Related papers: Exact sampling and counting for fixed-margin matri…
We describe a dynamic programming algorithm for exact counting and exact uniform sampling of matrices with specified row and column sums. The algorithm runs in polynomial time when the column sums are bounded. Binary or non-negative integer…
Consider the collection of all binary matrices having a specific sequence of row and column sums and consider sampling binary matrices uniformly from this collection. Practical algorithms for exact uniform sampling are not known, but there…
Data sets in the form of binary matrices are ubiquitous across scientific domains, and researchers are often interested in identifying and quantifying noteworthy structure. One approach is to compare the observed data to that which might be…
The number of non-negative integer matrices with given row and column sums appears in a variety of problems in mathematics and statistics but no closed-form expression for it is known, so we rely on approximations of various kinds. Here we…
Random sampling has become a critical tool in solving massive matrix problems. For linear regression, a small, manageable set of data rows can be randomly selected to approximate a tall, skinny data matrix, improving processing time…
We give an algorithm that generates a uniformly random contingency table with specified marginals, i.e. a matrix with non-negative integer values and specified row and column sums. Such algorithms are useful in statistics and combinatorics.…
We study the problem of transforming a multi-way contingency table into an equivalent table with uniform margins and same dependence structure. This is an old question which relates to recent advances in copula modeling for discrete random…
A sequential importance sampling algorithm is developed for the distribution that results when a matrix of independent, but not identically distributed, Bernoulli random variables is conditioned on a given sequence of row and column sums.…
We present a new approach for random sampling of contingency tables of any size and constraints based on a recently introduced $\textit{probabilistic divide-and-conquer}$ technique. A simple exact sampling algorithm is presented for…
In this paper, we consider the problem of counting and sampling structures in graphs. We define a class of "edge universal labeling problems"---which include proper $k$-colorings, independent sets, and downsets---and describe simple…
In the literature, derivations of exact null distributions of rank-sum statistics is often avoided in cases where one or more ties exist in the data. By deriving the null distribution in the no-ties case with the aid of classical $q$-series…
An algorithm for sampling exactly from the normal distribution is given. The algorithm reads some number of uniformly distributed random digits in a given base and generates an initial portion of the representation of a normal deviate in…
Matrix completion aims to reconstruct a data matrix based on observations of a small number of its entries. Usually in matrix completion a single matrix is considered, which can be, for example, a rating matrix in recommendation system.…
We apply a method recently introduced to the statistical literature to directly estimate the precision matrix from an ensemble of samples drawn from a corresponding Gaussian distribution. Motivated by the observation that cosmological…
Exact evaluation of $<{\rm Tr} S^p>$ is here performed for real symmetric matrices $S$ of arbitrary order $n$, up to some integer $p$, where the matrix entries are independent identically distributed random variables, with an arbitrary…
Perfect sampling is a technique that uses coupling arguments to provide a sample from the stationary distribution of a Markov chain in a finite time without ever computing the distribution. This technique is very efficient if all the events…
We consider the problem of selecting non-zero entries of a matrix $A$ in order to produce a sparse sketch of it, $B$, that minimizes $\|A-B\|_2$. For large $m \times n$ matrices, such that $n \gg m$ (for example, representing $n$…
We present a randomized approximation algorithm for counting contingency tables, mxn non-negative integer matrices with given row sums R=(r_1, ..., r_m) and column sums C=(c_1, ..., c_n). We define smooth margins (R,C) in terms of the…
The paper derives new results on the marginal likelihood of a two-way table which clarify the conditions under which Ecological inference is possible and lead to an efficient algorithm for maximizing the exact multinomial likelihood. The…
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,…