Related papers: Modeling Longitudinal Data on Riemannian Manifolds
Off-the-shelf Gaussian Process (GP) covariance functions encode smoothness assumptions on the structure of the function to be modeled. To model complex and non-differentiable functions, these smoothness assumptions are often too…
Functional principal component analysis is essential in functional data analysis, but the inferences will become unconvincing when some non-Gaussian characteristics occur, such as heavy tail and skewness. The focus of this paper is to…
Principal component analysis has been a main tool in multivariate analysis for estimating a low dimensional linear subspace that explains most of the variability in the data. However, in high-dimensional regimes, naive estimates of the…
Large longitudinal studies provide lots of valuable information, especially in medical applications. A problem which must be taken care of in order to utilize their full potential is that of correlation between intra-subject measurements…
Physical activity (PA) is significantly associated with many health outcomes. The wide usage of wearable accelerometer-based activity trackers in recent years has provided a unique opportunity for in-depth research on PA and its relations…
Most biological data are multidimensional, posing a major challenge to human comprehension and computational analysis. Principal component analysis is the most popular approach to rendering two- or three-dimensional representations of the…
We propose a novel method of finding principal components in multivariate data sets that lie on an embedded nonlinear Riemannian manifold within a higher-dimensional space. Our aim is to extend the geometric interpretation of PCA, while…
Many studies collect functional data from multiple subjects that have both multilevel and multivariate structures. An example of such data comes from popular neuroscience experiments where participants' brain activity is recorded using…
In this work we develop a novel and foundational framework for analyzing general Riemannian functional data, in particular a new development of tensor Hilbert spaces along curves on a manifold. Such spaces enable us to derive Karhunen-Loeve…
We consider spatially dependent functional data collected under a geostatistics setting, where locations are sampled from a spatial point process. The functional response is the sum of a spatially dependent functional effect and a spatially…
Functional Principal Components Analysis (FPCA) provides a parsimonious, semi-parametric model for multivariate, sparsely-observed functional data. Frequentist FPCA approaches estimate principal components (PCs) from the data, then…
Functional principal components analysis is a popular tool for inference on functional data. Standard approaches rely on an eigendecomposition of a smoothed covariance surface in order to extract the orthonormal functions representing the…
We consider the problem of reconstructing missing data on a smooth manifold from incomplete and nonuniform samples. While classical methods for manifold approximation typically assume quasi-uniform data, their performance deteriorates…
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…
Modern longitudinal studies collect multiple outcomes as the primary endpoints to understand the complex dynamics of the diseases. Oftentimes, especially in clinical trials, the joint variations among the multidimensional responses play a…
Modeling non-linear temporal trajectories is of fundamental interest in many application areas, such as in longitudinal microbiome analysis. Many existing methods focus on estimating mean trajectories, but it is also often of value to…
Estimation and inference with modern longitudinal data from wearable devices, which consist of biological signals at high-frequency time points, is burdened by massive computational costs. We propose a distributed estimation and inference…
Motivation: Although principal component analysis is frequently applied to reduce the dimensionality of matrix data, the method is sensitive to noise and bias and has difficulty with comparability and interpretation. These issues are…
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…
One develops a fast computational methodology for principal component analysis on manifolds. Instead of estimating intrinsic principal components on an object space with a Riemannian structure, one embeds the object space in a numerical…