Related papers: Good Random Matrices over Finite Fields
We give highly efficient algorithms, and almost matching lower bounds, for a range of basic statistical problems that involve testing and estimating the L_1 distance between two k-modal distributions $p$ and $q$ over the discrete domain…
Theory of Random Matrix Ensembles have proven to be a useful tool in the study of the statistical distribution of energy or transmission levels of a wide variety of physical systems. We give an overview of certain q-generalizations of the…
Over the past few decades, there has been extensive research on scattered subspaces, partly because of their link to MRD codes. These subspaces can be characterized using linearized polynomials over finite fields. Within this context,…
Diversity is an important principle in data selection and summarization, facility location, and recommendation systems. Our work focuses on maximizing diversity in data selection, while offering fairness guarantees. In particular, we offer…
Mixtures of $r$ independent distributions for two discrete random variables can be represented by matrices of nonnegative rank $r$. Likelihood inference for the model of such joint distributions leads to problems in real algebraic geometry…
Rough sets were proposed to deal with the vagueness and incompleteness of knowledge in information systems. There are may optimization issues in this field such as attribute reduction. Matroids generalized from matrices are widely used in…
Let $n$ be a positive integer and $X = [x_{ij}]_{1 \leq i, j \leq n}$ be an $n \times n$\linebreak \noindent sized matrix of independent random variables having joint uniform distribution $$\hbox{Pr} {x_{ij} = k \hbox{for} 1 \leq k \leq n}…
The Minimum Dominating Set (MDS) problem is one of the most fundamental and challenging problems in distributed computing. While it is well-known that minimum dominating sets cannot be approximated locally on general graphs, over the last…
Statistical inference from high-dimensional data with low-dimensional structures has recently attracted lots of attention. In machine learning, deep generative modeling approaches implicitly estimate distributions of complex objects by…
Random linear systems over the Galois Field modulo 2 have an interest in connection with problems ranging from computational optimization to complex networks. They are often approached using random matrices with Poisson-distributed or…
We review the development of random-matrix theory (RMT) during the last decade. We emphasize both the theoretical aspects, and the application of the theory to a number of fields. These comprise chaotic and disordered systems, the…
The purpose of this text is to provide an accessible introduction to a set of recently developed algorithms for factorizing matrices. These new algorithms attain high practical speed by reducing the dimensionality of intermediate…
In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…
We show a connection between sampling and optimization on discrete domains. For a family of distributions $\mu$ defined on size $k$ subsets of a ground set of elements that is closed under external fields, we show that rapid mixing of…
Let $n\geq2$ be a natural number. Let $M_n(\mathbb{K})$ be the ring of all $n \times n$ matrices over a field $\mathbb{K}$. Fix natural number $k$ satisfying $1<k\leq n$. Under a mild technical assumption over $\mathbb{K}$ we will show that…
We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…
Low rank approximation is an important tool used in many applications of signal processing and machine learning. Recently, randomized sketching algorithms were proposed to effectively construct low rank approximations and obtain approximate…
A distance matrix $A \in \mathbb R^{n \times m}$ represents all pairwise distances, $A_{ij}=\mathrm{d}(x_i,y_j)$, between two point sets $x_1,...,x_n$ and $y_1,...,y_m$ in an arbitrary metric space $(\mathcal Z, \mathrm{d})$. Such matrices…
In this paper we prove a result on the structure of the elements of an additive {\it maximum rank distance (MRD) code} over the field of order two, namely that in some cases such codes must contain a semifield spread set. We use this result…
Random matrix theory allows for the deduction of stability criteria for complex systems using only a summary knowledge of the statistics of the interactions between components. As such, results like the well-known elliptical law are…