Statistical challenges with high dimensionality: Feature selection in knowledge discovery

Jianqing Fan, Runze Li

Research output: Contribution to conferencePaper

166 Scopus citations

Abstract

Technological innovations have revolutionized the process of scientific research and knowledge discovery. The availability of massive data and challenges from frontiers of research and development have reshaped statistical thinking, data analysis and theoretical studies. The challenges of high-dimensionality arise in diverse fields of sciences and the humanities, ranging from computational biology and health studies to financial engineering and risk management. In all of these fields, variable selection and feature extraction are crucial for knowledge discovery. We first give a comprehensive overview of statistical challenges with high dimensionality in these diverse disciplines. We then approach the problem of variable selection and feature extraction using a unified framework: penalized likelihood methods. Issues relevant to the choice of penalty functions are addressed. We demonstrate that for a host of statistical problems, as long as the dimensionality is not excessively large, we can estimate the model parameters as well as if the best model is known in advance. The persistence property in risk minimization is also addressed. The applicability of such a theory and method to diverse statistical problems is demonstrated. Other related problems with high-dimensionality are also discussed.

Original languageEnglish (US)
Pages595-622
Number of pages28
StatePublished - Dec 1 2006
Event25th International Congress of Mathematicians, ICM 2006 - Madrid, Spain
Duration: Aug 22 2006Aug 30 2006

Other

Other25th International Congress of Mathematicians, ICM 2006
CountrySpain
CityMadrid
Period8/22/068/30/06

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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    Fan, J., & Li, R. (2006). Statistical challenges with high dimensionality: Feature selection in knowledge discovery. 595-622. Paper presented at 25th International Congress of Mathematicians, ICM 2006, Madrid, Spain.