Piecewise Aggregation for HMM Fitting: A Pre-Fitting Model for Seamless Integration with Time-Series Data

Abstract

We propose a simple, fast, deterministic pre-fitting approach which derives the Baum–Welch algorithm initial values directly from the input data. Such pre-fitting has the purpose of improving the fitting time for a given Hidden Markov Model (HMM) while maintaining the original Baum–Welch algorithm as the fitting one. The fitting time is improved by avoiding the Baum–Welch algorithm sensitiveness through the generation of parameters closer to the global maximum likelihood. Furthermore, by keeping the original Baum–Welch algorithm as the fitting one, we guarantee that all related methods will continue to work properly. On the other hand, the pre-fitting generates the HMM parameters directly derived from time-series data, without any data transformation, using an [Formula: see text] operation.