Expectation-Maximization Algorithm for Parameter Estimation
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The Expectation-Maximization (EM) algorithm is an iterative method used to estimate the parameters of statistical models that involve latent (unobserved) variables, such as missing data or hidden cluster assignments. It is especially useful for fitting Gaussian Mixture Models (GMMs), where the goal is to model data as a mixture of several Gaussian distributions.
How the EM Algorithm Works
The EM algorithm alternates between two steps:
- Expectation Step (E-step): Given the current parameter estimates (means, covariances, and mixing coefficients for GMMs), the algorithm computes the probability (or "responsibility") that each data point belongs to each Gaussian component. This step essentially fills in the missing information about which cluster