Related papers: Finding a dense submatrix of a random matrix. Shar…
Dense subgraph extraction is a fundamental problem in graph analysis and data mining, aimed at identifying cohesive and densely connected substructures within a given graph. It plays a crucial role in various domains, including social…
Recently, randomized algorithms for low-rank approximation of quaternion matrices have received increasing attention. However, for large-scale problems, existing quaternion orthonormalizations are inefficient, leading to slow rangefinders.…
We develop an online probabilistic metric-semantic mapping approach for mobile robot teams relying on streaming RGB-D observations. The generated maps contain full continuous distributional information about the geometric surfaces and…
We introduce the large average subtensor problem: given an order-$p$ tensor over $\mathbb{R}^{N\times \cdots \times N}$ with i.i.d. standard normal entries and a $k\in\mathbb{N}$, algorithmically find a $k\times \cdots \times k$ subtensor…
The matrix scaling problem, particularly the Sinkhorn-Knopp algorithm, has been studied for over 60 years. In practice, the algorithm often yields high-quality approximations within just a few iterations. Theoretically, however, the…
The matrix completion problem aims to reconstruct a low-rank matrix based on a revealed set of possibly noisy entries. Prior works consider completing the entire matrix with generalization error guarantees. However, the completion accuracy…
The problem of finding the densest subgraph in a given graph has several applications in graph mining, particularly in areas like social network analysis, protein and gene analyses etc. Depending on the application, finding dense subgraphs…
We provide faster algorithms for the problem of Gaussian summation, which occurs in many machine learning methods. We develop two new extensions - an O(Dp) Taylor expansion for the Gaussian kernel with rigorous error bounds and a new error…
We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP) based method to approximate the joint distribution of the unknown parameters and the data. In particular, we…
This work builds upon previous efforts in online incremental learning, namely the Incremental Gaussian Mixture Network (IGMN). The IGMN is capable of learning from data streams in a single-pass by improving its model after analyzing each…
Finding dense subgraphs of a large graph is a standard problem in graph mining that has been studied extensively both for its theoretical richness and its many practical applications. In this paper we introduce a new family of dense…
We apply a method recently introduced to the statistical literature to directly estimate the precision matrix from an ensemble of samples drawn from a corresponding Gaussian distribution. Motivated by the observation that cosmological…
In this paper, we present a polynomial-time algorithm that approximates sufficiently high-value Max 2-CSPs on sufficiently dense graphs to within $O(N^{\varepsilon})$ approximation ratio for any constant $\varepsilon > 0$. Using this…
The goal of this work is to fill a gap in [Yang, SIAM J. Matrix Anal. Appl, 41 (2020), 1797--1825]. In that work, an approximation procedure was proposed for orthogonal low-rank tensor approximation; however, the approximation lower bound…
Given a dynamic network, where edges appear and disappear over time, we are interested in finding sets of edges that have similar temporal behavior and form a dense subgraph. Formally, we define the problem as the enumeration of the maximal…
This paper investigates the fundamental limits for detecting a high-dimensional sparse matrix contaminated by white Gaussian noise from both the statistical and computational perspectives. We consider $p\times p$ matrices whose rows and…
We present a matrix factorization algorithm that scales to input matrices that are large in both dimensions (i.e., that contains morethan 1TB of data). The algorithm streams the matrix columns while subsampling them, resulting in low…
Many real-world networks can be modeled as graphs. Finding dense subgraphs is a key problem in graph mining with applications in diverse domains. In this paper, we consider two variants of the densest subgraph problem where multiple graph…
The problem of finding dense components of a graph is a widely explored area in data analysis, with diverse applications in fields and branches of study including community mining, spam detection, computer security and bioinformatics. This…
The problem of optimizing over random structures emerges in many areas of science and engineering, ranging from statistical physics to machine learning and artificial intelligence. For many such structures finding optimal solutions by means…