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Gibbs Sampling for the Uninitiated
In: DTIC (2010)
Abstract: This document is intended for computer scientists who would like to try out a Markov Chain Monte Carlo (MCMC) technique, particularly to do inference with Bayesian models on problems related to text processing. We try to keep theory to the absolute minimum needed, though we work through the details much more explicitly than you usually see even in "introductory" explanations. That means we've attempted to be ridiculously explicit in our exposition and notation. After providing the reasons and reasoning behind Gibbs sampling (and at least nodding our heads in the direction of theory), we work through an example application in detail -- the derivation of a Gibbs sampler for a Naive Bayes model. Along with the example, we discuss some practical implementation issues, including the integrating out of continuous parameters when possible. We conclude with some pointers to literature that we've found to be somewhat more friendly to uninitiated readers. ; Sponsored in part by the GALE program of the Defense Advanced Research Projects Agency (DARPA), the National Science Foundation (NSF), and the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), through the Army Research Laboratory. LAMP-TR-153.
Keyword: *BAYES THEOREM; *GIBBS SAMPLING; *MARKOV CHAIN MONTE CARLO; *MARKOV PROCESSES; *MONTE CARLO METHOD; *NAIVE BAYES MODEL; *NATURAL LANGUAGE; *SAMPLING; *STATISTICAL INFERENCE; *TEXT PROCESSING; ALGORITHMS; AUTOCORRELATION; BETA DISTRIBUTION; COMPUTATIONAL LINGUISTICS; CONVERGENCE; DIRICHLET DISTRIBUTION; DISTRIBUTION; DOCUMENT LABELS; DOCUMENTS; EXPECTED VALUES; INITIALIZATION; INTEGRALS; JOINT DISTRIBUTION; LABELS; Linguistics; MAP(MAXIMUM A POSTERIORI ESTIMATION); MAXIMUM LIKELIHOOD ESTIMATION; MCMC(MARKOV CHAIN MONTE CARLO); Numerical Mathematics; PARAMETER ESTIMATION; PARAMETERS; POSTERIOR PROBABILITIES; PROBABILITY ESTIMATION; STATE SPACE; Statistics and Probability; VALUE
URL: http://www.dtic.mil/docs/citations/ADA523027
http://oai.dtic.mil/oai/oai?&verb=getRecord&metadataPrefix=html&identifier=ADA523027
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