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In scientific applications, multivariate observations often come in tandem with temporal or spatial covariates, with which the underlying signals vary smoothly. The standard approaches such as principal component analysis and factor…
Multivariate spatio-temporal data arise more and more frequently in a wide range of applications; however, there are relatively few general statistical methods that can readily use that incorporate spatial, temporal and variable…
Given data, deep generative models, such as variational autoencoders (VAE) and generative adversarial networks (GAN), train a lower dimensional latent representation of the data space. The linear Euclidean geometry of data space pulls back…
This paper develops the non-intrusive formulation of the Least-squares shadowing (LSS) method, for computing the sensitivity of long-time averaged objectives in chaotic dynamical systems. This non-intrusive formulation constrains the…
Distributed lag non-linear models (DLNM) have gained popularity for modeling nonlinear lagged relationships between exposures and outcomes. When applied to spatially referenced data, these models must account for spatial dependence, a…
We introduce a new family of algorithms for detecting and estimating a rank-one signal from a noisy observation under prior information about that signal's direction, focusing on examples where the signal is known to have entries biased to…
Anomaly detection in spatiotemporal data is a challenging problem encountered in a variety of applications including hyperspectral imaging, video surveillance, and urban traffic monitoring. Existing anomaly detection methods are most suited…
We propose a method for adaptive nonlinear sequential modeling of vector-time series data. Data is modeled as a nonlinear function of past values corrupted by noise, and the underlying non-linear function is assumed to be approximately…
In this study, we develop an asymptotic theory of nonparametric regression for a locally stationary functional time series. First, we introduce the notion of a locally stationary functional time series (LSFTS) that takes values in a…
Transformer architectures have achieved remarkable success in various domains. While efficient alternatives to Softmax Attention have been widely studied, the search for more expressive mechanisms grounded in theoretical insight-even at…
Recent advances in digitization have led to the availability of multivariate time series data in various domains, enabling real-time monitoring of operations. Identifying abnormal data patterns and detecting potential failures in these…
Conventional nonlinear subspace learning techniques (e.g., manifold learning) usually introduce some drawbacks in explainability (explicit mapping) and cost-effectiveness (linearization), generalization capability (out-of-sample), and…
Using methods from algebraic graph theory and convex optimization, we study the relationship between local structural features of a network and spectral properties of its Laplacian matrix. In particular, we derive expressions for the…
Tensor decomposition has emerged as a prominent technique to learn low-dimensional representation under the supervision of reconstruction error, primarily benefiting data inference tasks like completion and imputation, but not…
Supervised topic models simultaneously model the latent topic structure of large collections of documents and a response variable associated with each document. Existing inference methods are based on variational approximation or Monte…
This paper is concerned with the statistical development of our spatial-temporal data mining procedure, LASR (pronounced ``laser''). LASR is the abbreviation for Longitudinal Analysis with Self-Registration of large-$p$-small-$n$ data. It…
Symmetric positive definite (SPD) matrix has been demonstrated to be an effective feature descriptor in many scientific areas, as it can encode spatiotemporal statistics of the data adequately on a curved Riemannian manifold, i.e., SPD…
We present an iterative algorithm for solving a class of \\nonlinear Laplacian system of equations in $\tilde{O}(k^2m \log(kn/\epsilon))$ iterations, where $k$ is a measure of nonlinearity, $n$ is the number of variables, $m$ is the number…
The well-established practice of time series analysis involves estimating deterministic, non-stationary trend and seasonality components followed by learning the residual stochastic, stationary components. Recently, it has been shown that…
In many real-world applications data exhibits non-stationarity, i.e., its distribution changes over time. One approach to handling non-stationarity is to remove or minimize it before attempting to analyze the data. In the context of brain…