Extended Baum Transformations for General Functions

The discrimination technique for estimating the parameters of Gaussian mixtures that is based on the Extended Baum transformations (EB) has had significant impact on the speech recognition community. There appear to be no published proofs that definitively show that these transformations increase the value of an objective function with iteration (i.e., so-called ”growth transformations”). The proof presented in the current paper is based on the linearization process and the explicit growth estimate for linear forms of Gaussian mixtures. We also derive new transformation formulae for estimating the parameters of Gaussian mixtures generalizing the EB algorithm, and run simulation experiments comparing different growth transformations.