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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.
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 ...
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.
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 Library of Efficient Data types and Algorithms (LEDA) is a proprietarily-licensed software library providing C++ implementations of a broad variety of algorithms for graph theory and computational geometry. [1] It was originally developed by the Max Planck Institute for Informatics Saarbrücken. [2]
The problem to be solved is to use the observations {r(t)} to create a good estimate of {x(t)}. Maximum likelihood sequence estimation is formally the application of maximum likelihood to this problem. That is, the estimate of {x(t)} is defined to be a sequence of values which maximize the functional = (),
Sieve estimators have been used extensively for estimating density functions in high-dimensional spaces such as in Positron emission tomography (PET). The first exploitation of Sieves in PET for solving the maximum-likelihood image reconstruction problem was by Donald Snyder and Michael Miller, [1] where they stabilized the time-of-flight PET problem originally solved by Shepp and Vardi. [2]