相关论文: Amplitude Mean of Functional Data on $\mathbb{S}^2…

The Argo data is a modern oceanography dataset that provides unprecedented global coverage of temperature and salinity measurements in the upper 2,000 meters of depth of the ocean. We study the Argo data from the perspective of functional…

Sparse functional/longitudinal data have attracted widespread interest due to the prevalence of such data in social and life sciences. A prominent scenario where such data are routinely encountered are accelerated longitudinal studies,…

Supervised operator learning centers on the use of training data, in the form of input-output pairs, to estimate maps between infinite-dimensional spaces. It is emerging as a powerful tool to complement traditional scientific computing,…

Robust estimation of location is a fundamental problem in statistics, particularly in scenarios where data contamination by outliers or model misspecification is a concern. In univariate settings, methods such as the sample median and…

Domain adaptation is an essential task in transfer learning to leverage data in one domain to bolster learning in another domain. In this paper, we present a new semi-supervised manifold alignment technique based on a two-step approach of…

We consider the approximation of manifold-valued functions by embedding the manifold into a higher dimensional space, applying a vector-valued approximation operator and projecting the resulting vector back to the manifold. It is well known…

We consider an analysis of variance type problem, where the sample observations are random elements in an infinite dimensional space. This scenario covers the case, where the observations are random functions. For such a problem, we propose…

The global dimensionality of a neural representation manifold provides rich insight into the computational process underlying both artificial and biological neural networks. However, all existing measures of global dimensionality are…

To detect differences between the mean curves of two samples in longitudinal study or functional data analysis, we usually need to partition the temporal or spatial domain into several pre-determined sub-areas. In this paper we apply the…

We present an approach to analyze $C^1(\mathbb{R}^m)$ functions that addresses limitations present in the Active Subspaces (AS) method of Constantine et al.(2015; 2014). Under appropriate hypotheses, our Active Manifolds (AM) method…

In many applications, input data are sampled functions taking their values in infinite dimensional spaces rather than standard vectors. This fact has complex consequences on data analysis algorithms that motivate modifications of them. In…

Measurement error is an important problem that has not been very well studied in the context of Functional Data Analysis. To the best of our knowledge, there are no existing methods that address the presence of functional measurement errors…

As the development of measuring instruments and computers has accelerated the collection of massive amounts of data, functional data analysis (FDA) has experienced a surge of attention. The FDA methodology treats longitudinal data as a set…

Data assimilation addresses the problem of identifying plausible state trajectories of dynamical systems given noisy or incomplete observations. In geosciences, it presents challenges due to the high-dimensionality of geophysical dynamical…

In recent years, partially observable functional data has gained significant attention in practical applications and has become the focus of increasing interest in the literature. In this thesis, we build upon the concept of data…

The aim of this paper is to describe a novel non-parametric noise reduction technique from the point of view of Bayesian inference that may automatically improve the signal-to-noise ratio of one- and two-dimensional data, such as e.g.…

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…

We propose a new method for functional nonparametric regression with a predictor that resides on a finite-dimensional manifold but is only observable in an infinite-dimensional space. Contamination of the predictor due to discrete/noisy…

The frequency-domain approach (FDA) to transient analysis of the boundary element method, although is appealing for engineering applications, is computationally expensive. This paper proposes a novel adaptive frequency sampling (AFS)…

This article introduces a nonparametric approach to spectral analysis of a high-dimensional multivariate nonstationary time series. The procedure is based on a novel frequency-domain factor model that provides a flexible yet parsimonious…