Related papers: Approximating Simplet Frequency Distribution for S…
A streaming algorithm to compute the spectral proper orthogonal decomposition (SPOD) of stationary random processes is presented. As new data becomes available, an incremental update of the truncated eigenbasis of the estimated…
This paper investigates the theoretical properties of Dirichlet kernel density estimators for compositional data supported on simplices, for the first time addressing scenarios involving time-dependent observations characterized by strong…
Sequence feature embedding is a challenging task due to the unstructuredness of sequence, i.e., arbitrary strings of arbitrary length. Existing methods are efficient in extracting short-term dependencies but typically suffer from…
Considering the large number of fractional operators that exist, and since it does not seem that their number will stop increasing soon at the time of writing this paper, it is presented for the first time, as far as the authors know, a…
A flexible conformal inference method is developed to construct confidence intervals for the frequencies of queried objects in very large data sets, based on a much smaller sketch of those data. The approach is data-adaptive and requires no…
Spectral clustering and Singular Value Decomposition (SVD) are both widely used technique for analyzing graph data. In this note, I will present their connections using simple linear algebra, aiming to provide some in-depth understanding…
Frequency estimation in streaming data often relies on sketches like Count-Min (CM) to provide approximate answers with sublinear space. However, CM sketches introduce additive errors that disproportionately impact low-frequency elements,…
Indexing of static and dynamic sets is fundamental to a large set of applications such as information retrieval and caching. Denoting the characteristic vector of the set by B, we consider the problem of encoding sets and multisets to…
Spectral clustering has become a popular technique due to its high performance in many contexts. It comprises three main steps: create a similarity graph between N objects to cluster, compute the first k eigenvectors of its Laplacian matrix…
We study data-driven least squares (LS) problems with semidefinite (SD) constraints and derive finite-sample guarantees on the spectrum of their optimal solutions when these constraints are relaxed. In particular, we provide a high…
We study the Stochastic Gradient Descent (SGD) method in nonconvex optimization problems from the point of view of approximating diffusion processes. We prove rigorously that the diffusion process can approximate the SGD algorithm weakly…
In this paper, we propose an efficient technique for estimating individual power spectral density (PSD) components, i.e., PSD of each desired sound source as well as of noise and reverberation, in a multi-source reverberant sound scene with…
The crux of resolving fine-grained visual classification (FGVC) lies in capturing discriminative and class-specific cues that correspond to subtle visual characteristics. Recently, frequency decomposition/transform based approaches have…
Estimates of image gradients play a ubiquitous role in image segmentation and classification problems since gradients directly relate to the boundaries or the edges of a scene. This paper proposes an unified approach to gradient estimation…
In the field of mathematics, a purely combinatorial equivalent to a simplicial complex, or more generally, a down-set, is an abstract structure known as a family of sets. This family is closed under the operation of taking subsets, meaning…
We present a browser application for estimating the number of frequent patterns, in particular itemsets, as well as the pattern frequency spectrum. The pattern frequency spectrum is defined as the function that shows for every value of the…
We investigate the statistical and computational limits of latent Diffusion Transformers (DiTs) under the low-dimensional linear latent space assumption. Statistically, we study the universal approximation and sample complexity of the DiTs…
We consider time-harmonic Maxwell's equations set in an heterogeneous medium with perfectly conducting boundary conditions. Given a divergence-free right-hand side lying in $L^2$, we provide a frequency-explicit approximability estimate…
Trajectory data, including time series and longitudinal measurements, are increasingly common in health-related domains such as biomedical research and epidemiology. Real-world trajectory data frequently exhibit heterogeneity across…
In this paper we propose and analyse a hybrid numerical-asymptotic boundary element method for the solution of problems of high frequency acoustic scattering by a class of sound-soft nonconvex polygons. The approximation space is enriched…