Enumerative combinatorics
Abstract dynamic programming models under commutativity conditions
SIAM Journal on Control and Optimization
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Learning in graphical models
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Learning to estimate scenes from images
Proceedings of the 1998 conference on Advances in neural information processing systems II
Fast Approximate Energy Minimization via Graph Cuts
IEEE Transactions on Pattern Analysis and Machine Intelligence
Dynamic Programming and Stochastic Control
Dynamic Programming and Stochastic Control
Parallel Optimization: Theory, Algorithms and Applications
Parallel Optimization: Theory, Algorithms and Applications
Probabilistic Networks and Expert Systems
Probabilistic Networks and Expert Systems
An efficient algorithm for finding the M most probable configurationsin probabilistic expert systems
Statistics and Computing
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Stochastic processes on graphs with cycles: geometric and variational approaches
Stochastic processes on graphs with cycles: geometric and variational approaches
Correctness of Local Probability Propagation in Graphical Models with Loops
Neural Computation
The generalized distributive law
IEEE Transactions on Information Theory
On the optimality of solutions of the max-product belief-propagation algorithm in arbitrary graphs
IEEE Transactions on Information Theory
Signal-space characterization of iterative decoding
IEEE Transactions on Information Theory
Tree-based reparameterization framework for analysis of sum-product and related algorithms
IEEE Transactions on Information Theory
Convergent Tree-Reweighted Message Passing for Energy Minimization
IEEE Transactions on Pattern Analysis and Machine Intelligence
Collaborative Multiagent Reinforcement Learning by Payoff Propagation
The Journal of Machine Learning Research
A Linear Programming Approach to Max-Sum Problem: A Review
IEEE Transactions on Pattern Analysis and Machine Intelligence
Minimizing Nonsubmodular Functions with Graph Cuts-A Review
IEEE Transactions on Pattern Analysis and Machine Intelligence
A parallel framework for loopy belief propagation
Proceedings of the 9th annual conference companion on Genetic and evolutionary computation
Using the Simulated Annealing Algorithm for Multiagent Decision Making
RoboCup 2006: Robot Soccer World Cup X
Graphical Models, Exponential Families, and Variational Inference
Foundations and Trends® in Machine Learning
Solving multiagent assignment Markov decision processes
Proceedings of The 8th International Conference on Autonomous Agents and Multiagent Systems - Volume 1
Convergence of min-sum message passing for quadratic optimization
IEEE Transactions on Information Theory
Message passing for maximum weight independent set
IEEE Transactions on Information Theory
Message-passing for Graph-structured Linear Programs: Proximal Methods and Rounding Schemes
The Journal of Machine Learning Research
Graph covers and quadratic minimization
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Bounded approximate decentralised coordination via the max-sum algorithm
Artificial Intelligence
Resource Allocation via Message Passing
INFORMS Journal on Computing
Max margin learning on domain-independent web information extraction
Proceedings of the 20th ACM international conference on Information and knowledge management
Data association based on optimization in graphical models with application to sensor networks
Mathematical and Computer Modelling: An International Journal
Resource Allocation via Message Passing
INFORMS Journal on Computing
Distributed relational temporal difference learning
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
Decentralized semantic coordination via belief propagation
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
Computer Vision and Image Understanding
Energy distribution view for monotonic dual decomposition
International Journal of Approximate Reasoning
Message-passing algorithms for quadratic minimization
The Journal of Machine Learning Research
| Hi-index | 0.12 |
Finding the maximum a posteriori (MAP) assignment of a discrete-state distribution specified by a graphical model requires solving an integer program. The max-product algorithm, also known as the max-plus or min-sum algorithm, is an iterative method for (approximately) solving such a problem on graphs with cycles. We provide a novel perspective on the algorithm, which is based on the idea of reparameterizing the distribution in terms of so-called pseudo-max-marginals on nodes and edges of the graph. This viewpoint provides conceptual insight into the max-product algorithm in application to graphs with cycles. First, we prove the existence of max-product fixed points for positive distributions on arbitrary graphs. Next, we show that the approximate max-marginals computed by max-product are guaranteed to be consistent, in a suitable sense to be defined, over every tree of the graph. We then turn to characterizing the nature of the approximation to the MAP assignment computed by max-product. We generalize previous work by showing that for any graph, the max-product assignment satisfies a particular optimality condition with respect to any subgraph containing at most one cycle per connected component. We use this optimality condition to derive upper bounds on the difference between the log probability of the true MAP assignment, and the log probability of a max-product assignment. Finally, we consider extensions of the max-product algorithm that operate over higher-order cliques, and show how our reparameterization analysis extends in a natural manner.