Description: Expectation Maximization (EM) is a fundamental statistical technique used to find maximum likelihood estimates of parameters in probabilistic models. This method is based on an iterative approach that alternates between two steps: the Expectation (E) step and the Maximization (M) step. In the E step, the expectation of the log-likelihood is computed given a dataset and the current parameters of the model. In the M step, the model parameters are updated to maximize this expectation. This process is repeated until convergence is reached, meaning that changes in the parameters are minimal. EM is particularly useful in situations where data is incomplete or where there are latent variables that are not directly observed. Its ability to handle uncertainty and incompleteness in data makes it a valuable tool across various disciplines, including statistics, machine learning, and artificial intelligence. Expectation Maximization allows researchers and analysts to obtain more accurate and robust estimates of model parameters, which in turn enhances the quality of inferences and predictions made from generative models.
History: The Expectation Maximization technique was first introduced in the 1970s, although its roots can be traced back to earlier work in statistics and probability theory. An important milestone in its development was the 1977 paper by Dempster, Laird, and Rubin, which formalized the EM algorithm and presented it as a tool for parameter estimation in statistical models with incomplete data. Since then, the algorithm has evolved and been adapted to various applications in fields such as biology, economics, and artificial intelligence.
Uses: Expectation Maximization is used in a variety of applications, including data analysis in situations with missing data, parameter estimation in mixture models, and learning generative models in artificial intelligence. It is also applied in signal processing, bioinformatics, and economics, where estimating parameters of complex models from incomplete or noisy data is required.
Examples: A practical example of Expectation Maximization is its use in pattern recognition, such as in Gaussian mixture models, where the distribution of data coming from multiple sources is estimated. Another example is in genetic data analysis, where EM models are used to infer population structure from incomplete genotype data.
