Related papers: Adaptive Functional Principal Component Analysis
This study presents a scalable data-driven algorithm designed to efficiently address the challenging problem of reachability analysis. Analysis of cyber-physical systems (CPS) relies typically on parametric physical models of dynamical…
The ability to manipulate complex systems, such as the brain, to modify specific outcomes has far-reaching implications, particularly in the treatment of psychiatric disorders. One approach to designing appropriate manipulations is to…
Motivated by risk assessment of coastal flooding, we consider time-consuming simulators with a spatial output. The aim is to perform sensitivity analysis (SA), quantifying the influence of input parameters on the output. There are three…
Due to developments in instruments and computers, functional observations are increasingly popular. However, effective methodologies for flexibly estimating the underlying trends with valid uncertainty quantification for a sequence of…
In functional data analysis, replicate observations of a smooth functional process and its derivatives offer a unique opportunity to flexibly estimate continuous-time ordinary differential equation models. Ramsay (1996) first proposed to…
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 component analysis (FPCA) based on the Karhunen--Lo\`{e}ve decomposition has been successfully applied in many applications, mainly for one sample problems. In this paper we consider common functional principal…
A set of curves or images of similar shape is an increasingly common functional data set collected in the sciences. Principal Component Analysis (PCA) is the most widely used technique to decompose variation in functional data. However, the…
We assume a nonparametric regression model where the signal is given by the sum of a piecewise constant function and a smooth function. To detect the change-points and estimate the regression functions, we propose PCpluS, a combination of…
With the advance of modern technology, more and more data are being recorded continuously during a time interval or intermittently at several discrete time points. They are both examples of "functional data", which have become a prevailing…
This paper introduces a robust approach to functional principal component analysis (FPCA) for relative data, particularly density functions. While recent papers have studied density data within the Bayes space framework, there has been…
We propose a new data-driven method to select the optimal number of relevant components in Principal Component Analysis (PCA). This new method applies to correlation matrices whose time autocorrelation function decays more slowly than an…
We propose a principal components regression method based on maximizing a joint pseudo-likelihood for responses and predictors. Our method uses both responses and predictors to select linear combinations of the predictors relevant for the…
The Principal Component Analysis (PCA) is a data dimensionality reduction technique well-suited for processing data from sensor networks. It can be applied to tasks like compression, event detection, and event recognition. This technique is…
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…
Robust principal component analysis (RPCA) is a widely used technique for recovering low-rank structure from matrices with missing entries and sparse, possibly large-magnitude corruptions. Although numerous algorithms achieve accurate point…
When measurements fall below or above a detection threshold, the resulting data are missing not at random (MNAR), posing challenges for statistical analysis. For example, in longitudinal biomarker studies, observations may be subject to…
Principal Component Analysis (PCA) is a popular tool for dimensionality reduction and feature extraction in data analysis. There is a probabilistic version of PCA, known as Probabilistic PCA (PPCA). However, standard PCA and PPCA are not…
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…
Principal Component Analysis (PCA) is a workhorse of modern data science. While PCA assumes the data conforms to Euclidean geometry, for specific data types, such as hierarchical and cyclic data structures, other spaces are more…