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Expectation conditional maximization (ECM) replaces each M step with a sequence of conditional maximization (CM) steps in which each parameter θ i is maximized individually, conditionally on the other parameters remaining fixed. [34] Itself can be extended into the Expectation conditional maximization either (ECME) algorithm. [35]
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.
An intuitive explanation of the algorithm from "Numerical Recipes": [5] The downhill simplex method now takes a series of steps, most steps just moving the point of the simplex where the function is largest (“highest point”) through the opposite face of the simplex to a lower point.
Some kind of expectation-maximization algorithm is used in the estimation of the parameters of Rasch models. Algorithms for implementing Maximum Likelihood estimation commonly employ Newton–Raphson iterations to solve for solution equations obtained from setting the partial derivatives of the log-likelihood functions equal to 0. Convergence ...
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 ...
This training algorithm is an instance of the more general expectation–maximization algorithm (EM): the prediction step inside the loop is the E-step of EM, while the re-training of naive Bayes is the M-step.
The general algorithm involves message passing and is substantially similar to the belief propagation algorithm (which is the generalization of the forward-backward algorithm). With an algorithm called iterative Viterbi decoding , one can find the subsequence of an observation that matches best (on average) to a given hidden Markov model.
Iterative methods include maximum a posteriori estimation and expectation-maximization algorithms. A good estimate of the PSF is helpful for quicker convergence but not necessary. Examples of non-iterative techniques include SeDDaRA, [3] the cepstrum transform and APEX. The cepstrum transform and APEX methods assume that the PSF has a specific ...