In this manuscript a unified framework for conducting inference on complex aggregated data in high dimensional settings is proposed. The data are assumed to be a collection of multiple non-Gaussian realizations with underlying undirected…
Functional data consist of trajectories observed over a continuous domain, such as time, space, or wavelength. Here we consider curves observed on different groups of subjects and propose a Bayesian multi-group functional factor analysis…
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…
The theory of quasi-arithmetic means is a powerful tool in the study of covariance functions across space-time. In the present study we use quasi-arithmetic functionals to make inferences about the permissibility of averages of functions…
For multivariate spatial Gaussian process (GP) models, customary specifications of cross-covariance functions do not exploit relational inter-variable graphs to ensure process-level conditional independence among the variables. This is…
In this paper, we study a smoothness regularization method for a varying coefficient model based on sparse and irregularly sampled functional data which is contaminated with some measurement errors. We estimate the one-dimensional…