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In statistics, an expectation–maximization (EM) algorithm is an iterative method to find (local) maximum likelihood or maximum a posteriori (MAP) estimates of parameters in statistical models, where the model depends on unobserved latent variables. [1]
The EM algorithm consists of two steps: the E-step and the M-step. Firstly, the model parameters and the () can be randomly initialized. In the E-step, the algorithm tries to guess the value of () based on the parameters, while in the M-step, the algorithm updates the value of the model parameters based on the guess of () of the E-step.
The expectation–maximization algorithm can be treated as a special case of the MM algorithm. [1] [2] However, in the EM algorithm conditional expectations are usually involved, while in the MM algorithm convexity and inequalities are the main focus, and it is easier to understand and apply in most cases. [3]
For a certain class of clustering algorithms (in particular k-means, k-medoids and expectation–maximization algorithm), there is a parameter commonly referred to as k that specifies the number of clusters to detect.
In electrical engineering, statistical computing and bioinformatics, the Baum–Welch algorithm is a special case of the expectation–maximization algorithm used to find the unknown parameters of a hidden Markov model (HMM). It makes use of the forward-backward algorithm to compute the statistics for the expectation step. The Baum–Welch ...
The algorithm uses several types of well known functions: Expectation maximization (EM). EM based heuristic for choosing the EM starting point. Maximum likelihood ratio based (LRT-based) heuristic for determining the best number of model-free parameters. Multi-start for searching over possible motif widths. Greedy search for finding multiple ...
This naturally suggests an iterative algorithm, much like EM (the expectation–maximization algorithm), in which the expectations (and possibly higher moments) of the latent variables are initialized in some fashion (perhaps randomly), and then the parameters of each distribution are computed in turn using the current values of the ...
Direct maximization of the likelihood (or of the posterior probability) is often complex given unobserved variables. A classical approach to this problem is the expectation-maximization algorithm , which alternates computing expected values of the unobserved variables conditional on observed data, with maximizing the complete likelihood (or ...