Related papers: Efficient Approximation of Volterra Series for Hig…

Tensor decomposition of high-dimensional data often struggles to capture semantically or physically meaningful structures, particularly when relying on reconstruction objectives and fixed-rank constraints. We introduce a no-rank tensor…

This paper presents the error analysis of numerical methods on graded meshes for stochastic Volterra equations with weakly singular kernels. We first prove a novel regularity estimate for the exact solution via analyzing the associated…

Object recognition is a key enabler across industry and defense. As technology changes, algorithms must keep pace with new requirements and data. New modalities and higher resolution sensors should allow for increased algorithm robustness.…

Computing with discrete representations of high-dimensional probability distributions is fundamental to uncertainty quantification, Bayesian inference, and stochastic modeling. However, storing and manipulating such distributions suffers…

Recent years have seen rapid advances in the data-driven analysis of dynamical systems based on Koopman operator theory and related approaches. On the other hand, low-rank tensor product approximations -- in particular the tensor train (TT)…

We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…

Efficient estimation of high-dimensional matrices-including covariance and precision matrices-is a cornerstone of modern multivariate statistics. Most existing studies have focused primarily on the theoretical properties of the estimators…

The widespread use of multisensor technology and the emergence of big datasets have created the need to develop tools to reduce, approximate, and classify large and multimodal data such as higher-order tensors. While early approaches…

We are concerned with nonparametric hypothesis testing of time series functionals. It is known that the popular autoregressive sieve bootstrap is, in general, not valid for statistics whose (asymptotic) distribution depends on moments of…

In this paper the efficiency of multilevel sparse tensor approximation methods for high-dimensional affine parametric diffusion equations is investigated. Methodologically, the recently presented Sparse Alternating Least Squares (SALS)…

Nonlinear differential equations rarely admit closed-form solutions, thus requiring numerical time-stepping algorithms to approximate solutions. Further, many systems characterized by multiscale physics exhibit dynamics over a vast range of…

We propose a new stochastic first-order algorithmic framework to solve stochastic composite nonconvex optimization problems that covers both finite-sum and expectation settings. Our algorithms rely on the SARAH estimator introduced in…

Large Language Models (LLMs) are widely used across various domains, processing millions of daily requests. This surge in demand poses significant challenges in optimizing throughput and latency while keeping costs manageable. The Key-Value…

Total hip arthroplasty (THA) is a widely used surgical procedure in orthopedics. For THA, it is of clinical significance to analyze the bone structure from the CT images, especially to observe the structure of the acetabulum and femoral…

Estimating the rate of rare conformational changes in molecular systems is one of the goals of Molecular Dynamics simulations. In the past decades, a lot of progress has been done in data-based approaches towards this problem. In contrast,…

Tensor analysis has been a widely studied in physics applications including circuit theory and electric machines. This paper reviews some of the main features of this type of representation for unbalanced power distribution systems and…

Matrix completion, the problem of completing missing entries in a data matrix with low dimensional structure (such as rank), has seen many fruitful approaches and analyses. Tensor completion is the tensor analog, that attempts to impute…

Volterra and polynomial regression models play a major role in nonlinear system identification and inference tasks. Exciting applications ranging from neuroscience to genome-wide association analysis build on these models with the…

High-dimensional, low sample-size (HDLSS) data problems have been a topic of immense importance for the last couple of decades. There is a vast literature that proposed a wide variety of approaches to deal with this situation, among which…

Multi Task Learning (MTL) efficiently leverages useful information contained in multiple related tasks to help improve the generalization performance of all tasks. This article conducts a large dimensional analysis of a simple but, as we…