Gradient steepness metrics using extended Baum-Welch transformations for universal pattern recognition tasks

In many pattern recognition tasks, given some input data and a family of models, the "best" model is defined as the one which maximizes the likelihood of the data given the model. Extended Baum- Welch (EBW) transformations are most commonly used as a discriminative technique for estimating parameters of Gaussian mixtures. In this paper, we use the EBW transformations to derive a novel gradient steepness measurement to find which model best explains the data. We use this gradient measurement to derive a variety of EBW metrics to explain model fit to the data. We apply these EBW metrics to audio segmentation via Hidden Markov Models (HMMs) and show that our gradient steepness measurement is robust across different EBW metrics and model complexities.