Factor graphs and the sum-product algorithm

By Frank R. Kschischang, Brendan J. Frey, Hans-Andrea Loeliger. 2001

5,682 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computer Networks and Communications

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Citations in the corpus

SNAS: Stochastic Neural Architecture Search (2018, methodology): “f the global cost, consistent with the credit assignment principle in SNAS. In SNAS, p (Z) is fully factorizable, making it possible to calculate E Z˘p [C(Z)] analytically with sum-product algorithm (Kschischang et al., 2001). Unfortunately, this expectation is non-trivial to calculate, we optimize ”
Deep Learning for Distributed Optimization: Applications to Wireless Resource Management (2019, methodology): “Moreover, distributed optimization techniques, such as the dual decomposition, the alternating direction method of multipliers (ADMM) [4], and the message-passing (MP) algorithm [5], are suitable only for separable objective and constraint functions, and the exchange of continuous-valued messages.”
Identification of direct residue contacts in protein–protein interaction by message passing (2009, methodology): “ since this itself is a very difficult global optimization problem (as exemplified by the notorious “spin-glass” problem (16)). This challenge is dealt with here by applying a messagepassing approach (17, 18). In recent years, insights from spin-glass physics have led to the development of generaliz”
Expectation Propagation for approximate Bayesian inference (2001, background): “In fact, it is the form used in in factor graphs (Kschischang et al., 2000).”
Structural-RNN: Deep Learning on Spatio-Temporal Graphs (2015, background): “Such interactions are commonly parameterized with a factor graph that conveys how a (complicated) function over the st-graph factorizes into simpler functions [35].”
Past, Present, and Future of Simultaneous Localization and Mapping: Toward the Robust-Perception Age (2016, positive): “a maximum a posteriori estimation problem, and often use the formalism of factor graphs [143] to reason about the interde-”
Inductive biases for deep learning of higher-level cognition (2020, background): “Any joint distribution can be expressed as a factor graph (Kschischang et al., 2001; Frey, 2012; Kok and Domingos, 2005), but we claim that the ones which can be conveniently described with natural language have the property that they should be sparse.”
Spatially coupled ensembles universally achieve capacity under belief propagation (2012, methodology): “This line of research was formalized by Kschischang, Frey, and Loeliger who introduced the notion of factor graphs [39].”
Belief Propagation, Dykstra's Algorithm, and Iterated Information Projections (2010, methodology): “From the factored likelihood function, we may sketch a factor graph [2] as in Fig.”
High-throughput LDPC decoders (2003, background): “An LDPC code is a linear block code defined by a sparse parity-check matrix and is described by a bipartite or factor graph [20] (see Fig.”
Efficient Inference in Large Conditional Random Fields (2006, methodology): “We describe its application to BP in factor graphs [5], a convenient representation when there are cliques over more than three nodes.”
Low-density parity-check codes based on finite geometries: A rediscovery and new results (2001, methodology): “A detail exposition of the SPA can be found in [10], [17]–[20], [33].”
Multi-source Deep Learning for Human Pose Estimation (2014, background): “φj(t) can be considered as a factor that explains t in factor graph [4, 23].”
Rate-adaptive codes for distributed source coding (2006, background): “However, the performance of the high compression codes so derived is very poor because their graphs contain unconnected or singly-connected source nodes; these structural features impede the transfer of information via the LDPC iterative decoding algorithm [20] [21].”
Bit-Interleaved Coded Modulation (2008, methodology): “The BP general computation rules are given as follows [62].”
Optical flow modeling and computation: A survey (2015, background): “Belief propagation is based on the max-product algorithm, which is able to ﬁnd the MAP of a probability distribution expressed as a product of factors, and thus representable in a factor graph (see [157] for a detailed introduction).”
A Fully-Connected Layered Model of Foreground and Background Flow (2013, background): “Graph cuts (GC) [4] and belief propagation (BP) [17] are popular optimizers for Ising/Potts models and can find better local optima than local search methods [28].”