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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…
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)…
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…
The Theory of Functional Connections (TFC) is a functional interpolation framework founded upon the so-called constrained expression: a functional that expresses the family of all possible functions that satisfy some user-specified, linear…
Understanding and predicting the electric consumption patterns in the short-, mid- and long-term, at the distribution and transmission level, is a fundamental asset for smart grids infrastructure planning, dynamic network reconfiguration,…
Functional Principal Component Analysis is a reference method for dimension reduction of curve data. Its theoretical properties are now well understood in the simplified case where the sample curves are fully observed without noise.…
Due to rapid advances in multielectrode recording technology, the local field potential (LFP) has again become a popular measure of neuronal activity in both basic research and clinical applications. Proper understanding of the LFP requires…
Multi-electrode arrays covering several square millimeters of neural tissue provide simultaneous access to population signals such as extracellular potentials and spiking activity of one hundred or more individual neurons. The…
The extraordinary advancements in neuroscientific technology for brain recordings over the last decades have led to increasingly complex spatio-temporal datasets. To reduce oversimplifications, new models have been developed to be able to…
Digital health technologies enable high-frequency collection of data in near-continuous time and capture rich information about the health of individuals. The raw data collected by these devices often have a hierarchical functional…
Constructing generative models for functional observations is an important task in statistical functional analysis. In general, functional data contains both phase (or x or horizontal) and amplitude (or y or vertical) variability. Tradi-…
Despite enormous research interest and rapid application of federated learning (FL) to various areas, existing studies mostly focus on supervised federated learning under the horizontally partitioned local dataset setting. This paper will…
Existing approaches for multivariate functional principal component analysis are restricted to data on the same one-dimensional interval. The presented approach focuses on multivariate functional data on different domains that may differ in…
Sparse functional data arise when measurements are observed infrequently and at irregular time points for each subject, often in the presence of measurement error. These characteristics introduce additional challenges for functional…
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…
Functional data analysis (FDA) methods have computational and theoretical appeals for some high dimensional data, but lack the scalability to modern large sample datasets. To tackle the challenge, we develop randomized algorithms for two…
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 component analysis (FPCA) has played an important role in the development of functional time series analysis. This note investigates how FPCA can be used to analyze cointegrated functional time series and proposes a…
Functional data analysis on nonlinear manifolds has drawn recent interest. Sphere-valued functional data, which are encountered for example as movement trajectories on the surface of the earth, are an important special case. We consider an…
In this paper, we address the problem of dimension reduction for time series of functional data $(X_t\colon t\in\mathbb{Z})$. Such {\it functional time series} frequently arise, e.g., when a continuous-time process is segmented into some…