Seminar Series Topics in Systems

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Seminar SeriesTopics in Systems
The Generalized Distributive Law The
distributive law states that if a,b,c are
elements of a semirring, abaca(bc). While both
expressions have the same value, the right hand
side uses one less operation (one product and one
sum versus two products and one sum). The
Generalized Distributive Law (GDL) or Junction
Tree Algorithm extends this idea to the
computation of more general "sums of products",
providing a way of organizing the calculations to
reduce the number of operations required. An
important application of the algorithm is the
computation of marginal distributions Consider a
set X of random variables, each of which takes
values in a finite set. If the joint distribution
of these variables is given as a product of
functions, the calculation of the marginal
distribution of a subset S of X amounts to the
computation of a "sum of products of functions"
(over all values of the variables in X\S). This
example is a special case of the "Marginalize a
Product Function" (MPF) problem. Recent work of
Payam Pakzad and Venkat Anantharam shows that
there are marginalization problems for which GDL
does not produce the best method of calculation.
They introduce a probability-theoretic framework
in which marginalization is viewed as the
computation of conditional expectations. This
approach allows to detect and exploit special
structures in the functions, thus obtaining more
efficient algorithms. In this seminar I will
discuss this new approach and its relation to the
more traditional Junction Tree Algorithm. Kurt
Plarre Coordinated Science Laboratory University
of Illinois at Urbana-Champaign 330 430
p.m. Tuesday, October 9, 2001 141 CSL