Training HMMs in GMTK

The Graphical Models ToolKit (GMTK) is a powerful and flexible prototyping language for designing dynamic Bayesian networks (DBNs). This tutorial is meant to help new users’ understanding of GMTK by presenting hidden Markov models (HMMs) which make use of some of the software’s large number of features. Generative and discriminative training approaches supported in GMTK are discussed with relevant examples, as well as testing using an HMM for a simple classification task. All described models and scripts are available in the tarball housing this document. The following examples are intended for those interested in using the Graphical Models ToolKit (GMTK) to perform various forms of inference/learning utilizing graphical models. Using GMTK, we will first train and test a hidden Markov model (HMM) whose emission states are discrete (Section 1), then train and test one whose emission states are real valued (conditionally Gaussian) (Section 2). Also discussed are generative and discriminative training approaches supported in GMTK. 1 Classifying the weather: discrete observations Consider the scenario wherein the area you work/reside only encounters three types of weather: sunny, rainy, and foggy. Assume that you go to work in an office everyday, and during your working hours you do not get to see nor experience a given days weather (you’re office also has no windows looking outside; this was my office in Hawaii ironically enough). Curiosity mounts as time goes on and you become more and more curious about what the daily weather is. Your hope lies in that you have an office mate who comes in hours later than you, and this office mate brings in an umbrella some days, and no umbrella all other days. In the framework of the HMM, the hidden layer is the state of the weather (indeed, it is hidden from you). The observed layer consists of the daily observations of weather your office mate has brought