We present an information-based uncertainty quantification method for general Markov random fields (MRFs). MRFs are structured, probabilistic graphical models over undirected graphs and provide a f...

Most approaches to topic modeling assume an independence between documents that is frequently violated. We present an topic model that makes use of one or more user-specified graphs describing relationships between documents. These graph are encoded in the form of a Markov random field over topics and serve to encourage related documents to have similar topic structures. Experiments on show upw...

A combinatorial random variable is a discrete random variable defined over a combinatorial set (e.g., a power set of a given set). In this paper we introduce combinatorial Markov random fields (Comrafs), which are Markov random fields where some of the nodes are combinatorial random variables. We argue that Comrafs are powerful models for unsupervised and semi-supervised learning. We put Comraf...

1. Markov property The Markov property of a stochastic sequence {Xn}n≥0 implies that for all n ≥ 1, Xn is independent of (Xk : k / ∈ {n− 1, n, n + 1}), given (Xn−1, Xn+1). Another way to write this is: Xn ⊥ (Xk : k / ∈ ∂{n}) | (Xk : k ∈ ∂{n}) where ∂{n} is the set of neighbors of site n. We would like to now generalize this Markov property from one-dimensional index sets to more arbitrary domains.

A noninvertible function of a first order Markov process, or of a nearestneighbor Markov random field, is called a hidden Markov model. Hidden Markov models are generally not Markovian. In fact, they may have complex and long range interactions, which is largely the reason for their utility. Applications include signal and image processing, speech recognition, and biological modeling. We show t...

In this paper we propose an extension to the standard Markov Random Field (MRF) model in order to handle layers. Our extension, which we call a Factorial MRF (FMRF), is analogous to the extension from Hidden Markov Models (HMM’s) to Factorial HMM’s. We present an efficient EM-based algorithm for inference on Factorial MRF’s. Our algorithm makes use of the fact that layers are a priori independe...