相关论文: Error term in the Cohen-Lenstra heuristic via rand…

This paper studies the problem of ergodicity of transition probability matrices in Markovian models, such as hidden Markov models (HMMs), and how it makes very difficult the task of learning to represent long-term context for sequential…

We present a novel $Q$-learning algorithm tailored to solve distributionally robust Markov decision problems where the corresponding ambiguity set of transition probabilities for the underlying Markov decision process is a Wasserstein ball…

We introduce a new random matrix model called distance covariance matrix in this paper, whose normalized trace is equivalent to the distance covariance. We first derive a deterministic limit for the eigenvalue distribution of the distance…

In this paper, we propose a hierarchical random compression method (HRCM) for kernel matrices in fast kernel summations. The HRCM combines the hierarchical framework of the H-matrix and a randomized sampling technique of the column and row…

It is conjectured that within the class group of any number field, for every integer $\ell \geq 1$, the $\ell$-torsion subgroup is very small (in an appropriate sense, relative to the discriminant of the field). In nearly all settings, the…

Reliable forward uncertainty quantification in engineering requires methods that account for aleatory and epistemic uncertainties. In many applications, epistemic effects arising from uncertain parameters and model form dominate prediction…

Credal sets are sets of probability distributions that are considered as candidates for an imprecisely known ground-truth distribution. In machine learning, they have recently attracted attention as an appealing formalism for uncertainty…

This paper proposes a family of weighted batch means variance estimators, which are computationally efficient and can be conveniently applied in practice. The focus is on Markov chain Monte Carlo simulations and estimation of the asymptotic…

This review article provides an overview of random matrix theory (RMT) with a focus on its growing impact on the formulation and inference of statistical models and methodologies. Emphasizing applications within high-dimensional statistics,…

Cohen, Lenstra, and Martinet have given conjectures for the distribution of class groups of extensions of number fields, but Achter and Malle have given theoretical and numerical evidence that these conjectures are wrong regarding the Sylow…

Hidden tree Markov models allow learning distributions for tree structured data while being interpretable as nondeterministic automata. We provide a concise summary of the main approaches in literature, focusing in particular on the…

We study a general framework of distributional computational graphs: computational graphs whose inputs are probability distributions rather than point values. We analyze the discretization error that arises when these graphs are evaluated…

Computing smoothing distributions, the distributions of one or more states conditional on past, present, and future observations is a recurring problem when operating on general hidden Markov models. The aim of this paper is to provide a…

Factorizing low-rank matrices has many applications in machine learning and statistics. For probabilistic models in the Bayes optimal setting, a general expression for the mutual information has been proposed using heuristic statistical…

We investigate the probability distribution of Chern numbers (quantum Hall effect integers) for a parametric version of the GUE random matrix ensemble, which is a model for a chaotic or disordered system. The numerically-calculated…

The problem of exactly generating a general random process (target process) by using another general random process (coin process) is studied. The performance of the interval algorithm, introduced by Han and Hoshi, is analyzed from the…

We introduce and study deferred N\"{o}rlund statistical convergence in probability, mean of order $r,$ distribution, and study the interrelation among them. Based upon the proposed method to illustrate the findings, we present new Korovkin…

Cross-Correlation random matrices have emerged as a promising indicator of phase transitions in spin systems. The core concept is that the evolution of magnetization encapsulates thermodynamic information [R. da Silva, Int. J. Mod. Phys. C,…

For random integer matrices $M_1,\ldots,M_k \in \operatorname{Mat}_n(\mathbb{Z})$ with independent entries, we study the distribution of the cokernel $\operatorname{cok}(M_1 \cdots M_k)$ of their product. We show that this distribution…

Learning-based low rank approximation algorithms can significantly improve the performance of randomized low rank approximation with sketch matrix. With the learned value and fixed non-zero positions for sketch matrices from learning-based…