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Related papers: Matrices with prescribed row and column sums

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We investigate the relationship between the structure of a discrete graphical model and the support of the inverse of a generalized covariance matrix. We show that for certain graph structures, the support of the inverse covariance matrix…

Machine Learning · Statistics 2014-01-07 Po-Ling Loh , Martin J. Wainwright

This paper surveys some combinatorial aspects of Smith normal form, and more generally, diagonal form. The discussion includes general algebraic properties and interpretations of Smith normal form, critical groups of graphs, and Smith…

Combinatorics · Mathematics 2016-04-05 Richard P. Stanley

The girth of a matrix is the least number of linearly dependent columns, in contrast to the rank which is the largest number of linearly independent columns. This paper considers the construction of {\it high-girth} matrices, whose…

Information Theory · Computer Science 2015-02-06 Emmanuel Abbe , Yuval Wigderson

In this paper, we have established boundaries of cardinal numbers of nonempty sets in finite non-$T_1$ topological spaces using interval analysis. For a finite set with known cardinality, we give interval estimations based on the closure…

General Topology · Mathematics 2019-09-02 J. F. Peters , I. J. Dochviri

The theory of the column-row determinants has been considered for matrices over a non-split quaternion algebra. In this paper the concepts of column-row determinants are extending to a split quaternion algebra. New definitions of the column…

Rings and Algebras · Mathematics 2014-05-08 Ivan Kyrchei

We describe a framework for systematic enumeration of families combinatorial structures which possess a certain regularity. More precisely, we describe how to obtain the differential equations satisfied by their generating series. These…

Combinatorics · Mathematics 2008-02-28 Marni Mishna

Random matrix ensembles are introduced that respect the local tensor structure of Hamiltonians describing a chain of $n$ distinguishable spin-half particles with nearest-neighbour interactions. We prove a central limit theorem for the…

Mathematical Physics · Physics 2017-06-19 J. P. Keating , N. Linden , H. J. Wells

We investigate eigenvector statistics of the Truncated Unitary ensemble $\mathrm{TUE}(N,M)$ in the weakly non-unitary case $M=1$, that is when only one row and column are removed. We provide an explicit description of generalized overlaps…

Probability · Mathematics 2023-02-02 Guillaume Dubach

In standard clustering problems, data points are represented by vectors, and by stacking them together, one forms a data matrix with row or column cluster structure. In this paper, we consider a class of binary matrices, arising in many…

Machine Learning · Statistics 2014-02-06 Jiaming Xu , Rui Wu , Kai Zhu , Bruce Hajek , R. Srikant , Lei Ying

It is well known that any positive matrix can be scaled to have prescribed row and column sums by multiplying its rows and columns by certain positive scaling factors (which are unique up to a positive scalar). This procedure is known as…

Probability · Mathematics 2023-07-12 Boris Landa

We show that the {\em column sum optimization problem}, of finding a $(0,1)$-matrix with prescribed row sums which minimizes the sum of evaluations of given functions at its column sums, can be solved in polynomial time, either when all…

Optimization and Control · Mathematics 2021-04-28 Shmuel Onn

The problem of extracting a well conditioned submatrix from any rectangular matrix (with normalized columns) has been studied for some time in functional and harmonic analysis; see…

Functional Analysis · Mathematics 2016-12-07 Stephane Chretien , Sebastien Darses

This note gives a simple analysis of a randomized approximation scheme for matrix multiplication proposed by Sarlos (2006) based on a random rotation followed by uniform column sampling. The result follows from a matrix version of…

Data Structures and Algorithms · Computer Science 2012-11-26 Daniel Hsu , Sham M. Kakade , Tong Zhang

An increasing number of applications is concerned with recovering a sparse matrix from noisy observations. In this paper, we consider the setting where each row of the unknown matrix is sparse. We establish minimax optimal rates of…

Statistics Theory · Mathematics 2015-09-02 O. Klopp , A. B. Tsybakov

In this short note we extend some of the recent results on matrix completion under the assumption that the columns of the matrix can be grouped (clustered) into subspaces (not necessarily disjoint or independent). This model deviates from…

Information Theory · Computer Science 2017-08-04 Vaneet Aggarwal , Shuchin Aeron

The paper gives an overview of recent advances in structural equation modeling. A structural equation model is a multivariate statistical model that is determined by a mixed graph, also known as a path diagram. Our focus is on the…

Statistics Theory · Mathematics 2016-12-20 Mathias Drton

This survey describes probabilistic algorithms for linear algebra computations, such as factorizing matrices and solving linear systems. It focuses on techniques that have a proven track record for real-world problem instances. The paper…

Numerical Analysis · Mathematics 2021-03-17 Per-Gunnar Martinsson , Joel Tropp

A binary contingency table is an m x n array of binary entries with prescribed row sums r=(r_1,...,r_m) and column sums c=(c_1,...,c_n). The configuration model for uniformly sampling binary contingency tables proceeds as follows. First,…

Probability · Mathematics 2011-10-13 Jose Blanchet , Alexandre Stauffer

The CP 2002 paper entitled "Breaking Row and Column Symmetries in Matrix Models" by Flener et al. (https://link.springer.com/chapter/10.1007%2F3-540-46135-3_31) describes some of the first work for identifying and analyzing row and column…

Artificial Intelligence · Computer Science 2019-10-04 Alan M. Frisch , Brahim Hnich , Zeynep Kiziltan , Ian Miguel , Toby Walsh

Biclustering is a method for detecting homogeneous submatrices in a given observed matrix, and it is an effective tool for relational data analysis. Although there are many studies that estimate the underlying bicluster structure of a…

Methodology · Statistics 2021-07-16 Chihiro Watanabe , Taiji Suzuki