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Abstract:
We derive a first-order approximation of the density of
maximum entropy for a continuous 1-D random variable, given a
number of simple constraints. This results in a density expansion
which is somewhat similar to the classical polynomial density
expansions by Gram-Charlier and Edgeworth. Using this approximation
of density, an approximation of 1-D differential entropy is
derived. The approximation of entropy is both more exact and more
robust against outliers than the classical approximation based on
the polynomial density expansions, without being computationally
more expensive. The approximation has applications, for example, in
independent component analysis and projection pursuit.
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