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View Code? Open in Web Editor NEWFit a convex sum of positive basis functions to any probability distribution
Home Page: https://bfit.qcdevs.org/
License: GNU General Public License v3.0
Fit a convex sum of positive basis functions to any probability distribution
Home Page: https://bfit.qcdevs.org/
License: GNU General Public License v3.0
Problem: Tsallis Divergence is not lower-bounded, hence minimization will leads towards negative infinity.
Definition The Tsallis Divergence is defined as :
where if alpha approaches one then this approaches the Kullback-Leibler. This can be proven by using L Hopital rule (since bottom and top evaluate to zero then we satisfy L Hopital assumption) and showing that
Plotting this, it does seem to approach it.
Implementation: I'm putting in the constraint that the integral should match. I'm use mask value of 1e-12 to g(x) from the division of f(x) with g(x) and set the ratio (f(x)/g(x)) to zero if g(x) < 1e-12.
Choosing Alpha
Reference
[1] - Paul "Information Theory, the shape function and the Hirshfield atom"
[2] - Farnaz "Hirshfield partioning from non-extensive entropies"
Going to do: I'm going to run these alpha for longer periods of time.
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