Related papers: Functional Moments Regression
We propose generalized conditional functional principal components analysis (GC-FPCA) for the joint modeling of the fixed and random effects of non-Gaussian functional outcomes. The method scales up to very large functional data sets by…
Gaussian process regression is a powerful method for predicting states based on given data. It has been successfully applied for probabilistic predictions of structural systems to quantify, for example, the crack growth in mechanical…
We introduce inferential methods for prediction based on functional random effects in generalized functional mixed effects models. This is similar to the inference for random effects in generalized linear mixed effects models (GLMMs), but…
This paper presents an approach for constrained Gaussian Process (GP) regression where we assume that a set of linear transformations of the process are bounded. It is motivated by machine learning applications for high-consequence…
Gaussian process (GP) models that combine both categorical and continuous input variables have found use in analysis of longitudinal data and computer experiments. However, standard inference for these models has the typical cubic scaling,…
Gaussian Process (GP) regression is a flexible non-parametric approach to approximate complex models. In many cases, these models correspond to processes with bounded physical properties. Standard GP regression typically results in a proxy…
Gaussian process (GP) priors are non-parametric generative models with appealing modelling properties for Bayesian inference: they can model non-linear relationships through noisy observations, have closed-form expressions for training and…
Between 2011 and 2014 NHANES collected objectively measured physical activity data using wrist-worn accelerometers for tens of thousands of individuals for up to seven days. In this study, we analyze minute-level indicators of being active,…
The accurate prediction of time-changing variances is an important task in the modeling of financial data. Standard econometric models are often limited as they assume rigid functional relationships for the variances. Moreover, function…
We introduce Latent Gaussian Process Regression which is a latent variable extension allowing modelling of non-stationary multi-modal processes using GPs. The approach is built on extending the input space of a regression problem with a…
Longitudinal studies frequently incorporate covariates that evolve over time, creating complex dependence structures between outcomes and predictors. When covariates are time dependent, standard power analysis tools--largely developed for…
Modelling a large bundle of curves arises in a broad spectrum of real applications. However, existing literature relies primarily on the critical assumption of independent curve observations. In this paper, we provide a general theory for…
Mechanistic simulation models are inverted against observations in order to gain inference on modeled processes. However, with the increasing ability to collect high resolution observations, these observations represent more patterns of…
Functional data are often extremely high-dimensional and exhibit strong dependence structures but can often prove valuable for both prediction and inference. The literature on functional data analysis is well developed; however, there has…
In this paper we propose a generalized Gaussian process concurrent regression model for functional data where the functional response variable has a binomial, Poisson or other non-Gaussian distribution from an exponential family while the…
One of the key challenges in revenue management is unconstraining demand data. Existing state of the art single-class unconstraining methods make restrictive assumptions about the form of the underlying demand and can perform poorly when…
We extend Gaussian perturbation models in classical functional data analysis to the three-dimensional rotational group where a zero-mean Gaussian process in the Lie algebra under the Lie exponential spreads multiplicatively around a central…
Earth observation from satellite sensory data poses challenging problems, where machine learning is currently a key player. In recent years, Gaussian Process (GP) regression has excelled in biophysical parameter estimation tasks from…
Gaussian Processes (GPs) have been widely used in machine learning to model distributions over functions, with applications including multi-modal regression, time-series prediction, and few-shot learning. GPs are particularly useful in the…
Continuous-time state estimation is gaining in popularity due to its abilities to provide smooth solutions, handle asynchronous sensors, and interpolate between data points. While there are two main paradigms, parametric (e.g., temporal…