Related papers: Amplitude Mean of Functional Data on $\mathbb{S}^2…
Functional data are ubiquitous in scientific modeling. For instance, quantities of interest are modeled as functions of time, space, energy, density, etc. Uncertainty quantification methods for computer models with functional response have…
In the era of big data, an ever-growing volume of information is recorded, either continuously over time or sporadically, at distinct time intervals. Functional Data Analysis (FDA) stands at the cutting edge of this data revolution,…
Dimension reduction is crucial in functional data analysis (FDA). The key tool to reduce the dimension of the data is functional principal component analysis. Existing approaches for functional principal component analysis usually involve…
Data augmentation has been widely employed to improve the generalization of deep neural networks. Most existing methods apply fixed or random transformations. However, we find that sample difficulty evolves along with the model's…
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…
Anomaly detection aims to identify observations that deviate from the typical pattern of data. Anomalous observations may correspond to financial fraud, health risks, or incorrectly measured data in practice. We show detecting anomalies in…
In this paper, we introduce a new extension of the Singular Spectrum Analysis (SSA) called functional SSA to analyze functional time series. The new methodology is developed by integrating ideas from functional data analysis and univariate…
There is growing interest in using the close connection between differential geometry and statistics to model smooth manifold-valued data. In particular, much work has been done recently to generalize principal component analysis (PCA), the…
Data augmentation, by the introduction of auxiliary variables, has become an ubiquitous technique to improve convergence properties, simplify the implementation or reduce the computational time of inference methods such as Markov chain…
Meta-analysis aims to combine effect measures from several studies. For continuous outcomes, the most popular effect measures use simple or standardized differences in sample means. However, a number of applications focus on the absolute…
Many measurements in computer vision and machine learning manifest as non-Euclidean data samples. Several researchers recently extended a number of deep neural network architectures for manifold valued data samples. Researchers have…
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…
The Detrending Moving Average (DMA) algorithm has been widely used in its several variants for characterizing long-range correlations of random signals and sets (one-dimensional sequences or high-dimensional arrays) either over time or…
Time series classification problems have drawn increasing attention in the machine learning and statistical community. Closely related is the field of functional data analysis (FDA): it refers to the range of problems that deal with the…
Variable importance measures are the main tools to analyze the black-box mechanisms of random forests. Although the mean decrease accuracy (MDA) is widely accepted as the most efficient variable importance measure for random forests, little…
We propose modeling raw functional data as a mixture of a smooth function and a high-dimensional factor component. The conventional approach to retrieving the smooth function from the raw data is through various smoothing techniques.…
In modern industrial settings, advanced acquisition systems allow for the collection of data in the form of profiles, that is, as functional relationships linking responses to explanatory variables. In this context, statistical process…
Functional data analysis (FDA) is a part of modern multivariate statistics that analyses data providing information about curves, surfaces or anything else varying over a certain continuum. In economics and empirical finance we often have…
Considering the challenges posed by the space and time complexities in handling extensive scientific volumetric data, various data representations have been developed for the analysis of large-scale scientific data. Multivariate functional…
Prompted by modern technologies in data acquisition, the statistical analysis of spatially distributed function-valued quantities has attracted a lot of attention in recent years. In particular, combinations of functional variables and…