Related papers: On the Rank of Random Sparse Matrices
In this paper we count the number of some particular quadruple persymmetric rank i matrices over F_2.
This paper aims at achieving a simultaneously sparse and low-rank estimator from the semidefinite population covariance matrices. We first benefit from a convex optimization which develops $l_1$-norm penalty to encourage the sparsity and…
In this paper, we investigate the invertibility of sparse symmetric matrices. We show that for an $n\times n$ sparse symmetric random matrix $A$ with $A_{ij} = \delta_{ij} \xi_{ij}$ is invertible with high probability. Here, $\delta_{ij}$s,…
This paper studies inference in linear models with a high-dimensional parameter matrix that can be well-approximated by a ``spiked low-rank matrix.'' A spiked low-rank matrix has rank that grows slowly compared to its dimensions and nonzero…
This paper studies the inference about linear functionals of high-dimensional low-rank matrices. While most existing inference methods would require consistent estimation of the true rank, our procedure is robust to rank misspecification,…
We study the properties of elections that have a given position matrix (in such elections each candidate is ranked on each position by a number of voters specified in the matrix). We show that counting elections that generate a given…
We describe a framework for random pairwise comparisons matrices, inspired by selected constructions releted to the so called inconsistency reduction of pairwise comparisons (PC) matrices. In to build up structures on random pairwise…
An interval matrix is a matrix whose entries are intervals in the set of real numbers. Let $p , q $ be nonzero natural numbers and let $\mu =( [m_{i,j}, M_{i,j}])_{i,j}$ be a $p \times q$ interval matrix; given a $p \times q$ matrix $A$…
The process of rank aggregation is intimately intertwined with the structure of skew-symmetric matrices. We apply recent advances in the theory and algorithms of matrix completion to skew-symmetric matrices. This combination of ideas…
This paper deals with the problem of robust matrix completion -- retrieving a low-rank matrix and a sparse matrix from the compressed counterpart of their superposition. Though seemingly not an unresolved issue, we point out that the…
A fooling-set matrix has nonzero diagonal, but at least one in every pair of diagonally opposite entries is 0. Dietzfelbinger et al. '96 proved that the rank of such a matrix is at least $\sqrt n$. It is known that the bound is tight (up to…
Matrix completion is a problem that arises in many data-analysis settings where the input consists of a partially-observed matrix (e.g., recommender systems, traffic matrix analysis etc.). Classical approaches to matrix completion assume…
In this paper, we study the symmetric rank of products of linear forms and an irreducible quadratic form. The main result presents a new, non-trivial lower bound for the rank, and the arguments rely on the apolarity lemma. In the special…
We discuss the question of how to pick a matrix uniformly (in an appropriate sense) at random from groups big and small. We give algorithms in some cases, and indicate interesting problems in others.
We show that almost surely the rank of the adjacency matrix of the Erd\"os-R\'enyi random graph $G(n,p)$ equals the number of non-isolated vertices for any $c\ln n/n<p<1/2$, where $c$ is an arbitrary positive constant larger than 1/2. In…
The square root rank of a nonnegative matrix $A$ is the minimum rank of a matrix $B$ such that $A=B \circ B$, where $\circ$ denotes entrywise product. We show that the square root rank of the slack matrix of the correlation polytope is…
In this paper we expose our main results about rank problems concerning persymmetric matrices over F_2 associated to some exponential sums.
Comparing alternatives in pairs is a very well known technique of ranking creation. The answer to how reliable and trustworthy ranking is depends on the inconsistency of the data from which it was created. There are many indices used for…
Low-rank matrix completion addresses the problem of completing a matrix from a certain set of generic specified entries. Over the complex numbers a matrix with a given entry pattern can be uniquely completed to a specific rank, called the…
Homogeneity, low rank, and sparsity are three widely adopted assumptions in multi-response regression models to address the curse of dimensionality and improve estimation accuracy. However, there is limited literature that examines these…