Related papers: Regular Decomposition: an information and graph th…
Graph partitioning problems emerge in a wide variety of complex systems, ranging from biology to finance, but can be rigorously analyzed and solved only for a few graph ensembles. Here, an ensemble of equitable graphs, i.e. random graphs…
Dynamic Mode Decomposition (DMD) is a data-driven method related to Koopman operator theory that extracts information about dominant dynamics from data snapshots. In this paper we examine techniques to accelerate the application of DMD to…
In a nutshell, submodular functions encode an intuitive notion of diminishing returns. As a result, submodularity appears in many important machine learning tasks such as feature selection and data summarization. Although there has been a…
The paper introduces a general framework for derivation of continuum equations governing meso-scale dynamics of large particle systems. The balance equations for spatial averages such as density, linear momentum, and energy were previously…
We study how to solve semidefinite programming relaxations for large scale polynomial optimization. When interior-point methods are used, typically only small or moderately large problems could be solved. This paper studies regularization…
With the advances in data acquisition technology, tensor objects are collected in a variety of applications including multimedia, medical and hyperspectral imaging. As the dimensionality of tensor objects is usually very high,…
In deep neural nets, lower level embedding layers account for a large portion of the total number of parameters. Tikhonov regularization, graph-based regularization, and hard parameter sharing are approaches that introduce explicit biases…
Due to the substantial scale of Large Language Models (LLMs), the direct application of conventional compression methodologies proves impractical. The computational demands associated with even minimal gradient updates present challenges,…
The Isolation Lemma of Mulmuley, Vazirani and Vazirani [Combinatorica'87] provides a self-reduction scheme that allows one to assume that a given instance of a problem has a unique solution, provided a solution exists at all. Since its…
Deep Neural Networks have achieved remarkable success relying on the developing availability of GPUs and large-scale datasets with increasing network depth and width. However, due to the expensive computation and intensive memory,…
Matrix reduction is the standard procedure for computing the persistent homology of a filtered simplicial complex with $m$ simplices. Its output is a particular decomposition of the total boundary matrix, from which the persistence diagrams…
The dynamic mode decomposition (DMD) is a data-driven method used for identifying the dynamics of complex nonlinear systems. It extracts important characteristics of the underlying dynamics using measured time-domain data produced either by…
Dynamic Mode Decomposition (DMD) and its variants, such as extended DMD (EDMD), are broadly used to fit simple linear models to dynamical systems known from observable data. As DMD methods work well in several situations but perform poorly…
The so-called motorcycle graph has been employed in recent years for various purposes in the context of structured and aligned block decomposition of 2D shapes and 2-manifold surfaces. Applications are in the fields of surface…
We prove a robust contraction decomposition theorem for $H$-minor-free graphs, which states that given an $H$-minor-free graph $G$ and an integer $p$, one can partition in polynomial time the vertices of $G$ into $p$ sets $Z_1,\dots,Z_p$…
A fundamental problem associated with the task of network reconstruction from dynamical or behavioral data consists in determining the most appropriate model complexity in a manner that prevents overfitting, and produces an inferred network…
A regularized version of Mixture Models is proposed to learn a principal graph from a distribution of $D$-dimensional data points. In the particular case of manifold learning for ridge detection, we assume that the underlying manifold can…
We consider the problem of sampling and approximately counting an arbitrary given motif $H$ in a graph $G$, where access to $G$ is given via queries: degree, neighbor, and pair, as well as uniform edge sample queries. Previous algorithms…
Random network models, constrained to reproduce specific statistical features, are often used to represent and analyze network data and their mathematical descriptions. Chief among them, the configuration model constrains random networks by…
This paper is concerned with nonparametric estimation of the weighted stochastic block model. We first show that the model implies a set of multilinear restrictions on the joint distribution of edge weights of certain subgraphs involving…