NDLI: Two approaches of using heavy tails in high dimensional EDA

Content Provider	IEEE Xplore Digital Library
Author	Sanyang, Momodou L. Muehlbrandt, Hanno Kaban, Ata
Copyright Year	2014
Abstract	We consider the problem of high dimensional black-box optimisation via Estimation of Distribution Algorithms (EDA). The Gaussian distribution is commonly used as a search operator in most of the EDA methods. However there are indications in the literature that heavy tailed distributions may perform better due to their higher exploration capabilities. Univariate heavy tailed distributions were already proposed for high dimensional problems. In 2D problems it has been reported that a multivariate heavy tailed (such as Cauchy) search distribution is able to blend together the strengths of multivariate modelling with a high exploration power. In this paper, we study whether a similar scheme would work well in high dimensional search problems. To get around of the difficulty of multivariate model building in high dimensions we employ a recently proposed random projections (RP) ensemble based approach which we modify to get samples from a multivariate Cauchy using the scale-mixture representation of the Cauchy distribution. Our experiments show that the resulting RP-based multivariate Cauchy EDA consistently improves on the performance of the univariate Cauchy search distribution. However, intriguingly, the RP-based multivariate Gaussian EDA has the best performance among these methods. It appears that the highly explorative nature of the multivariate Cauchy sampling is exacerbated in high dimensional search spaces and the population based search loses its focus and effectiveness as a result. Finally, we present an idea to increase exploration while maintaining exploitation and focus by using the RP-based multivariate Gaussian EDA in which the RP matrices are drawn with i.i.d. Heavy tailed entries. This achieves improved performance and is competitive with the state of the art.
Starting Page	653
Ending Page	660
File Size	312701
Page Count	8
File Format	PDF
e-ISBN	9781479942749
DOI	10.1109/ICDMW.2014.184
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2014-12-14
Publisher Place	China
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Estimation of Distribution Algorithm Random Projection Sociology Buildings Multivariate Gaussian EDA Search problems Educational institutions Covariance matrices Multivariate Cauchy EDA Optimization
Content Type	Text
Resource Type	Article

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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