# Factor graphs and the sum-product algorithm

@article{Kschischang2001FactorGA, title={Factor graphs and the sum-product algorithm}, author={Frank R. Kschischang and Brendan J. Frey and Hans-Andrea Loeliger}, journal={IEEE Trans. Inf. Theory}, year={2001}, volume={47}, pages={498-519} }

Algorithms that must deal with complicated global functions of many variables often exploit the manner in which the given functions factor as a product of "local" functions, each of which depends on a subset of the variables. [] Key Method Following a single, simple computational rule, the sum-product algorithm computes-either exactly or approximately-various marginal functions derived from the global function. A wide variety of algorithms developed in artificial intelligence, signal processing, and digitalâ€¦

## 4,785 Citations

### Convergence Analysis of Reweighted Sum-Product Algorithms

- Computer ScienceIEEE Transactions on Signal Processing
- 2008

This paper studies the convergence and stability properties of the family of reweighted sum-product algorithms, a generalization of the widely used sum-Product or belief propagation algorithm, in which messages are adjusted with graph-dependent weights.

### The Entropy Message Passing: A New Algorithm Over Factor Graphs

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It is shown how the EMP can be used for efficient computation of the model entropy and of the complex expressions which appear in the Expectation Maximization and the gradient descent algorithms.

### Discrete geometric analysis of message passing algorithm on graphs

- Mathematics, Computer ScienceArXiv
- 2010

The primary contribution of this thesis is the discovery of a formula that establishes the relation between the LBP, the Bethe free energy and the graph zeta function, and provides new techniques for analysis of the L BP algorithm.

### On the Xed Points of the Max-product Algorithm on the Xed Points of the Max-product Algorithm

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Here it is proved that the posterior probability of the max-product assignment is guaranteed to be greater than all other assignments in a particular large region around that assignment in any subset of nodes that form no more than a single loop in the graph.

### An Introduction to factor graphs - Signal Processing Magazine, IEEE

- Computer Science
- 2001

A unified perspective of probability propagation in Bayesian networks and artificial intelligence is given in terms of (Forney-style) factor graphs.

### Faster Algorithms for Max-Product Message-Passing

- Computer ScienceJ. Mach. Learn. Res.
- 2011

It is demonstrated that message-passing operations in graphical models with maximal cliques that are larger than their constituent factors are equivalent to some variant of matrix multiplication in the tropical semiring, for which an O(N2.5) expected-case solution is offered.

### A factor-graph approach to Lagrangian and Hamiltonian dynamics

- Computer Science2011 IEEE International Symposium on Information Theory Proceedings
- 2011

This paper aims at extending the field of possible applications of factor graphs to Lagrangian and Hamiltonian dynamics, and finds that duality results for factor graphs allow to easily derive Noether's theorem.

### The sum-product algorithm: algebraic independence and computational aspects

- Computer ScienceKybernetika
- 2013

This work shows that the variable sets involved in an acyclic factorization satisfy a relation that is a natural generalization of probability-theoretic independence, and shows that for the Boolean semiring the sum-product algorithm reduces to a classical algorithm of database theory.

### Message-Passing Algorithms for Inference and Optimization

- Computer Science
- 2011

The Divide and Concur algorithm is a projection-based constraint satisfaction algorithm that deals naturally with continuous variables, and converges to exact answers for problems where the solution sets of the constraints are convex.

### Double-edge factor graphs: Definition, properties, and examples

- Mathematics, Computer Science2017 IEEE Information Theory Workshop (ITW)
- 2017

This paper introduces a class of factor graphs, called double-edge factor graphs (DE-FGs), which allow local functions to be complex-valued and only require them, in some suitable sense, to be positive semi-definite kernel functions.

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