Editing Expectation–maximization algorithm (section)

{{Short description|Iterative method for finding maximum likelihood estimates in statistical models}}
{{Machine learning}}

In [[statistics]], an '''expectation–maximization''' ('''EM''') '''algorithm''' is an [[iterative method]] to find (local) [[maximum likelihood]] or [[maximum a posteriori]] (MAP) estimates of [[parameter]]s in [[statistical model]]s, where the model depends on unobserved [[latent variable]]s.<ref>{{cite journal |last1=Meng |first1=X.-L. |last2=van Dyk |first2=D. |title=The EM algorithm – an old folk-song sung to a fast new tune |journal=J. Royal Statist. Soc. B |date=1997 |volume=59 |issue=3 |pages=511–567|doi=10.1111/1467-9868.00082 |s2cid=17461647 |doi-access=free }}</ref> The EM iteration alternates between performing an expectation (E) step, which creates a function for the expectation of the [[Likelihood function#Log-likelihood|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 [[Normal distribution|gaussians]], or to solve the multiple linear regression problem.<ref>Jeongyeol Kwon, Constantine Caramanis

''Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics'', PMLR 108:1727-1736, 2020.</ref>

[[File:EM Clustering of Old Faithful data.gif|right|frame|EM clustering of [[Old Faithful]] eruption data. The random initial model (which, due to the different scales of the axes, appears to be two very flat and wide ellipses) is fit to the observed data. In the first iterations, the model changes substantially, but then converges to the two modes of the [[geyser]]. Visualized using [[ELKI]].]]