HyperISM: A data-driven model for parameter estimation of hypercubic Markov models

Markov Models are widely used in speech recognition, bioinformatics, finance and natural language processing. This work introduces HyperISM (Hypercubic Intermediate States Model), a novel data-driven model for parameter estimation in Markov chains defined on hypercubic acyclic graphs. Given observed vertices of the hypercube, HyperISM constructs a minimal state space by introducing fractional intermediate states only where needed to maintain connectivity, significantly reducing the number of states compared to traditional full hypercube approaches. We evaluate HyperISM against two baseline models on hypercubes of dimensions 3, 7 and 10 using the Baum–Welch algorithm. Experimental results demonstrate that HyperISM achieves comparable accuracy while substantially reducing execution time, number of states and iteration count, with efficiency gains becoming more pronounced for higher-dimensional hypercubes and larger datasets. HyperISM can broadly be applicable to evolutionary dynamics, disease progression modelling and other domains involving sequential state transitions.