Related papers: Exact sampling and counting for fixed-margin matri…

This is a survey of the recent progress and open questions on the structure of the sets of 0-1 and non-negative integer matrices with prescribed row and column sums. We discuss cardinality estimates, the structure of a random matrix from…

We investigate the rank of random (symmetric) sparse matrices. Our main finding is that with high probability, any dependency that occurs in such a matrix is formed by a set of few rows that contains an overwhelming number of zeros. This…

In this paper, we propose several models, which can realize synchronization of complex networks in finite time effectively. The results apply to heterogeneous dynamic networks, too. The mechanism of finite time convergence is revealed.…

Clustering has many important applications in computer science, but real-world datasets often contain outliers. Moreover, the presence of outliers can make the clustering problems to be much more challenging. To reduce the complexities,…

Finding a suitable measurement matrix is an important topic in compressed sensing. Though the known random matrix, whose entries are drawn independently from a certain probability distribution, can be used as a measurement matrix and…

In this paper, we consider the estimation and inference of precision matrices of a rich class of locally stationary and nonlinear time series assuming that only one realization of the time series is observed. Using a Cholesky decomposition…

We show that, under mild assumptions, the spectrum of a sum of independent random matrices is close to that of the Gaussian random matrix whose entries have the same mean and covariance. This nonasymptotic universality principle yields…

We outline how modern likelihood theory, which provides essentially exact inferences in a variety of parametric statistical problems, may routinely be applied in practice. Although the likelihood procedures are based on analytical…

The two-sample test is a fundamental problem in statistics with a wide range of applications. In the realm of high-dimensional data, nonparametric methods have gained prominence due to their flexibility and minimal distributional…

Finite mixtures of matrix normal distributions are a powerful tool for classifying three-way data in unsupervised problems. The distribution of each component is assumed to be a matrix variate normal density. The mixture model can be…

We study the problem of sampling a uniformly random directed rooted spanning tree, also known as an arborescence, from a possibly weighted directed graph. Classically, this problem has long been known to be polynomial-time solvable; the…

Matrix completion is a classical problem that has received recurring interest across a wide range of fields. In this paper, we revisit this problem in an ultra-sparse sampling regime, where each entry of an unknown, $n\times d$ matrix $M$…

We consider the binomial random set model $[n]_p$ where each element in $\{1,\dots,n\}$ is chosen independently with probability $p:=p(n)$. We show that for essentially all regimes of $p$ and very general conditions for a matrix $A$ and a…

In this paper we study the problem of computing max-entropy distributions over a discrete set of objects subject to observed marginals. Interest in such distributions arises due to their applicability in areas such as statistical physics,…

Most implementations of sampling algorithms for continuous distributions use floating-point numbers, which introduce round-off errors and approximations. These errors can be difficult to analyze, and can cause security issues when used in…

We build a new perspective to count perfect matchings of a given graph. This idea is motivated by a construction on the relative cohomology group of surfaces. As an application of our theory, we reprove the celebrated Aztec Diamond theorem,…

This paper addresses the problem of estimating the containment and similarity between two sets using only random samples from each set, without relying on sketches of full sets. The study introduces a binomial model for predicting the…

We describe an MCMC method for sampling distributions with soft constraints, which are constraints that are almost but not exactly satisfied. We sample a total distribution that is a convex combination of the target soft distribution with…

Exact matrix completion and low rank matrix estimation problems has been studied in different underlying conditions. In this work we study exact low-rank completion under non-degenerate noise model. Non-degenerate random noise model has…

Motivated by the popularity of stochastic rounding in the context of machine learning and the training of large-scale deep neural network models, we consider stochastic nearness rounding of real matrices $\mathbf{A}$ with many more rows…