Related papers: Contingency tables with uniformly bounded entries

Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of…

We derive exact matrix integral representations for different sums over partitions. The characteristic feature of all obtained matrix models is the presence of logarithmic (or, vice versa, exponential) terms in the potential. Our derivation…

Let d=(d_1,d_2,..., d_n) be a vector of non-negative integers. We study the number of symmetric 0-1 matrices whose row sum vector equals d. While previous work has focussed on the case of zero diagonal, we allow diagonal entries to equal 1.…

We estimate the frequency of singular matrices and of matrices of a given rank whose entries are parametrised by arbitrary polynomials over the integers and modulo a prime $p$. In particular, in the integer case, we improve a recent bound…

In a recent paper (Cucker, Krick, Malajovich and Wschebor, A Numerical Algorithm for Zero Counting. I: Complexity and accuracy, J. Compl.,24:582-605, 2008) we analyzed a numerical algorithm for computing the number of real zeros of a…

Data used for analytics and machine learning often take the form of tables with categorical entries. We introduce a family of lossless compression algorithms for such data that proceed in four steps: $(i)$ Estimate latent variables…

We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…

A recent conjecture of Caputo, Carlen, Lieb, and Loss, and, independently, of the author, states that the maximum of the permanent of a matrix whose rows are unit vectors in l_p is attained either for the identity matrix I or for a constant…

This paper introduces a matrix quantile factor model for matrix-valued data with low-rank structure. We estimate the row and column factor spaces via minimizing the empirical check loss function with orthogonal rotation constraints. We show…

Today, data analysts largely rely on intuition to determine whether missing or withheld rows of a dataset significantly affect their analyses. We propose a framework that can produce automatic contingency analysis, i.e., the range of values…

In this paper, we consider matrix completion from non-uniformly sampled entries including fully observed and partially observed columns. Specifically, we assume that a small number of columns are randomly selected and fully observed, and…

We propose a novel stochastic algorithm that randomly samples entire rows and columns of the matrix as a way to approximate an arbitrary matrix function using the power series expansion. This contrasts with existing Monte Carlo methods,…

We present a general methodology for performing statistical inference on the components of a real-valued matrix parameter for which rows and columns are subject to order restrictions. The proposed estimation procedure is based on an…

We obtain sharp asymptotic estimates on the number of $n \times n$ contingency tables with two linear margins $Cn$ and $BCn$. The results imply a second order phase transition on the number of such contingency tables, with a critical value…

In this paper we show that the agglomeration of rows or columns of a contingency table with a hierarchical clustering algorithm yields statistical models defined through toric ideals. In particular, starting from the classical independence…

We consider the computation of the matrix logarithm by using numerical quadrature. The efficiency of numerical quadrature depends on the integrand and the choice of quadrature formula. The Gauss--Legendre quadrature has been conventionally…

The ability of many powerful machine learning algorithms to deal with large data sets without compromise is often hampered by computationally expensive linear algebra tasks, of which calculating the log determinant is a canonical example.…

We formulate conjectures regarding the maximum value and maximizing matrices of the permanent and of diagonal products on the set of stochastic matrices with bounded rank. We formulate equivalent conjectures on upper bounds for these…

We study the problem of maximizing R{\'e}nyi entropy of order $2$ (equivalently, minimizing the index of coincidence) over the set of joint distributions with prescribed marginals. A closed-form optimizer is known under a feasibility…

The trapping redundancy of a linear code is the number of rows of a smallest parity-check matrix such that no submatrix forms an $(a,b)$-trapping set. This concept was first introduced in the context of low-density parity-check (LDPC) codes…