Due to the intractable partition function, the exact likelihood function for a Markov random field (MRF), in many situations, can only be approximated. Major approximation approaches include pseudolikelihood [2] and Laplace approximation [33]. In this paper, we propose a novel way of approximating the likelihood function through first approximating the marginal likelihood functions of individua...

We describe a learning procedure for a generative model that contains a hidden Markov Random Field (MRF) which has directed connections to the observable variables. The learning procedure uses a variational approximation for the posterior distribution over the hidden variables. Despite the intractable partition function of the MRF, the weights on the directed connections and the variational app...

Scoring structures of undirected graphical models by means of evaluating the marginal likelihood is very hard. The main reason is the presence of the partition function which is intractable to evaluate, let alone integrate over. We propose to approximate the marginal likelihood by employing two levels of approximation: we assume normality of the posterior (the Laplace approximation) and approxi...

This paper discusses how to construct approximations to a unimodal hidden Gaussian Markov random field on a graph of dimensionnwhen the likelihood consists of mutually independent data. We demonstrate that a class of non-Gaussian approximations can be constructed for a wide range of likelihood models. They have the appealing properties that exact samples can be drawn from them, the normalisatio...

1 Background. Evolution through divergence gives rise to different, though related, present-day genomes that shared common ancestors. Portions of genomes could be seen as genomic entities spawned through some dynamic changes in content and order of the ancestral genome. Certain regions, through selection, are conserved over time. Such genomic portions (be they gene-coding regions, conserved non...

Relational Markov Random Fields (rMRF’s) are a general and flexible framework for reasoning about the joint distribution over attributes of a large number of interacting entities, such as graphs, social networks or gene networks. When modeling such a network using an rMRF one of the major problems is choosing the set of features to include in the model and setting their weights. The main comput...

Recently, a framework for multiscale stochastic modeling was introduced based on coarse-to-fine scale-recursive dynamics defined on trees. This model class has some attractive characteristics which lead to extremely efficient, statistically optimal signal and image processing algorithms. In this paper, we show that this model class is also quite rich. In particular, we describe how 1-D Markov p...

Markov Random Fields (MRF’s) can be used for a wide variety of vision problems. In this paper we focus on MRF’s with two-valued clique potentials, which form a generalized Potts model. We show that the maximum a posteriori estimate of such an MRF can be obtained by solving a multiway minimum cut problem on a graph. We develop efficient algorithms for computing good approximations to the minimum...

Abstract: The optical flow can be viewed as the assignment problem between the pixels of consecutive video frames. The problem to determine the optical flow is addressed for many decades because of its central relevance. This paper gives a short resume about classical methods. Afterwards advanced Markov random fields are developed. The challenge and beauty of this approach consists of the large...

Acknowledgments I would like to thank my advisor, Pradeep Ravikumar, for inspiration, guidance, and encouragement on this work. In addition, I would like to thank Ali Jalali for his collaboration and work on the proof techniques and theoretical analysis used in this paper. Also, I would also like to thank Inderjit Dhillon and the students of his lab for motivation and many stimulating conversat...