Inequalities for Differentiable Functions with Application to Some Statistical Problems

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 prove that a set of invariant points for EB transformation coincides with a set of critical points of the objective function. And finally we derive new transformation formulae for estimating the parameters of Gaussian mixtures generalizing the EB algorithm, and run simulation experiments comparing different growth transformations.

By: Dimitri Kanevsky

Published in: RC23055 in 2004


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