527 research outputs found
Regina Lectures on Fat Points
These notes are a record of lectures given in the Workshop on Connections
Between Algebra and Geometry at the University of Regina, May 29--June 1, 2012.
The lectures were meant as an introduction to current research problems related
to fat points for an audience that was not expected to have much background in
commutative algebra or algebraic geometry (although sections 8 and 9 of these
notes demand somewhat more background than earlier sections).Comment: 32 pages, 3 figure
Mixture decompositions of exponential families using a decomposition of their sample spaces
We study the problem of finding the smallest such that every element of
an exponential family can be written as a mixture of elements of another
exponential family. We propose an approach based on coverings and packings of
the face lattice of the corresponding convex support polytopes and results from
coding theory. We show that is the smallest number for which any
distribution of -ary variables can be written as mixture of
independent -ary variables. Furthermore, we show that any distribution of
binary variables is a mixture of elements
of the -interaction exponential family.Comment: 17 pages, 2 figure
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