EMderived

EMderived is a term used in statistics and data analysis to describe quantities, estimates, or models that are derived from the Expectation-Maximization (EM) algorithm. The EM algorithm is an iterative framework for maximum likelihood estimation in models with latent variables or incomplete data. In an EM-derived result, the parameters are obtained by alternating between an E-step, which computes the expected value of missing or latent data given current parameters, and an M-step, which maximizes the complete-data likelihood with respect to the parameters.

Common settings include Gaussian mixture models, factor analysis with missing data, and hidden Markov models; EM-derived estimates are widely used because they can handle missing information without direct observation of latent variables. Convergence is reached when the change in parameter values or the observed-data log-likelihood falls below a threshold. However, EM-derived estimates may converge to local maxima, and their quality can depend on initialization, model specification, and stopping criteria. In some cases, acceleration or alternative convergence checks are used to improve performance.

Extensions and related methods include Monte Carlo EM, variational EM, and online or stochastic EM, which adapt the E or M steps for large data sets or intractable expectations. The term EM-derived is often used to contrast results with those obtained by direct optimization of the observed-data likelihood or by other inference approaches such as Bayesian methods. The concept emerged from the widespread adoption of the EM algorithm after its introduction by Dempster, Laird, and Rubin in 1977.