Из серии Foundations and Trends in Signal Processing издательства
NOWPress, 2011, -76 pp.
Про алгоритм максимума правдоподобия (expectation maximization) – описание, тренинг, приложения
This introduction to the expectation–maximization (EM) algorithm provides an intuitive and mathematically rigorous understanding of EM. Two of the most popular applications of EM are described in detail: estimating Gaussian mixture models (GMMs), and estimating hidden Markov models (HMMs). EM solutions are also derived for leaing an optimal mixture of fixed models, for estimating the parameters of a compound Dirichlet distribution, and for dis-entangling superimposed signals. Practical issues that arise in the use of EM are discussed, as well as variants of the algorithm that help deal with these challenges.
The Expectation-Maximization Method.
The EM Algorithm.
Contrasting EM with a Simple Variant.
Using a Prior with EM (MAP EM).
Specifying the Complete Data.
A Toy Example.
Analysis of EM.
Convergence.
Maximization–Maximization.
Leaing Mixtures.
Leaing an Optimal Mixture of Fixed Models.
Leaing a GMM.
Estimating a Constrained GMM.
More EM Examples.
Leaing a Hidden Markov Model.
Estimating Multiple Transmitter Locations.
Estimating a Compound Dirichlet Distribution.
EM Variants.
EM May Not Find the Global Optimum.
EM May Not Simplify the Computation.
Speed.
When Maximizing the Likelihood Is Not the Goal.
Conclusions and Some Historical Notes.
Про алгоритм максимума правдоподобия (expectation maximization) – описание, тренинг, приложения
This introduction to the expectation–maximization (EM) algorithm provides an intuitive and mathematically rigorous understanding of EM. Two of the most popular applications of EM are described in detail: estimating Gaussian mixture models (GMMs), and estimating hidden Markov models (HMMs). EM solutions are also derived for leaing an optimal mixture of fixed models, for estimating the parameters of a compound Dirichlet distribution, and for dis-entangling superimposed signals. Practical issues that arise in the use of EM are discussed, as well as variants of the algorithm that help deal with these challenges.
The Expectation-Maximization Method.
The EM Algorithm.
Contrasting EM with a Simple Variant.
Using a Prior with EM (MAP EM).
Specifying the Complete Data.
A Toy Example.
Analysis of EM.
Convergence.
Maximization–Maximization.
Leaing Mixtures.
Leaing an Optimal Mixture of Fixed Models.
Leaing a GMM.
Estimating a Constrained GMM.
More EM Examples.
Leaing a Hidden Markov Model.
Estimating Multiple Transmitter Locations.
Estimating a Compound Dirichlet Distribution.
EM Variants.
EM May Not Find the Global Optimum.
EM May Not Simplify the Computation.
Speed.
When Maximizing the Likelihood Is Not the Goal.
Conclusions and Some Historical Notes.