Related papers: Markov bases for noncommutative Fourier analysis o…

After the phenomenal success of the PageRank algorithm, many researchers have extended the PageRank approach to ranking graphs with richer structures beside the simple linkage structure. In some scenarios we have to deal with…

Mutually unbiased bases correspond to highly useful pairs of measurements in quantum information theory. In the smallest composite dimension, six, it is known that between three and seven mutually unbiased bases exist, with a decades-old…

Sequential scaling is a prominent inference-time scaling paradigm, yet its performance improvements are typically modest and not well understood, largely due to the prevalence of heuristic, non-principled approaches that obscure clear…

The Markov assumption (MA) is fundamental to the empirical validity of reinforcement learning. In this paper, we propose a novel Forward-Backward Learning procedure to test MA in sequential decision making. The proposed test does not assume…

For a matroid with an ordered (or "labelled") basis, a basis exchange step removes one element with label $l$ and replaces it by a new element that results in a new basis, and with the new element assigned label $l$. We prove that one…

We consider multilevel low rank (MLR) matrices, defined as a row and column permutation of a sum of matrices, each one a block diagonal refinement of the previous one, with all blocks low rank given in factored form. MLR matrices extend low…

Stochastic gradient Markov chain Monte Carlo (SGMCMC) is a popular class of algorithms for scalable Bayesian inference. However, these algorithms include hyperparameters such as step size or batch size that influence the accuracy of…

In recent decades, a number of profound theorems concerning approximation of hard counting problems have appeared. These include estimation of the permanent, estimating the volume of a convex polyhedron, and counting (approximately) the…

Let $\{X_n\}_{n\in\N}$ be a Markov chain on a measurable space $\X$ with transition kernel $P$ and let $V:\X\r[1,+\infty)$. The Markov kernel $P$ is here considered as a linear bounded operator on the weighted-supremum space $\cB_V$…

Although Buchberger's algorithm, in theory, allows us to compute Gr\"obner bases over any field, in practice, however, the computational efficiency depends on the arithmetic of the ground field. Consider a field $K = \mathbb{Q}(\alpha)$, a…

We consider the problem of symmetrising a neural network along a group homomorphism: given a homomorphism $\varphi : H \to G$, we would like a procedure that converts $H$-equivariant neural networks to $G$-equivariant ones. We formulate…

The utility of a Markov chain Monte Carlo algorithm is, in large part, determined by the size of the spectral gap of the corresponding Markov operator. However, calculating (and even approximating) the spectral gaps of practical Monte Carlo…

The subject of this paper is to introduce a novel permutation-based nonparametric approach for the problem of ranking several multivariate populations with respect to both experimental and observation studies to be referred to the most…

We apply a Bayesian data analysis scheme known as the Markov Chain Monte Carlo (MCMC) to the tomographic reconstruction of quantum states. This method yields a vector, known as the Markov chain, which contains the full statistical…

Markov chain Monte Carlo algorithms are invaluable tools for exploring stationary properties of physical systems, especially in situations where direct sampling is unfeasible. Common implementations of Monte Carlo algorithms employ…

We propose a Markov chain Monte Carlo-based deconvolution method designed to estimate the number of peaks in spectral data, along with the optimal parameters of each radial basis function. Assuming cases where the number of peaks is…

We consider a series of configurations defined by fibers of a given base configuration. We prove that Markov degree of the configurations is bounded from above by the Markov complexity of the base configuration. As important examples of…

This paper investigates methods for estimating the optimal stochastic control policy for a Markov Decision Process with unknown transition dynamics and an unknown reward function. This form of model-free reinforcement learning comprises…

A key goal in the design of probabilistic inference algorithms is identifying and exploiting properties of the distribution that make inference tractable. Lifted inference algorithms identify symmetry as a property that enables efficient…

This article is partly a survey and partly a research paper. It tackles the use of Groebner bases for addressing problems of numerical semigroups, which is a topic that has been around for some years, but it does it in a systematic way…