Probability density function estimation using the MinMax measure

Author

Srikanth, Munirathnam ; Kesavan, H.K. ; Roe, Peter H.

Author_Institution

Dept. of Comput. Sci. & Eng., State Univ. of New York, Buffalo, NY, USA

Volume

30

Issue

1

fYear

2000

fDate

2/1/2000 12:00:00 AM

Firstpage

77

Lastpage

83

Abstract

The problem of initial probability assignment which is consistent with the available information about a probabilistic system is called a direct problem. E.T. Jaynes´ (1957) maximum entropy principle (MaxEnt) provides a method for solving direct problems when the available information is in the form of moment constraints. On the other hand, given a probability distribution, the problem of finding a set of constraints which makes the given distribution a maximum entropy distribution is called an inverse problem. A method based on the MinMax measure to solve the above inverse problem is presented. The MinMax measure of information, defined by Kapur, Baciu and Kesavan (1995), is a quantitative measure of the information contained in a given set of moment constraints. It is based on both maximum and minimum entropy. Computational issues in the determination of the MinMax measure arising from the complexity in arriving at minimum entropy probability distributions (MinEPD) are discussed. The method to solve inverse problems using the MinMax measure is illustrated by solving the problem of estimating a probability density function of a random variable based on sample data

Keywords

computational complexity; estimation theory; function approximation; inverse problems; maximum entropy methods; minimax techniques; minimum entropy methods; probability; MinMax measure; Shannon entropy measure; available information; computational complexity; direct problem; entropy optimization; initial probability assignment; inverse problem; maximum entropy distribution; maximum entropy principle; minimum entropy probability distributions; moment constraints; probabilistic system; probability density function estimation; quantitative information measure; random variable; sample data; Density measurement; Distributed computing; Entropy; Gaussian distribution; Helium; Inverse problems; Minimax techniques; Probability density function; Probability distribution; Random variables;

fLanguage

English

Journal_Title

Systems, Man, and Cybernetics, Part C: Applications and Reviews, IEEE Transactions on

Publisher

ieee

ISSN

1094-6977

Type

jour

DOI

10.1109/5326.827456

Filename

827456