Die Erwartungs-Maximierungs-Methode (EM) Algorithmus is a powerful statistical technique used primarily for Parameterschätzung 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-Schätzung herausfordernde Aufgaben verwendet wird.
Der EM-Algorithmus besteht aus zwei Hauptschritten, die iterativ angewendet werden:
- Erwartungsschritt (E-Schritt): In this step, the algorithm computes the Erwartungswert 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.
- Maximierungsschritt (M-Schritt): 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 versteckten Markov-Modelle.
Einer der wichtigsten Vorteile des EM-Algorithmus ist seine Fähigkeit, mit unvollständigen Daten konfrontiert wird effectively, making it a go-to choice for many researchers and practitioners dealing with real-world datasets where missing information is common.