The Baum-Welch algorithm with limiting distribution constraints.

We present a method of incorporating limiting distribution information in the Baum–Welch algorithm for estimating parameters of discrete-time, finite-state, Hidden Markov Models. We find that having, even imperfect, limiting distribution information can dramatically improve transition probability estimates. Additionally, we find that when (1) the underlying process is weakly correlated with the observable signal, and (2) the length of the data sequence is short, the additional information provided by the limiting distribution is substantial.