Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
An Introduction to Variational Methods for Graphical Models
Machine Learning
Information Theory, Inference & Learning Algorithms
Information Theory, Inference & Learning Algorithms
The Journal of Machine Learning Research
Pattern Recognition and Machine Learning (Information Science and Statistics)
Pattern Recognition and Machine Learning (Information Science and Statistics)
Kernel methods, syntax and semantics for relational text categorization
Proceedings of the 17th ACM conference on Information and knowledge management
A framework for estimating complex probability density structures in data streams
Proceedings of the 17th ACM conference on Information and knowledge management
Fast mining of complex time-stamped events
Proceedings of the 17th ACM conference on Information and knowledge management
Graphical Models, Exponential Families, and Variational Inference
Foundations and Trends® in Machine Learning
Efficient training methods for conditional random fields
Efficient training methods for conditional random fields
A generalized mean field algorithm for variational inference in exponential families
UAI'03 Proceedings of the Nineteenth conference on Uncertainty in Artificial Intelligence
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Ising mean field is a basic variational inference method for Ising model, which can provide an effective approximate solution for large-scale inference problem. The main idea is to transform a probabilistic inference problem into a functional extremum problem by variational calculus, and solve the functional extremum problem to obtain approximate marginal distributions. The process of solving the functional extremum is an important step and a computational core for variational inference. But the traditional full variational iteration methods make the variable information intercross with each other deeply. From the view of incomplete variational iterations, we propose a message family propagation method for Ising mean field to compute a marginal distribution family of object variable. First we define the concepts of iteration tree and pruning iteration tree to describe the iteration computation process of Ising mean field inference. Then we design the message family propagation method based on the iteration trees. The method propagates mean field message families and belief message families from bottom to top of the iteration tree, and presents a marginal distribution family of variable in root node. Finally we prove the marginal distribution bound theorem, which shows that the marginal distribution family computed by the method in the pruning iteration tree contains the exact marginal stribution. Theoretical and experimental results illustrate that the message family propagation method is valid and the marginal distribution bounds are tight.