The Expectation-Maximization (EM) Algorithm is a powerful statistical technique used primarily for parameter estimation in models that involve latent (hidden) variables. It is particularly useful in situations where the data is incomplete or has missing values, making direct maximum likelihood estimation challenging.
The EM algorithm consists of two main steps that are iteratively applied:
- Expectation Step (E-step): In this step, the algorithm computes the expected value of the log-likelihood function, considering the current estimate of the parameters and the latent variables. Essentially, it uses the known data to estimate the missing data based on the current model parameters.
- Maximization Step (M-step): After the E-step, this step updates the model parameters by maximizing the expected log-likelihood found in the E-step. The new parameters are then used in the next iteration.
This iterative process continues until convergence, which typically means that the change in the estimated parameters falls below a pre-defined threshold. The EM algorithm is widely applicable in various fields, such as machine learning, computer vision, and bioinformatics, particularly for clustering tasks (e.g., Gaussian Mixture Models) and in training hidden Markov models.
One of the key advantages of the EM algorithm is its ability to handle incomplete data effectively, making it a go-to choice for many researchers and practitioners dealing with real-world datasets where missing information is common.