Related papers: A Hierarchical Model for Aggregated Functional Dat…

Gaussian processes (GPs) are nonparametric priors over functions. Fitting a GP implies computing a posterior distribution of functions consistent with the observed data. Similarly, deep Gaussian processes (DGPs) should allow us to compute a…

In environmental studies, realistic simulations are essential for understanding complex systems. Statistical emulation with Gaussian processes (GPs) in functional data models have become a standard tool for this purpose. Traditional…

This paper is concerned with inference based on the mean function of a functional time series, which is defined as a collection of curves obtained by splitting a continuous time record, e.g. into daily or annual curves. We develop a normal…

Mixed membership models, or partial membership models, are a flexible unsupervised learning method that allows each observation to belong to multiple clusters. In this paper, we propose a Bayesian mixed membership model for functional data.…

We study nonparametric clustering of smooth random curves on the basis of the L2 gradient flow associated to a pseudo-density functional and we show that the clustering is well-defined both at the population and at the sample level. We…

We introduce Bayesian hierarchical models for predicting high-dimensional tabular survey data which can be distributed from one or multiple classes of distributions (e.g., Gaussian, Poisson, Binomial, etc.). We adopt a Bayesian…

Gaussian processes are a versatile framework for learning unknown functions in a manner that permits one to utilize prior information about their properties. Although many different Gaussian process models are readily available when the…

A model involving Gaussian processes (GPs) is introduced to simultaneously handle multi-task learning, clustering, and prediction for multiple functional data. This procedure acts as a model-based clustering method for functional data as…

Bayesian inference and kernel methods are well established in machine learning. The neural network Gaussian process in particular provides a concept to investigate neural networks in the limit of infinitely wide hidden layers by using…

Shape constrained regression analysis has applications in dose-response modeling, environmental risk assessment, disease screening and many other areas. Incorporating the shape constraints can improve estimation efficiency and avoid…

Joint modeling of multiview graphs with a common set of nodes between views and auxiliary predictors is an essential, yet less explored, area in statistical methodology. Traditional approaches often treat graphs in different views as…

Gaussian process models are flexible, Bayesian non-parametric approaches to regression. Properties of multivariate Gaussians mean that they can be combined linearly in the manner of additive models and via a link function (like in…

Modelling spatio-temporal processes has become an important issue in current research. Since Gaussian processes are essentially determined by their second order structure, broad classes of covariance functions are of interest. Here, a new…

Functional data analysis finds widespread application across various fields. While functional data are intrinsically infinite-dimensional, in practice, they are observed only at a finite set of points, typically over a dense grid. As a…

This paper proposes and analyzes fully data driven methods for inference about the mean function of a stochastic process from a sample of independent trajectories of the process, observed at discrete time points and corrupted by additive…

In this paper, we develop a quantile functional regression modeling framework that models the distribution of a set of common repeated observations from a subject through the quantile function, which is regressed on a set of covariates to…

Covariate measurement error in nonparametric regression is a common problem in nutritional epidemiology and geostatistics, and other fields. Over the last two decades, this problem has received substantial attention in the frequentist…

We present a novel extension of multi-output Gaussian processes for handling heterogeneous outputs. We assume that each output has its own likelihood function and use a vector-valued Gaussian process prior to jointly model the parameters in…

We consider the statistical problem of estimating constituent curves from observations of their aggregated curves, referred to as \textit{aggregated functional data}, in models with strictly positive random errors following a Gamma…

We develop sampling algorithms to fit Bayesian hierarchical models, the computational complexity of which scales linearly with the number of observations and the number of parameters in the model. We focus on crossed random effect and…