Expectation–maximization algorithm

Machine learning and data mining
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In statistics, an expectation–maximization (EM) algorithm is an iterative method to find (local) maximum likelihood or maximum a posteriori (MAP) estimates of parameters in statistical models, where the model depends on unobserved latent variables.^[1] The EM iteration alternates between performing an expectation (E) step, which creates a function for the expectation of the log-likelihood evaluated using the current estimate for the parameters, and a maximization (M) step, which computes parameters maximizing the expected log-likelihood found on the E step. These parameter-estimates are then used to determine the distribution of the latent variables in the next E step. It can be used, for example, to estimate a mixture of gaussians, or to solve the multiple linear regression problem.^[2]

^ Meng, X.-L.; van Dyk, D. (1997). "The EM algorithm – an old folk-song sung to a fast new tune". J. Royal Statist. Soc. B. 59 (3): 511–567. doi:10.1111/1467-9868.00082. S2CID 17461647.
^ Jeongyeol Kwon, Constantine Caramanis Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:1727-1736, 2020.