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# Sequence of Experts Transforms for Lossless Dimensionality Reduction

What Presentation Oct 21, 2008 from 04:00 pm to 04:30 pm Seminarraum 183-2 Yll Haxhimusa yll@prip.tuwien.ac.at 18370 Andreas Tuerk vCal iCal
This talk develops the concept of a sequence of expert transforms
(SOET). Given a subset $X$ of a finite dimensional vector space and N
classes on X an SOET consists of a number of transforms T_1,...,T_S of X
and associated functions p_{T_s}(n,y)
for y\in T_s(X) which assign probabilities to the classes n=1,\ldots,N.
These class probability functions are used to build a sequence of
products of experts p_{T_1\times\ldots\times T_s}(n,x) , s=1,\ldots,S
which become increasingly better approximations to the posterior
probabilities of the classes p(n|x) given x\in X . It is shown that
special types of SOET's can be efficiently trained by minimising the
Kullback-Leibler distance between the class posteriors
p(n|x) and the products of experts p_{T_1\times\ldots\times
T_s}(n,x) with the help of a quasi-Newton algorithm.
In some cases the problem of minimising the Kullback-Leibler distance
is even convex and as a result the quasi-Newton algorithm converges to
the unique solution. In this talk SOET's are applied to
the tasks of classification and channel compression where it is shown
that the cost of transmission and the cost of encoding and decoding can
be substantially reduced without increasing the error rate. Since the
costs of transmission, encoding and decoding are intrinsically linked to
notions of dimensionality SOET's can therefore be seen to provide
lossless dimensionality reduction.