The well-known Baum-Eagon (1967) inequality provides an effective iterative scheme for homogeneous polynomials with positive coefficients over a domain of probability values /spl Delta/. The Baum-Eagon inequality was extended to rational functions over /spl Delta/ by Gopalakrishnan et. al. (see IEEE Trans. Inform. Theory, Jan. 1991) and a variant of this extended inequality was used by Merialdo (see Proc. ICASSP-88, 1988, and IEEE Trans. Acoust., Speech, Signal Processing, April 1994) for the maximum mutual information training of a connected digit recognizer. However, in many applications (e.g. corrective training) we are interested in maximizing an objective function over a domain D that is different from /spl Delta/ and may be defined by non-linear constraints. We show how to extend the basic inequality of Gopalakrishnan to (not necessary rational) functions that are defined on general manifolds. We describe an effective iterative scheme that is based on this inequality and its application to estimation problems via minimum information discrimination.
[1]
Dimitri Kanevsky,et al.
An inequality for rational functions with applications to some statistical estimation problems
,
1991,
IEEE Trans. Inf. Theory.
[2]
Renato De Mori,et al.
High-performance connected digit recognition using maximum mutual information estimation
,
1994,
IEEE Trans. Speech Audio Process..
[3]
L. Baum,et al.
An inequality with applications to statistical estimation for probabilistic functions of Markov processes and to a model for ecology
,
1967
.
[4]
I. Csiszár.
$I$-Divergence Geometry of Probability Distributions and Minimization Problems
,
1975
.
[5]
B. Merialdo.
Phonetic recognition using hidden Markov models and maximum mutual information training
,
1988,
ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.