A. Dempster, N. Laird, and D. Rubin. Maximum likelihood estimation from incomplete data via the em algorithm (with discussion). Royal Statistical Soc. B, 39:1-- 38, 1977. Home/Search Document Not in Database Summary Related Articles Check |
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....in (14) Note that the left side (17) of the alternation is a nonconvex, complex and di#cult to optimize prior. Note also that the hyperparameter estimation (18) is a mixture decomposition problem for which the well understood and e#cient EM (Expectation Maximization) algorithm is available [6] [7] 5] for optimization. In Sec. IV A directly below, we give a brief overview of the EM mixture algorithm. In this section, we address these optimization issues. We will do this by transforming the objectives in (17) and (18) and by using a grouped coordinate descent algorithm on (18) and a ....
A. P. Dempster, N. M. Laird, and D. B. Rubin, "Maximum Likelihood Estimation from Incomplete Data via the EM Algorithm," J. Royal Statist. Soc. B, vol. 39, pp. 1--38, 1977.
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....with the Baum Welch algorithm, the process may converge to a local maximum. References . Hidden Markov models were originally invented and are commonly used for speech recognition. For additional material on this subject, see [9] For a more comprehensive overview on the EM technique, see [1]. For a detailed discussion about the adaptation of HMMs to computational biology algorithms see [4] chapters 3 6) Applications of profile HMMs for multiple alignment of proteins can be found in [5] and for finding genes in the DNA can be found in [7, 6] ....
N. M. Laird A. P. Dempster and D. B. Rubin. Maximum likelihood estimation from incomplete data. Journal of the Royal Statistics Society, 39:1--38, 1977.
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....doing, we will be able to guarantee that we recover feasible solutions to the original constrained optimization problem, by Theorem 1. 4. 1 Derivation of the EM IS iterative algorithm Recall that a log linear model is determined by its parameter vector # (6) Therefore to derive the EM algorithm [21] one typically decomposes the log likelihood L(#) as a function of # into p(y) log p # (y) Q(#, # # ) H(#, # # ) for all # # (15) where Q(#, # # ) p # # (z y) log p # (x) dz) 16) and H(#, # # ) p # # (z y) log p # (z y) dz) 17) Here x = y, z) Q(#, # # ) is the ....
.... Q(#, # ) as a function of #, followed by a maximization step M, which finds # = # to maximize Q(#, # ) Each iteration of EM monotonically non decreases L(#) and very generally, if EM converges to a fixed point # # , then # # is a stationary point of L(#) which is usually a local maximum [21, 43]. For log linear models in particular, we have p # (j) z y) log p # (x) dz) 18) p # (j) z y) by plugging the log linear form (6) into (18) and recalling that x = y, z) Crucially, it turns out that maximizing Q(#, # (the M step) is equivalent ....
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A. Dempster, N. Laird and D. Rubin, "Maximum likelihood estimation from incomplete data via the EM algorithm," Journal of Royal Statistical Society, Series B, Vol. 39, pp 1-38, 1977
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A. Dempster, N. Laird, and D. Rubin. Maximum likelihood estimation from incomplete data via the em algorithm (with discussion). Royal Statistical Soc. B, 39:1-- 38, 1977.
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Dempster, A. P., Laird, N. M. and Rubin, D. B. (1977). Maximum likelihood estimation from incomplete data via the EM algorithm (with discussion). Journal of the Royal Statistical Society B, 39, 1--38.
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Dempster, A.P., Laird, N., and Rubin, D.B., Maximum likelihood estimation from incomplete data using the EM algorithm (with discussion), J. Roy. Statist. Soc., Series B, 39:1--38, 1976.
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A. Dempster, N. Laird, and D.Rubin. Maximum likelihood estimation from incomplete data via the EM algorithm. J. Royal Statistical Soc. B, 39:1--38, 1977.
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