Factor graphs and the Sum-Product Algorithm

By Xiaowei Jin. 2002

1,781 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/8e617b8c63dd35d9913bbc104d0666ffd10e9e6a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Greedy Direction Method of Multiplier for MAP Inference of Large Output Domain (2017, methodology): “• Algorithm implemented in libDAI [32], including the Loopy Belief Propagation (LBP) [33], the Tree-Reweighted Belief Propagation (TRWBP) [15], the Tree Expectation Propagation (TreeEP)[34], the Double-loop GBP (HAK) [35], and Generalized Belief Propagation (GBP) [36].”
Bounded approximate decentralised coordination via the max-sum algorithm (2009, methodology): “A promising direction is to iterative ly apply our algorithm while clustering variable and function nodes (as proposed in [17] ) to remove cycles without removing dependencies.”
Layered segmentation and optical flow estimation over time (2012, methodology): “Discrete optimization techniques, such as belief propagation [15] and graph cuts [4, 14], have been used in singlelayer robust optical flow formulations [17, 24].”
An Approximate, Efficient LP Solver for LP Rounding (2013, background): “In this result, E(·) denotes expectation over all the random variables i(j) indicating the update indices chosen at each iteration.”
An Introduction to Conditional Random Fields for Relational Learning (2007, methodology): “Graphically, we represent the factorization (1.1) by a factor graph [Kschischang et al., 2001].”
Inference of direct residue contacts in two-component signaling. (2010, methodology): “…inference algorithm in the second section is given in detail in Weigt et al. (2009) and based on standard Belief Propagation methods described in Kschischang et al. (2001), Mezard and Mora (2009), and Yedidia et al. (2001), we will dispense with the derivation and describe only implementation…”
Compressive Sensing-Based Adaptive Active User Detection and Channel Estimation: Massive Access Meets Massive MIMO (2019, methodology): “The factorization in (15) can be represented by a bipartite graph, which consists of variable nodes, factor nodes, and the corresponding edges [38].”
Coded Slotted ALOHA: A Graph-Based Method for Uncoordinated Multiple Access (2014, methodology): “This connection was exploited in [16] to de sign via density evolution [18] IRSA configurations with remarkably high peak throughput va lues, and in [17] to interpret the original ZigZag algorithm as an instance of the sum-prod uct algorithm on factor graphs [19] and, consequently, to develop a soft”
Towards Robust Skill Generalization: Unifying Learning from Demonstration and Motion Planning (2017, background): “Any probability distribution P can be represented as a product of functions organized as a bipartite factor graph [24] G = {Θ,F , E}, P (Θ) ∝ ∏”
Channel Estimation for OFDM (2014, methodology): “Although the Forney style has several advantages [115] compared to the original ones in [22], we will use the”
Accelerated training of max-margin Markov networks with kernels (2011, methodology): “In ExpGrad, the dual variables α correspond to a factorized distribution, and in each iteration its potential functions on the cliques are updated using the exponentiated gradient rule.”
Decoding Algorithms for Nonbinary LDPC Codes Over GF$(q)$ (2007, methodology): “3 Extended Min-Sum Algorithm in the Logarithm Domain (EMS) In this section, we present a reduced complexity decoding algorithm for LDPC codes over GF(q), based on a generalization of the MS algorithm used for binary LDPC codes [11, 14, 16, 18, 26].”
Iterative multiuser joint decoding: unified framework and asymptotic analysis (2001, methodology): “Black circles denote state variablesand the squares denote the trellis transition functions(see [22]).”