Related papers: Reducing the Ising model to matchings
Computing a minimum path cover (MPC) of a directed acyclic graph (DAG) is a fundamental problem with a myriad of applications, including reachability. Although it is known how to solve the problem by a simple reduction to minimum flow,…
Perfect sampling is a technique that uses coupling arguments to provide a sample from the stationary distribution of a Markov chain in a finite time without ever computing the distribution. This technique is very efficient if all the events…
Probabilistic models are conceptually powerful tools for finding structure in data, but their practical effectiveness is often limited by our ability to perform inference in them. Exact inference is frequently intractable, so approximate…
The Metropolis-Hastings method is often used to construct a Markov chain with a given $\pi$ as its stationary distribution. The method works even if $\pi$ is known only up to an intractable constant of proportionality. Polynomial time…
In this paper, we provide polynomial-time algorithms for different extensions of the matching counting problem, namely maximal matchings, path matchings (linear forest) and paths, on graph classes of bounded clique-width. For maximal…
In this paper we give a fully polynomial randomized approximation scheme (FPRAS) for the number of matchings in k-uniform hypergraphs whose intersection graphs contain few claws. Our method gives a generalization of the canonical path…
Markov jump processes (MJPs) are continuous-time stochastic processes widely used in a variety of applied disciplines. Inference for MJPs typically proceeds via Markov chain Monte Carlo, the state-of-the-art being a uniformization-based…
Markov chains are convenient means of generating realizations of networks with a given (joint or otherwise) degree distribution, since they simply require a procedure for rewiring edges. The major challenge is to find the right number of…
Full Bayesian computational inference for model determination in undirected graphical models is currently restricted to decomposable graphs, except for problems of very small scale. In this paper we develop new, more efficient methodology…
We present a novel method for computing reachability probabilities of parametric discrete-time Markov chains whose transition probabilities are fractions of polynomials over a set of parameters. Our algorithm is based on two key…
Generalized-ensemble Monte Carlo simulations such as the multicanonical method and similar techniques are among the most efficient approaches for simulations of systems undergoing discontinuous phase transitions or with rugged free- energy…
We use the cavity method to study parallel dynamics of disordered Ising models on a graph. In particular, we derive a set of recursive equations in single site probabilities of paths propagating along the edges of the graph. These equations…
Graph canonization is the problem of computing a unique representative, a canon, from the isomorphism class of a given graph. This implies that two graphs are isomorphic exactly if their canons are equal. We show that graphs of bounded tree…
In this paper, we introduce a graph matching method that can account for constraints of arbitrary order, with arbitrary potential functions. Unlike previous decomposition approaches that rely on the graph structures, we introduce a…
The usual setting for learning the structure and parameters of a graphical model assumes the availability of independent samples produced from the corresponding multivariate probability distribution. However, for many models the mixing time…
Recent work has shown that probabilistic models based on pairwise interactions-in the simplest case, the Ising model-provide surprisingly accurate descriptions of experiments on real biological networks ranging from neurons to genes.…
An important problem arising in the study of complex networks, for instance in community detection and motif finding, is the sampling of graphs with fixed degree sequence. The equivalent problem of generating random 0,1 matrices with fixed…
Finding optimal pathways in chemical reaction networks is essential for elucidating and designing chemical processes, with significant applications such as synthesis planning and metabolic pathway analysis. Such a chemical pathway-finding…
We compare convergence rates of Metropolis--Hastings chains to multi-modal target distributions when the proposal distributions can be of ``local'' and ``small world'' type. In particular, we show that by adding occasional long-range jumps…
It was recently proposed in https://journals.aps.org/pre/abstract/10.1103/PhysRevE.94.043322 [Herdeiro & Doyon Phys.,Rev.,E (2016)] a numerical method showing a precise sampling of the infinite plane 2d critical Ising model for finite…