Related papers: On Mixing in Pairwise Markov Random Fields with Ap…

We study model embeddability, which is a variation of the famous embedding problem in probability theory, when apart from the requirement that the Markov matrix is the matrix exponential of a rate matrix, we additionally ask that the rate…

A novel field theoretical approach towards modelling dynamic networking in complex systems is presented. An equilibrium networking formalism which utilises Gaussian fields is adapted to model the dynamics of particles that can bind and…

Traditionally, covariant scalar field theory models are either super renormalizable, strictly renormalizable, or nonrenormalizable. The goal of `Mixed Models' is to make sense of sums of these distinct examples, e.g.,…

We establish a log-supermodularity property for probability distributions on binary patterns observed at the tips of a tree that are generated under any 2--state Markov process. We illustrate the applicability of this result in…

In many data analyses, each measurement may come with a simple yes/no correction; for example, belonging to one of two populations or being contaminated or not. Ignoring such binary effects may bias the results, while accounting for them…

Finding the most likely (MAP) configuration of a Markov random field (MRF) is NP-hard in general. A promising, recent technique is to reduce the problem to finding a maximum weight stable set (MWSS) on a derived weighted graph, which if…

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…

Representing the conditional independences present in a multivariate random vector via graphs has found widespread use in applications, and such representations are popularly known as graphical models or Markov random fields. These models…

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…

Exponential random graph models have become increasingly important in the study of modern networks ranging from social networks, economic networks, to biological networks. They seek to capture a wide variety of common network tendencies…

We designed a model-based analysis to predict the occurrence of population patterns in distributed spiking activity. Using a maximum entropy principle with a Markovian assumption, we obtain a model that accounts for both spatial and…

Random networks are increasingly used to analyse complex transportation networks, such as airline routes, roads and rail networks. So far, this research has been focused on describing the properties of the networks with the help of random…

Matching problems are ubiquitous. They occur in economic markets, labor markets, internet advertising, and elsewhere. In this paper we focus on an application of matching for social media. Our goal is to distribute content from information…

Mixture models have found uses in many areas. To list a few: unsupervised learning, empirical Bayes, latent class and trait models. The current applications of mixture models to empirical data is limited to computing a mixture model from…

Network Models with couplings between link pairs are the simplest models for a class of networks with Higher Order interactions. In this paper we give an analytic, general solution to this family of Random Graph Models extending previous…

We construct a novel class of stochastic blockmodels using Bayesian nonparametric mixtures. These model allows us to jointly estimate the structure of multiple networks and explicitly compare the community structures underlying them, while…

Belief Propagation (BP) is a widely used approximation for exact probabilistic inference in graphical models, such as Markov Random Fields (MRFs). In graphs with cycles, however, no exact convergence guarantees for BP are known, in general.…

We use Markov categories to generalize the basic theory of Markov chains and hidden Markov models to an abstract setting. This comprises characterizations of hidden Markov models in terms of conditional independences and algorithms for…

In the study of Markov chain mixing times, analysis has centered on the performance from a worst-case starting state. Here, in the context of Glauber dynamics for the one-dimensional Ising model, we show how new ideas from information…

Stochastic reaction network models arise in intracellular chemical reactions, epidemiological models and other population process models, and are a class of continuous time Markov chains which have the nonnegative integer lattice as state…