Related papers: On Checking Null Rank Conditions of Rational Matri…
So-called linear rank statistics provide a means for distribution-free (even in finite samples), yet highly flexible, two-sample testing in the setting of univariate random variables. Their flexibility derives from a choice of weights that…
We develop a Stata command, bootranktest, for implementing the matrix rank test of Chen and Fang (2019) in linear instrumental variable regression models. Existing rank tests employ critical values that may be too small, and hence may not…
Matrix completion is a modern missing data problem where both the missing structure and the underlying parameter are high dimensional. Although missing structure is a key component to any missing data problems, existing matrix completion…
Log-linear models are typically fitted to contingency table data to describe and identify the relationship between different categorical variables. However, the data may include observed zero cell entries. The presence of zero cell entries…
This work develops novel rational Krylov methods for updating a large-scale matrix function f(A) when A is subject to low-rank modifications. It extends our previous work in this context on polynomial Krylov methods, for which we present a…
We give the complete stably rational classification of algebraic tori of dimensions $4$ and $5$ over a field $k$. In particular, the stably rational classification of norm one tori whose Chevalley modules are of rank $4$ and $5$ is given.…
Given a nonnegative matrix M with rational entries, we consider two quantities: the usual positive semidefinite (psd) rank, where the matrix is factored through the cone of real symmetric psd matrices, and the rational-restricted psd rank,…
Over the years, numerous rank estimators for factor models have been proposed in the literature. This article focuses on information criterion-based rank estimators and investigates their consistency in rank selection. The gap conditions…
In [Mulmuley, 1987], Mulmuley gave an algorithm reducing the computation of the matrix rank function to that of determinants, of which the proof for the verification is elementary. In this article, we formalize this argument in the bounded…
The identity testing of rational formulas (RIT) in the free skew field efficiently reduces to computing the rank of a matrix whose entries are linear polynomials in noncommuting variables\cite{HW15}. This rank computation problem has…
The fastest known algorithms for dealing with structured matrices, in the sense of the displacement rank measure, are randomized. For handling classical displacement structures, they achieve the complexity bounds…
In this paper we study the low rank matrix completion problem using tools from Schur complement. We give a sufficient and necessary condition such that the completed matrix is globally unique with given data. We assume the observed entries…
Consider a matrix $\mathbf{F} \in \mathbb{K}[x]^{m \times n}$ of univariate polynomials over a field $\mathbb{K}$. We study the problem of computing the column rank profile of $\mathbf{F}$. To this end we first give an algorithm which…
Ranking is used for a wide array of problems, most notably information retrieval (search). There are a number of popular approaches to the evaluation of ranking such as Kendall's $\tau$, Average Precision, and nDCG. When dealing with…
We give the first algorithm for Matrix Completion whose running time and sample complexity is polynomial in the rank of the unknown target matrix, linear in the dimension of the matrix, and logarithmic in the condition number of the matrix.…
Given a special biserial algebra $\Lambda$ over an algebraically closed field, let $\mathrm{rad}_\Lambda$ denote the radical of its module category. The authors showed with Sinha that the stable rank of a special biserial algebra $\Lambda$,…
We introduce a novel approach to the automated termination analysis of computer programs: we use neural networks to represent ranking functions. Ranking functions map program states to values that are bounded from below and decrease as a…
Liveness properties are traditionally proven using a ranking function that maps system states to some well-founded set. Carrying out such proofs in first-order logic enables automation by SMT solvers. However, reasoning about many natural…
A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. This includes numerical stabilization of Gaussian elimination…
Rational verification is the problem of determining which temporal logic properties will hold in a multi-agent system, under the assumption that agents in the system act rationally, by choosing strategies that collectively form a…