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The EM algorithm was explained and given its name in a classic 1977 paper by Arthur Dempster, Nan Laird, and Donald Rubin. [3] They pointed out that the method had been "proposed many times in special circumstances" by earlier authors. One of the earliest is the gene-counting method for estimating allele frequencies by Cedric Smith. [4]
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.
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 ...
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 ...
Several of these models correspond to well-known heuristic clustering methods. For example, k-means clustering is equivalent to estimation of the EII clustering model using the classification EM algorithm. [8] The Bayesian information criterion (BIC) can be used to choose the best clustering model as well as the number of clusters. It can also ...
To produce a project estimate the project manager: Decomposes the project into a list of estimable tasks, i.e. a work breakdown structure; Estimates the expected value E(task) and the standard deviation SD(task) of this estimate for each task time
where are the input samples and () is the kernel function (or Parzen window). is the only parameter in the algorithm and is called the bandwidth. This approach is known as kernel density estimation or the Parzen window technique. Once we have computed () from the equation above, we can find its local maxima using gradient ascent or some other optimization technique. The problem with this ...