期待値最大化法（EM） アルゴリズム is a powerful statistical technique used primarily for パラメータ推定 in models that involve latent (hidden) variables. It is particularly useful in situations where the data is incomplete or has missing values, making direct 最尤推定 挑戦的です。
EMアルゴリズムは、主に2つのステップから構成され、それらを反復的に適用します。
- 期待値ステップ（Eステップ）： In this step, the algorithm computes the 期待値 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.
- 最大化ステップ（Mステップ）： 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 隠れマルコフモデル.
EMアルゴリズムの主な利点の一つは、 不完全なデータ effectively, making it a go-to choice for many researchers and practitioners dealing with real-world datasets where missing information is common.