Luttrell S P, October 1989, The Gibbs Machine applied to hidden Markov model problems. Part 1: Basic theory, RSRE technical report (Malvern, UK), SP4/99
I show how a hidden Markov model can be expressed as a Gibbs distribution. I review my Gibbs distribution training algorithm (a 'Gibbs Machine' rather than a 'Boltzmann Machine'), which I use to perform gradient ascent on the relative entropy between the Gibbs distribution and the data distribution. I demonstrate how this reduces to elementary matrix computations of exactly the same form as encountered in the Baum-Welch re-estimation method. Although this toy problem is amenable to Baum-Welch re-estimation, the same cannot be said of non-tree-like Markov models. In such cases I propose that a hybrid Baum-Welch/Gibbs Machine optimisation scheme should be used.