Related papers: Detecting changes in Hilbert space data based on "…
A crucial assumption to reduce computational complexity in spatial-temporal data analysis is separability, which factors the covariance structure into a purely spatial and a purely temporal component. In this paper, we develop statistical…
In climate studies, detecting spatial patterns that largely deviate from the sample mean still remains a statistical challenge. Although a Principal Component Analysis (PCA), or equivalently a Empirical Orthogonal Functions (EOF)…
Principal Components Analysis is a widely used technique for dimension reduction and characterization of variability in multivariate populations. Our interest lies in studying when and why the rotation to principal components can be used…
Let $X$ be a mean zero Gaussian random vector in a separable Hilbert space ${\mathbb H}$ with covariance operator $\Sigma:={\mathbb E}(X\otimes X).$ Let $\Sigma=\sum_{r\geq 1}\mu_r P_r$ be the spectral decomposition of $\Sigma$ with…
Quickest change detection (QCD) is a fundamental problem in many applications. Given a sequence of measurements that exhibits two different distributions around a certain flipping point, the goal is to detect the change in distribution…
The functional linear model extends the notion of linear regression to the case where the response and covariates are iid elements of an infinite dimensional Hilbert space. The unknown to be estimated is a Hilbert-Schmidt operator, whose…
We study non-linear data-dimension reduction. We are motivated by the classical linear framework of Principal Component Analysis. In nonlinear case, we introduce instead a new kernel-Principal Component Analysis, manifold and feature space…
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…
Many modern applications of online changepoint detection require the ability to process high-frequency observations, sometimes with limited available computational resources. Online algorithms for detecting a change in mean often involve…
Useful relations describing arbitrary parameters of given quantum systems can be derived from simple physical constraints imposed on the vectors in the corresponding Hilbert space. This is well known and it usually proceeds by partitioning…
Multivariate time series can often have a large number of dimensions, whether it is due to the vast amount of collected features or due to how the data sources are processed. Frequently, the main structure of the high-dimensional time…
This paper is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a low-rank component and a sparse component. Can we recover each component individually? We prove that under some suitable assumptions,…
A new test for structural changes in functional data is investigated. It is based on Hilbert space theory and critical values are deduced from bootstrap iterations. Thus a new functional central limit theorem for the block bootstrap in a…
Detecting abrupt changes in the community structure of a network from noisy observations is a fundamental problem in statistics and machine learning. This paper presents an online change detection algorithm called Spectral-CUSUM to detect…
Time series, as frequently the case in neuroscience, are rarely stationary, but often exhibit abrupt changes due to attractor transitions or bifurcations in the dynamical systems producing them. A plethora of methods for detecting such…
We study change-point detection for high-dimensional data in regimes where inference must be performed from small batches of observations. Our primary focus is the high-dimensional, low sample size (HDLSS) regime, where the sequence length…
We consider the problem of estimating the common time of a change in the mean parameters of panel data when dependence is allowed between the panels in the form of a common factor. A CUSUM type estimator is proposed, and we establish first…
In this paper we investigate the problem of estimating the regression function in models with correlated observations. The data is obtained from several experimental units each of them forms a time series. We propose a new estimator based…
We present a general theory to quantify the uncertainty from imposing structural assumptions on the second-order structure of nonstationary Hilbert space-valued processes, which can be measured via functionals of time-dependent spectral…
Finite-dimensional approximations of the Koopman operator rely critically on identifying nearly invariant subspaces. This invariance proximity can be rigorously quantified via the principal angles between a candidate subspace and its image…