A generalized family of parameter estimation techniques

The extended Baum-Welch (EBW) transformations is one of a variety of techniques to estimate parameters of Gaussian mixture models. In this paper, we provide a theoretical framework for general parameter estimation and show the relationship between these different techniques. We introduce a general family of model parameter updates that generalizes a Baum-Welch (BW) recursive process to an arbitrary objective function of Gaussian Mixture Models, and show how other common parameter estimation techniques belong to this family of model update rules. Furthermore, we formulate the construction of an even more general family of update rules that has any specified value as a gradient steepness which belongs to the family of EBW gradient steepness, measuring how much an initial model is moved to an estimated updated model.