Abstract
The maximum entropy principle introduced by Jaynes proposes that a data distribution should maximize the entropy subject to constraints imposed by the available knowledge. Jaynes provided a solution for the case when constraints were imposed on the expected value of a set of scalar functions of the data. These expected values are typically moments of the distribution. This paper describes how the method of maximum entropy PDF projection can be used to generalize the maximum entropy principle to constraints on the joint distribution of this set of functions.
Highlights
The maximum entropy principle of Jaynes [1] proposes that the probability density functions (PDF) should have maximum entropy subject to constraints imposed by the knowledge one has about the density
Before maximum entropy PDF projection, comparing feature extraction methods had to be done based on secondary factors such as classification results
The solution to Problem 1 is based on PDF projection [10]
Summary
The estimation of probability density functions (PDF) is the cornerstone of classical decision theory as applied to real-world problems. The maximum entropy principle of Jaynes [1] proposes that the PDF should have maximum entropy subject to constraints imposed by the knowledge one has about the density. Jaynes worked out the case when the knowledge about p(x) consists of the expected value of a set of K measurements. He considered the K scalar functions φ1 (x), φ2 (x) . The distribution maximizing (1) subject to (2) is: p(x) = e−[λ0 +λ1 φ1 (x)+λ2 φ2 (x)+...λK φK (x)] , where λ0 is the log of the partition function:.
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