Polynomial-time approximation algorithms for the Ising model
SIAM Journal on Computing
A family of algorithms for approximate bayesian inference
A family of algorithms for approximate bayesian inference
Stochastic processes on graphs with cycles: geometric and variational approaches
Stochastic processes on graphs with cycles: geometric and variational approaches
Computing upper and lower bounds on likelihoods in intractable networks
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
Linear response algorithms for approximate inference in graphical models
Neural Computation
On the choice of regions for generalized belief propagation
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
On the uniqueness of loopy belief propagation fixed points
Neural Computation
Dynamic Hierarchical Markov Random Fields for Integrated Web Data Extraction
The Journal of Machine Learning Research
Convexity arguments for efficient minimization of the Bethe and Kikuchi free energies
Journal of Artificial Intelligence Research
Piecewise training for structured prediction
Machine Learning
Message-passing for Graph-structured Linear Programs: Proximal Methods and Rounding Schemes
The Journal of Machine Learning Research
Towards an integrated protein-protein interaction network
RECOMB'05 Proceedings of the 9th Annual international conference on Research in Computational Molecular Biology
Lifted online training of relational models with stochastic gradient methods
ECML PKDD'12 Proceedings of the 2012 European conference on Machine Learning and Knowledge Discovery in Databases - Volume Part I
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Bounds on the log partition function are important in a variety of contexts, including approximate inference, model fitting, decision theory, and large deviations analysis [11, 5, 4]. We introduce a new class of upper bounds on the log partition function, based on convex combinations of distributions in the exponential domain, that is applicable to an arbitrary undirected graphical model. In the special case of convex combinations of tree-structured distributions, we obtain a family of variational problems, similar to the Bethe free energy, but distinguished by the following desirable properties: (i) they are convex, and have a unique global minimum; and (ii) the global minimum gives an upper bound on the log partition function. The global minimum is defined by stationary conditions very similar to those defining fixed points of belief propagation (BP) or tree-based reparameterization [see 13, 14]. As with BP fixed points, the elements of the minimizing argument can be used as approximations to the marginals of the original model. The analysis described here can be extended to structures of higher treewidth (e.g., hypertrees), thereby making connections with more advanced approximations (e.g., Kikuchi and variants [15, 10]).