Using a graphical representation based on the Wolff algorithm, the (classical) d-dimensional XY model and some related spin-systems are studied. It is proved that in d = 2, the predicted discontinuity in the spin-wave stiffness indeed occurs. Further, the critical properties of the spin-system are related to percolation properties of the graphical representation. In particular, a suitably defin...

We present a graphical model for beat tracking in recorded music. Using a probabilistic graphical model allows us to incorporate local information and global smoothness constraints in a principled manner. We evaluate our model on a set of varied and difficult examples, and achieve impressive results. By using a fast dual-tree algorithm for graphical model inference, our system runs in less time...

We demonstrate that tensor decompositions can be used to transform graphical models into structurally simpler graphical models that approximate the same joint probability distribution. In this way, standard inference algorithms such as the junction tree algorithm, can be used in order to use the transformed graphical model for approximate inference. The usefulness of the technique is demonstrat...

Probabilistic graphical models are tools that are used to represent the probability distribution of a vector of random variables X = (X1, . . . , XN ). In this paper we introduce functions f(x1, . . . , xN) defined over the given vector. These functions also are random variables. The main result of the paper is an algorithm for finding the expected value and other moments for some classes of f(...

Graphical models are an increasingly popular approach for speech and language processing. As researchers design ever more complex models it becomes crucial to find triangulations that make inference problems tractable. This paper presents a genetic algorithm for triangulation search that is well-suited for speech and language graphical models. It is unique in two ways: First, it can find triang...

The von Mises model encodes a multivariate circular distribution as an undirected probabilistic graphical model. Presently, the only algorithm for performing inference in the model is Gibbs sampling, which becomes inefficient for large graphs. To address this issue, we introduce an Expectation Propagation based algorithm for performing inference in the von Mises graphical model. Our approach in...

Affinity propagation (AP) was recently introduced as an unsupervised learning algorithm for exemplar-based clustering. We present a derivation of AP that is much simpler than the original one and is based on a quite different graphical model. The new model allows easy derivations of message updates for extensions and modifications of the standard AP algorithm. We demonstrate this by adjusting t...

This paper studies graphical model selection, i.e., the problem of estimating a graph of statistical relationships among a collection of random variables. Conventional graphical model selection algorithms are passive, i.e., they require all the measurements to have been collected before processing begins. We propose an active learning algorithm that uses junction tree representations to adapt f...

This report1 presents probabilistic graphical models that are based on imprecise probabilities using a comprehensive language. In particular, the discussion is focused on credal networks and discrete domains. It describes the building blocks of credal networks, algorithms to perform inference, and discusses on complexity results and related work. The goal is to present an easy-to-follow introdu...

Given a positive even integer n we show how to generate the set G n of graphical partitions of n that is those partitions of n which correspond to the degree sequences of simple undirected graphs The algorithm is based on a recurrence for G n and the total time used by the algorithm independent of output is O jG n j which is constant average time per graphical partition This is the rst algorith...