相关论文: Markov bases: a 25 year update

We introduce a novel framework for causal explanations of stochastic, sequential decision-making systems built on the well-studied structural causal model paradigm for causal reasoning. This single framework can identify multiple,…

This paper studies Hoeffding's inequality for Markov chains under the generalized concentrability condition defined via integral probability metric (IPM). The generalized concentrability condition establishes a framework that interpolates…

Empirical likelihood is a powerful semi-parametric method increasingly investigated in the literature. However, most authors essentially focus on an i.i.d. setting. In the case of dependent data, the classical empirical likelihood method…

A variety of enhanced statistical and numerical methods are now routinely used to extract comprehensible and relevant thermodynamic information from the vast amount of complex, high-dimensional data obtained from intensive molecular…

Understanding the stability and long-time behavior of generative models is a fundamental problem in modern machine learning. This paper provides quantitative bounds on the sampling error of score-based generative models by leveraging…

We develop a general theory for Markov chains whose transition probabilities are the coefficients of descent operators on combinatorial Hopf algebras. These model the breaking-then-recombining of combinational objects. Examples include the…

Developing satisfactory methodology for the analysis of Markov random field is a very challenging task. Indeed, due to the Markovian dependence structure, the normalizing constant of the fields cannot be computed using standard analytical…

A susceptibility propagation that is constructed by combining a belief propagation and a linear response method is used for approximate computation for Markov random fields. Herein, we formulate a new, improved susceptibility propagation by…

Cross-sectional observations from a dynamical system can be modeled via steady-state distributions of Markov processes. The major challenge is then to determine whether the process parameters can be identified and estimated from the…

Many economic models feature monotone Markov dynamics on state spaces that may be noncompact. Establishing existence, uniqueness, and stability of stationary distributions in such settings has required a patchwork of sufficient conditions,…

In this work, we study a natural nonparametric estimator of the transition probability matrices of a finite controlled Markov chain. We consider an offline setting with a fixed dataset, collected using a so-called logging policy. We develop…

We introduce simple conditions ensuring that invariant distributions of a Feller Markov chain on a compact Riemannian manifold are absolutely continuous with a lower semi-continuous, continuous or smooth density with respect to the…

This article presents several results establishing connections be- tween Markov chains and dynamical systems, from the point of view of open systems in physics. We show how all Markov chains can be understood as the information on one…

In this paper, we analyze the dynamics of spreading processes taking place over time-varying networks. A common approach to model time-varying networks is via Markovian random graph processes. This modeling approach presents the following…

In two-way contingency tables we sometimes find that frequencies along the diagonal cells are relatively larger(or smaller) compared to off-diagonal cells, particularly in square tables with the common categories for the rows and the…

We study the problem of finite-horizon probabilistic invariance for discrete-time Markov processes over general (uncountable) state spaces. We compute discrete-time, finite-state Markov chains as formal abstractions of general Markov…

We consider a discrete-time Markov chain $(X^t,Y^t)$, $t=0,1,2,...$, where the $X$-component forms a Markov chain itself. Assume that $(X^t)$ is Harris-ergodic and consider an auxiliary Markov chain ${\hat{Y}^t}$ whose transition…

Multiplex networks are a common modeling framework for interconnected systems and multimodal data, yet we still lack fundamental insights for how multiplexity affects stochastic processes. We introduce a novel ``Markov chains of Markov…

We investigate a method for extracting nonlinear principal components (NPCs). These NPCs maximize variation subject to smoothness and orthogonality constraints; but we allow for a general class of constraints and multivariate probability…

Improved rates of convergence for ergodic Markov chains and relaxed conditions for them, as well as analogous convergence results for some non-homogeneous Markov chains are studied. The setting from the previous works is extended. Examples…