Maximum entropy reconstruction using derivative information, 1. Fisher information and convex duality

Maximum entropy reconstruction using derivative information, 1. Fisher information and convex duality

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Article ID: iaor20041090
Country: United States
Volume: 21
Issue: 2
Start Page Number: 442
End Page Number: 468
Publication Date: May 1996
Journal: Mathematics of Operations Research
Authors: , ,
Abstract:

Maximum entropy spectral density estimation is a technique for reconstructing an unknown density function from some known measurements by maximizing a given measure of entropy of the estimate. Here we present a variety of new entropy measures which attempt to control derivative values of the densities. Our models apply among others to the inference problem based on the averaged Fisher information measure. The duality theory we develop resembles models used in convex optimal control problems. We present a variety of examples, including relaxed moment matching with Fisher information and best interpolation on a strip.

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