Learning Causally Linked Markov Random Fields
نویسندگان
چکیده
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 approximation itself can be learned by maximizing a lower bound on the log probability of the observed data. The parameters of the MRF are learned by using the mean field version of contrastive divergence [1]. We show that this hybrid model simultaneously learns parts of objects and their inter-relationships from intensity images. We discuss the extension to multiple MRF’s linked into in a chain graph by directed connections.
منابع مشابه
Subset Selection for Gaussian Markov Random Fields
Given a Gaussian Markov random field, we consider the problem of selecting a subset of variables to observe which minimizes the total expected squared prediction error of the unobserved variables. We first show that finding an exact solution is NP-hard even for a restricted class of Gaussian Markov random fields, called Gaussian free fields, which arise in semi-supervised learning and computer ...
متن کاملA Note on Semi-Supervised Learning using Markov Random Fields
This paper describes conditional-probability training of Markov random fields using combinations of labeled and unlabeled data. We capture the similarities between instances learning the appropriate distance metric from the data. The likelihood model and several training procedures are presented.
متن کاملOn Mixing in Pairwise Markov Random Fields with Application to Social Networks
We consider pairwise Markov random fields which have a number of important applications in statistical physics, image processing and machine learning such as Ising model and labeling problem to name a couple. Our own motivation comes from the need to produce synthetic models for social networks with attributes. First, we give conditions for rapid mixing of the associated Glauber dynamics and co...
متن کاملSemi-supervised Clustering using Combinatorial MRFs
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 learning by showing their relationship with...
متن کامل