Related papers: Dynamic Markov Bases
We formulate a probabilistic Markov property in discrete time under a dynamic risk framework with minimal assumptions. This is useful for recursive solutions to risk-sensitive versions of dynamic optimisation problems such as optimal…
Markov decision processes are typically used for sequential decision making under uncertainty. For many aspects however, ranging from constrained or safe specifications to various kinds of temporal (non-Markovian) dependencies in task and…
Leveraging recent work on data-driven methods for constructing a finite state space Markov process from dynamical systems, we address two problems for obtaining further reduced statistical representations. The first problem is to extract…
Modeling the dynamics of non-stationary stochastic systems requires balancing the representational power of deep learning with the mathematical transparency of classical models. While classical Markov transition operators provide explicit,…
Data-based inference of directed interactions in complex dynamical systems is a problem common to many disciplines of science. In this work, we study networks of spatially separate dynamical entities, which could represent physical systems…
Markov chains are a convenient means of generating realizations of networks, since they require little more than a procedure for rewiring edges. If a rewiring procedure exists for generating new graphs with specified statistical properties,…
Graphical models are popular statistical tools which are used to represent dependent or causal complex systems. Statistically equivalent causal or directed graphical models are said to belong to a Markov equivalent class. It is of great…
Recently, Bj{\o}ru et al. proposed a novel divide-and-conquer algorithm for bounding counterfactual probabilities in structural causal models (SCMs). They assumed that the SCMs were learned from purely observational data, leading to an…
This paper deals with the Bayesian analysis of graphical models of marginal independence for three way contingency tables. We use a marginal log-linear parametrization, under which the model is defined through suitable zero-constraints on…
Markov networks are popular models for discrete multivariate systems where the dependence structure of the variables is specified by an undirected graph. To allow for more expressive dependence structures, several generalizations of Markov…
Recent advancements in graph representation learning have shifted attention towards dynamic graphs, which exhibit evolving topologies and features over time. The increased use of such graphs creates a paramount need for generative models…
We study the problem of generating connected random graphs with no self-loops or multiple edges and that, in addition, have a given degree sequence. The generation method we focus on is the edge-switching Markov-chain method, whose…
The methodology of Markov basis initiated by Diaconis and Sturmfels(1998) stimulated active research on Markov bases for more than ten years. It also motivated improvements of algorithms for Grobner basis computation for toric ideals, such…
The success of generative modeling in continuous domains has led to a surge of interest in generating discrete data such as molecules, source code, and graphs. However, construction histories for these discrete objects are typically not…
Markov Population Models are a widespread formalism used to model the dynamics of complex systems, with applications in Systems Biology and many other fields. The associated Markov stochastic process in continuous time is often analyzed by…
Time-varying parameter (TVP) regression models can involve a huge number of coefficients. Careful prior elicitation is required to yield sensible posterior and predictive inferences. In addition, the computational demands of Markov Chain…
We propose a flexible nonparametric Bayesian modelling framework for multivariate time series of count data based on tensor factorisations. Our models can be viewed as infinite state space Markov chains of known maximal order with…
Given a Markovian Brownian martingale $Z$, we build a process $X$ which is a martingale in its own filtration and satisfies $X_1 = Z_1$. We call $X$ a dynamic bridge, because its terminal value $Z_1$ is not known in advance. We compute…
We consider the problem of flexible modeling of higher order Markov chains when an upper bound on the order of the chain is known but the true order and nature of the serial dependence are unknown. We propose Bayesian nonparametric…
We consider a sequence of matrices that are associated to Markov dynamical systems and use determinant-free linear algebra techniques (as well as some algebra and complex analysis) to rigorously estimate the eigenvalues of every matrix…