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Motivated by applications in topological DNA-based data storage, we introduce and study a novel setting of Non-Adaptive Group Testing (NAGT) with runlength constraints on the columns of the test matrix, in the sense that any two 1's must be…
This paper theoretically reanalyzes the convergence of the mini-batch stochastic gradient descent (SGD) for a structured minimization problem involving a finite-sum function with its gradient being stochastically approximated, and an…
Determinantal point processes (DPPs) have attracted substantial attention as an elegant probabilistic model that captures the balance between quality and diversity within sets. DPPs are conventionally parameterized by a positive…
Distributed algorithms to solve linear equations in multi-agent networks have attracted great research attention and many iteration-based distributed algorithms have been developed. The convergence speed is a key factor to be considered for…
Subset selection problems ask for a small, diverse yet representative subset of the given data. When pairwise similarities are captured by a kernel, the determinants of submatrices provide a measure of diversity or independence of items…
The persistence diagram, which describes the topological features of a dataset, is a key descriptor in Topological Data Analysis. The "Discrete Morse Sandwich" (DMS) method has been reported to be the most efficient algorithm for computing…
As networks continue to increase in size, current methods must be capable of handling large numbers of nodes and edges in order to be practically relevant. Instead of working directly with the entire (large) network, analyzing sub-networks…
In this short note, we address the identifiability issues inherent in the Degree-Corrected Stochastic Block Model (DCSBM). We provide a rigorous proof demonstrating that the parameters of the DCSBM are identifiable up to a scaling factor…
The statistical properties of the density map (DM) approach to counting microbiological objects on images are studied in detail. The DM is given by U$^2$-Net. Two statistical methods for deep neural networks are utilized: the bootstrap and…
We introduce a new class of large structured random matrices characterized by four fundamental properties which we discuss. We prove that this class is stable under matrix-valued and pointwise non-linear operations. We then formulate an…
The Degree Corrected Stochastic Block Model (DCSBM) was introduced by \cite{karrer2011stochastic} as a generalization of the stochastic block model in which vertices of the same community are allowed to have distinct degree distributions.…
We propose a new method for computing Dynamic Mode Decomposition (DMD) evolution matrices, which we use to analyze dynamical systems. Unlike the majority of existing methods, our approach is based on a variational formulation consisting of…
We propose the -- to the best of our knowledge -- first fully functional implementation of the ``Separation by a Convex Body'' (SCB) approach first outlined in Grzybowski et al. [1] for classification, separating two data sets using an…
Distance metric learning is successful in discovering intrinsic relations in data. However, most algorithms are computationally demanding when the problem size becomes large. In this paper, we propose a discriminative metric learning…
A saturated D-optimal design is a {+1,-1} square matrix of given order with maximal determinant. We search for saturated D-optimal designs of orders 19 and 37, and find that known matrices due to Smith, Cohn, Orrick and Solomon are optimal.…
A method is presented for producing analytical results applicable to the standard two-party deterministic dense coding protocol, wherein communication of K perfectly distinguishable messages is attainable with the aid of K selected local…
The lasso model has been widely used for model selection in data mining, machine learning, and high-dimensional statistical analysis. However, with the ultrahigh-dimensional, large-scale data sets now collected in many real-world…
Score-based graph generative models (SGGMs) have proven effective in critical applications such as drug discovery and protein synthesis. However, their theoretical behavior, particularly regarding convergence, remains underexplored. Unlike…
Network-distributed optimization has attracted significant attention in recent years due to its ever-increasing applications. However, the classic decentralized gradient descent (DGD) algorithm is communication-inefficient for large-scale…
Spatially-coupled (SC) codes are a class of low-density parity-check (LDPC) codes that is gaining increasing attention. Multi-dimensional (MD) SC codes are constructed by connecting copies of an SC code via relocations in order to mitigate…