Tractable variational structures for approximating graphical models
Proceedings of the 1998 conference on Advances in neural information processing systems II
Global Optimization with Polynomials and the Problem of Moments
SIAM Journal on Optimization
Variational Approximations between Mean Field Theory and the Junction Tree Algorithm
UAI '00 Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
Graphical Models, Exponential Families, and Variational Inference
Foundations and Trends® in Machine Learning
Journal of Artificial Intelligence Research
Sequential mean field variational analysis of structured deformable shapes
Computer Vision and Image Understanding
Log-determinant relaxation for approximate inference in discrete Markov random fields
IEEE Transactions on Signal Processing - Part I
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In intractable, undirected graphical models, an intuitive way of creating structured mean field approximations is to select an acyclic tractable subgraph. We show that the hardness of computing the objective function and gradient of the mean field objective qualitatively depends on a simple graph property. If the tractable subgraph has this property---we call such subgraphs v-acyclic---a very fast block coordinate ascent algorithm is possible. If not, optimization is harder, but we show a new algorithm based on the construction of an auxiliary exponential family that can be used to make inference possible in this case as well. We discuss the advantages and disadvantages of each regime and compare the algorithms empirically.