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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.
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 ...
The mixture of experts, being similar to the gaussian mixture model, can also be trained by the expectation-maximization algorithm, just like gaussian mixture models. Specifically, during the expectation step, the "burden" for explaining each data point is assigned over the experts, and during the maximization step, the experts are trained to ...
Simulation of such complicated structures is often extremely computationally expensive to run, possibly taking upwards of hours per execution. The Nelder–Mead method requires, in the original variant, no more than two evaluations per iteration, except for the shrink operation described later, which is attractive compared to some other direct ...
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.