Journal ArticleDOI
Factor graphs and the sum-product algorithm
Reads0
Chats0
TLDR
A generic message-passing algorithm, the sum-product algorithm, that operates in a factor graph, that computes-either exactly or approximately-various marginal functions derived from the global function.Abstract:
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. Such a factorization can be visualized with a bipartite graph that we call a factor graph, In this tutorial paper, we present a generic message-passing algorithm, the sum-product algorithm, that operates in a factor graph. 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 digital communications can be derived as specific instances of the sum-product algorithm, including the forward/backward algorithm, the Viterbi algorithm, the iterative "turbo" decoding algorithm, Pearl's (1988) belief propagation algorithm for Bayesian networks, the Kalman filter, and certain fast Fourier transform (FFT) algorithms.read more
Citations
More filters
Pattern Recognition and Machine Learning
TL;DR: Probability distributions of linear models for regression and classification are given in this article, along with a discussion of combining models and combining models in the context of machine learning and classification.
Journal ArticleDOI
Network information flow
TL;DR: This work reveals that it is in general not optimal to regard the information to be multicast as a "fluid" which can simply be routed or replicated, and by employing coding at the nodes, which the work refers to as network coding, bandwidth can in general be saved.
Journal ArticleDOI
Clustering by Passing Messages Between Data Points
Brendan J. Frey,Delbert Dueck +1 more
TL;DR: A method called “affinity propagation,” which takes as input measures of similarity between pairs of data points, which found clusters with much lower error than other methods, and it did so in less than one-hundredth the amount of time.
Book
Graphical Models, Exponential Families, and Variational Inference
TL;DR: The variational approach provides a complementary alternative to Markov chain Monte Carlo as a general source of approximation methods for inference in large-scale statistical models.
Book
Prediction, learning, and games
Nicolò Cesa-Bianchi,Gábor Lugosi +1 more
TL;DR: In this paper, the authors provide a comprehensive treatment of the problem of predicting individual sequences using expert advice, a general framework within which many related problems can be cast and discussed, such as repeated game playing, adaptive data compression, sequential investment in the stock market, sequential pattern analysis, and several other problems.
References
More filters
Book
Computers and Intractability: A Guide to the Theory of NP-Completeness
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
Journal ArticleDOI
Learning representations by back-propagating errors
TL;DR: Back-propagation repeatedly adjusts the weights of the connections in the network so as to minimize a measure of the difference between the actual output vector of the net and the desired output vector, which helps to represent important features of the task domain.
Journal ArticleDOI
A tutorial on hidden Markov models and selected applications in speech recognition
TL;DR: In this paper, the authors provide an overview of the basic theory of hidden Markov models (HMMs) as originated by L.E. Baum and T. Petrie (1966) and give practical details on methods of implementation of the theory along with a description of selected applications of HMMs to distinct problems in speech recognition.
Book
Low-Density Parity-Check Codes
TL;DR: A simple but nonoptimum decoding scheme operating directly from the channel a posteriori probabilities is described and the probability of error using this decoder on a binary symmetric channel is shown to decrease at least exponentially with a root of the block length.