Related papers: Robust Functional Principal Component Analysis for…
Principal Component Analysis (PCA) is a cornerstone of dimensionality reduction, yet its classical formulation relies critically on second-order moments and is therefore fragile in the presence of heavy-tailed data and impulsive noise.…
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…
Classical multivariate principal component analysis has been extended to functional data and termed functional principal component analysis (FPCA). Most existing FPCA approaches do not accommodate covariate information, and it is the goal…
When considering functional principal component analysis for sparsely observed longitudinal data that take values on a nonlinear manifold, a major challenge is how to handle the sparse and irregular observations that are commonly…
Traditional Functional Principal Component Analysis typically focuses on densely observed univariate functional data, yet many applications, particularly in longitudinal studies, involve multivariate functional data observed sparsely and…
Principal component analysis (PCA) is a standard dimensionality reduction technique used in various research and applied fields. From an algorithmic point of view, classical PCA can be formulated in terms of operations on a multivariate…
Fan et al. [$\mathit{Annals}$ $\mathit{of}$ $\mathit{Statistics}$ $\textbf{47}$(6) (2019) 3009-3031] constructed a distributed principal component analysis (PCA) algorithm to reduce the communication cost between multiple servers…
Accounting for phase variability is a critical challenge in functional data analysis. To separate it from amplitude variation, functional data are registered, i.e., their observed domains are deformed elastically so that the resulting…
The analysis of multivariate functional curves has the potential to yield important scientific discoveries in domains such as healthcare, medicine, economics and social sciences. However, it is common for real-world settings to present…
We develop statistical models for samples of distribution-valued stochastic processes featuring time-indexed univariate distributions, with emphasis on functional principal component analysis. The proposed model presents an intrinsic rather…
A ubiquitous feature of data of our era is their extra-large sizes and dimensions. Analyzing such high-dimensional data poses significant challenges, since the feature dimension is often much larger than the sample size. This thesis…
Functional data analysis is concerned with the analysis of infinite-dimensional data functions. Functional principal component analysis (FPCA) is a key method to obtain finite-dimensional summaries. Consistency of FPCA has been…
We propose a new fast generalized functional principal components analysis (fast-GFPCA) algorithm for dimension reduction of non-Gaussian functional data. The method consists of: (1) binning the data within the functional domain; (2)…
This article presents factor copula approaches to model temporal dependency of non-Gaussian (continuous/discrete) longitudinal data. Factor copula models are canonical vine copulas which explain the underlying dependence structure of a…
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…
The declining response rates in probability surveys along with the widespread availability of unstructured data has led to growing research into non-probability samples. Existing robust approaches are not well-developed for non-Gaussian…
We propose a nonparametric method to explicitly model and represent the derivatives of smooth underlying trajectories for longitudinal data. This representation is based on a direct Karhunen--Lo\`eve expansion of the unobserved derivatives…
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…
Principal component analysis (PCA) frequently suffers from the disturbance of outliers and thus a spectrum of robust extensions and variations of PCA have been developed. However, existing extensions of PCA treat all samples equally even…
The advance of modern sensor technologies enables collection of multi-stream longitudinal data where multiple signals from different units are collected in real-time. In this article, we present a non-parametric approach to predict the…