Convergence analysis of the acyclic hypercubic HMM Baum-Welch algorithm

The Baum–Welch algorithm has been widely used in predicting evolutionary processes ranging from genetic to biological changes, including the evolution of drug resistance. Due to its importance, the convergence of the algorithm ensures accurate predictions. This study analytically investigates the boundedness of the forward and backward algorithms and the convergence of the acyclic hypercubic HMM Baum–Welch algorithm using relevant definitions, theorems, and the Frobenius norm. To demonstrate this, numerical iterations were performed on specific examples of drug resistance fitted to the acyclic hypercubic model to examine convergence properties. The results reveal that the convergence rate is inversely proportional to the size of the hypercube. • Analyse convergence of the Baum-Welch algorithm on acyclic hypercubes. • Apply mathematical rigour using definition, lemmas, and key theorems. • Validate convergence through synthetic data simulations. • Identify the link between convergence rate and hypercube dimension.