EM Algorithm
The EM algorithm is a generic framework that can be employed in the optimization of many generative models. It was originally proposed in Dempster A. P., Laird N. M., Rubin D. B., Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society, B, 39(1):1–38, 11/1977, where the authors also proved its convergence at different levels of genericity. Many machine learning problems have the objective of finding a flexible way to express the data-generating process behind datasets. For example, given a set of pictures representing faces , we are generally interested in discovering at least an approximation of the distribution pdata from where the training sample has been drawn.
The reason is obvious: we can never work with all possible data points and, moreover, a synthetic expression (for example, a neural network or a mixture of distributions) allows us to draw new samples or to evaluate the likelihood of other datasets.
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