Related papers: Random sampling of Latin squares via binary contin…
In this note, we study large deviations of the number $\mathbf{N}$ of intercalates ($2\times2$ combinatorial subsquares which are themselves Latin squares) in a random $n\times n$ Latin square. In particular, for constant $\delta>0$ we…
We propose a sampling-based method for computing the tensor ring (TR) decomposition of a data tensor. The method uses leverage score sampled alternating least squares to fit the TR cores in an iterative fashion. By taking advantage of the…
We recall the Alon-Tarsi conjecture on the number of even latin squares. We introduce a map which switches the parity of a latin square under certain requirements. An example is included.
Standard approaches to probabilistic reasoning require that one possesses an explicit model of the distribution in question. But, the empirical learning of models of probability distributions from partial observations is a problem for which…
Stochastic billiards can be used for approximate sampling from the boundary of a bounded convex set through the Markov Chain Monte Carlo (MCMC) paradigm. This paper studies how many steps of the underlying Markov chain are required to get…
This article considers stochastic algorithms for efficiently solving a class of large scale non-linear least squares (NLS) problems which frequently arise in applications. We propose eight variants of a practical randomized algorithm where…
We consider chance-constrained problems with discrete random distribution. We aim for problems with a large number of scenarios. We propose a novel method based on the stochastic gradient descent method which performs updates of the…
A Latin square is reduced if its first row and column are in natural order. For Latin squares of a particular order $n$ there are four possible different parities. We confirm a conjecture of Stones and Wanless by showing asymptotic equality…
Importance sampling has been reported to produce algorithms with excellent empirical performance in counting problems. However, the theoretical support for its efficiency in these applications has been very limited. In this paper, we…
The randomized extended Kaczmarz method, proposed by Zouzias and Freris (SIAM J. Matrix Anal. Appl. 34: 773-793, 2013), is appealing for solving least-squares problems. However, its randomly selecting rows and columns of A with probability…
An algorithm that uses the cycle structure of the rows, or the columns, of a Latin square to compute its autotopy group is introduced. As a result, a bound for the size of the autotopy group is obtained. This bound is used to show that the…
A simple method to produce a random order type is to take the order type of a random point set. We conjecture that many probability distributions on order types defined in this way are heavily concentrated and therefore sample inefficiently…
We present a new random walk for uniformly sampling high-dimensional convex bodies. It achieves state-of-the-art runtime complexity with stronger guarantees on the output than previously known, namely in R\'enyi divergence (which implies…
We develop an efficient algorithm for sampling the eigenvalues of random matrices distributed according to the Haar measure over the orthogonal or unitary group. Our technique samples directly a factorization of the Hessenberg form of such…
Suppose that $k$ is a function of $n$ and $n\to\infty$. We show that with probability $1-O(1/n)$, a uniformly random $k\times n$ Latin rectangle contains no proper Latin subsquare of order $4$ or more, proving a conjecture of Divoux, Kelly,…
In social and biomedical sciences testing in contingency tables often involves order restrictions on cell-probabilities parameters. We develop objective Bayes methods for order-constrained testing and model comparison when observations…
Sampling from binary quadratic distributions (BQDs) is a fundamental but challenging problem in discrete optimization and probabilistic inference. Previous work established theoretical guarantees for stochastic localization (SL) in…
Motivated by the least squares solver Blendenpik, we investigate three strategies for uniform sampling of rows from m x n matrices Q with orthonormal columns. The goal is to determine, with high probability, how many rows are required so…
In this paper, we investigate the randomized algorithms for block matrix multiplication from random sampling perspective. Based on the A-optimal design criterion, the optimal sampling probabilities and sampling block sizes are obtained. To…
Computing the marginal likelihood or evidence is one of the core challenges in Bayesian analysis. While there are many established methods for estimating this quantity, they predominantly rely on using a large number of posterior samples…