Expectation-Maximization (EM) is a widely used algorithm in machine learning and statistics, particularly for problems involving latent or hidden variables. It is an iterative method employed to find maximum likelihood estimates or maximum a posteriori estimates in the presence of missing or unobserved data. EM is particularly useful when the data is incomplete or when certain variables are not directly observable.
The EM algorithm consists of two main steps: the E-step (Expectation step) and the M-step (Maximization step). In the E-step, the algorithm calculates the expected value of the log-likelihood function with respect to the current estimates of the latent variables. It computes the probability distribution over the hidden variables given the observed data and current parameter estimates. This step provides a way to handle the uncertainty associated with unobserved data. A part from it by obtaining a Machine Learning Course, you can advance your career in Machine Learning. With this course, you can demonstrate your expertise in designing and implementing a model building, creating AI and machine learning solutions, performing feature engineering, many more fundamental concepts, and many more critical concepts among others.
After the E-step, in the M-step, the algorithm updates the model parameters to maximize the expected log-likelihood computed in the previous step. The M-step essentially involves finding the values of the parameters that make the model fit the observed data as closely as possible while taking into account the missing data through the expected values from the E-step.
The algorithm then iterates between the E-step and M-step until convergence, where the log-likelihood maximization reaches a satisfactory level or the parameters stabilize. At this point, the EM algorithm has found the maximum likelihood estimates of the model parameters.
EM is commonly used in various machine learning applications, such as clustering, mixture models, and Gaussian mixture models (GMMs). For example, in clustering problems, EM can help identify underlying clusters and estimate their corresponding parameters. EM has also found applications in natural language processing, computer vision, and many other fields where dealing with missing or latent variables is essential for accurate modeling and inference.
Although EM is a powerful and widely used algorithm, it has its limitations, such as sensitivity to initialization and the possibility of converging to local optima. Therefore, researchers often combine EM with other optimization techniques or use it as a building block for more complex algorithms to overcome these limitations. Nonetheless, EM remains a fundamental tool in the arsenal of machine learning and statistical modeling, providing valuable solutions to a wide range of real-world problems.
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