Related papers: Generative Models for Functional Data using Phase …
Functional data analyses typically proceed by smoothing, followed by functional PCA. This paradigm implicitly assumes that rough variation is due to nuisance noise. Nevertheless, relevant functional features such as time-localised or short…
Random Phase Approximation (RPA) provides a very convenient tool to study the ensembles of weakly interacting waves, commonly called Wave Turbulence. In its traditional formulation, RPA assumes that phases of interacting waves are random…
We develop a robust Bayesian functional principal component analysis (RB-FPCA) method that utilizes the skew elliptical class of distributions to model functional data, which are observed over a continuous domain. This approach effectively…
Applications of functional data with large numbers of predictors have grown precipitously in recent years, driven, in part, by rapid advances in genotyping technologies. Given the large numbers of genetic mutations encountered in genetic…
We propose a novel class of prior distributions for sequences of orthogonal functions, which are frequently required in various statistical models such as functional principal component analysis (FPCA). Our approach constructs priors…
Devising domain- and model-agnostic evaluation metrics for generative models is an important and as yet unresolved problem. Most existing metrics, which were tailored solely to the image synthesis setup, exhibit a limited capacity for…
Regularized variants of Principal Components Analysis, especially Sparse PCA and Functional PCA, are among the most useful tools for the analysis of complex high-dimensional data. Many examples of massive data, have both sparse and…
In a physical system, changing parameters such as temperature can induce a phase transition: an abrupt change from one state of matter to another. Analogous phenomena have recently been observed in large language models. Typically, the task…
Functional principal component analysis (FPCA) is an important technique for dimension reduction in functional data analysis (FDA). Classical FPCA method is based on the Karhunen-Lo\`{e}ve expansion, which assumes a linear structure of the…
Elastic Riemannian metrics have been used successfully in the past for statistical treatments of functional and curve shape data. However, this usage has suffered from an important restriction: the function boundaries are assumed fixed and…
Multivariate functional data are becoming ubiquitous with advances in modern technology and are substantially more complex than univariate functional data. We propose and study a novel model for multivariate functional data where the…
We consider the problem of constructing nonparametric undirected graphical models for high-dimensional functional data. Most existing statistical methods in this context assume either a Gaussian distribution on the vertices or linear…
In climate studies, detecting spatial patterns that largely deviate from the sample mean still remains a statistical challenge. Although a Principal Component Analysis (PCA), or equivalently a Empirical Orthogonal Functions (EOF)…
A reduced-rank mixed effects model is developed for robust modeling of sparsely observed paired functional data. In this model, the curves for each functional variable are summarized using a few functional principal components, and the…
In Functional Data Analysis, data are commonly assumed to be smooth functions on a fixed interval of the real line. In this work, we introduce a comprehensive framework for the analysis of functional data, whose domain is a two-dimensional…
This paper presents a novel approach to functional principal component analysis (FPCA) in Bayes spaces in the setting where densities are the object of analysis, but only few individual samples from each density are observed. We use the…
Augmentation by generative modelling yields a promising alternative to the accumulation of surgical data, where ethical, organisational and regulatory aspects must be considered. Yet, the joint synthesis of (image, mask) pairs for…
To detect differences between the mean curves of two samples in longitudinal study or functional data analysis, we usually need to partition the temporal or spatial domain into several pre-determined sub-areas. In this paper we apply the…
This article introduces a full mathematical and numerical framework for treating functional shapes (or fshapes) following the landmarks of shape spaces and shape analysis. Functional shapes can be described as signal functions supported on…
Methodology is proposed to uncover structural breaks in functional data that is "fully functional" in the sense that it does not rely on dimension reduction techniques. A thorough asymptotic theory is developed for a fully functional break…