Global convergence of the EM algorithm for unconstrained latent variable models with categorical indicators

Area of Science:

• Statistics
• Machine Learning
• Information Theory

Background:

• The expectation-maximization (EM) algorithm is widely used for parameter estimation in latent variable models.
• Ensuring convergence to a global optimum is crucial for reliable model fitting.
• Latent variable models with categorical indicators present unique challenges for optimization.

Purpose of the Study:

• To present sufficient conditions for the global convergence of the EM algorithm.
• To interpret the EM algorithm within an information-theoretic framework.
• To establish an optimal bound for unconstrained latent class models.

Main Methods:

• Interpreting the EM algorithm as alternating minimization of Kullback-Leibler divergence between convex sets.
• Analyzing convergence properties in an information-theoretic context.
• Applying the conditions to unconstrained latent class models.

Main Results:

• Sufficient conditions for global convergence of the EM algorithm are provided.
• The EM algorithm is shown to be equivalent to minimizing Kullback-Leibler divergence.
• Unconstrained latent class models satisfy these convergence conditions.

Conclusions:

• The study establishes theoretical guarantees for the EM algorithm's convergence in specific latent variable models.
• This work provides a benchmark for evaluating more constrained latent variable models.
• The information-theoretic interpretation offers new insights into EM algorithm optimization.