NDLI: Optimal order reduction of probability distributions by maximizing mutual information

Content Provider	IEEE Xplore Digital Library
Author	Vidyasagar, M.
Copyright Year	2011
Description	Author affiliation: Cecil & Ida Green Endowed Chair, Erik Jonsson School of Engineering & Computer Science, University of Texas at Dallas, 800 W. Campbell Road, EC38, Richardson, 75080, USA (Vidyasagar, M.)
Abstract	In a companion paper [16], we defined a metric distance between two probability distributions φ, ψ defined on sets of different cardinality, called the variation of information metric d. In this paper we study of problem of finding an optimal reduced-order approximation in the variation of information metric. Let φ denote the probability distribution of high dimension that is to be approximated. It is shown first that any optimal approximation of φ must be an aggregation of φ. Then it is shown that any optimal aggregation of φ is one that has maximum entropy. Using these two results, we then formulate the problem of optimal order reduction as a nonstandard bin-packing problem with overstuffing. Unfortunately this problem is NP-hard. So a greedy algorithm is presented to solve this problem, and an upper bound on its performance is presented. The application of the greedy algorithm is illustrated via a large example.
Starting Page	716
Ending Page	721
File Size	307521
Page Count	6
File Format	PDF
ISBN	9781612848006
ISSN	07431546
e-ISBN	9781612848013
e-ISBN	9781612847993
DOI	10.1109/CDC.2011.6160501
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-12-12
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Measurement Tin Probability distribution Entropy Approximation methods Vectors Greedy algorithms
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Control and Systems Engineering Modeling and Simulation

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