A robust approach based on conditional value-at-risk measure to statistical learning problems

In statistical learning problems, measurement errors in the observed data degrade the reliability of estimation. There exist several approaches to handle those uncertainties in observations. In this paper, we propose to use the conditional value-at-risk (CVaR) measure in order to depress influence o...

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Bibliographic Details
Published in:European journal of operational research 2009-10, Vol.198 (1), p.287-296
Main Authors: Takeda, Akiko, Kanamori, Takafumi
Format: Article
Language:English
Subjects:
Applied sciences
Approximation
Computer science
control theory
systems
Conditional value-at-risk
Data mining
Data mining Uncertainty modelling Stochastic programming Conditional value-at-risk Support vector machine
Data processing. List processing. Character string processing
Estimating techniques
Exact sciences and technology
Measurement errors
Memory organisation. Data processing
Monte Carlo simulation
Operational research and scientific management
Operational research. Management science
Portfolio theory
Reliability
Reliability theory. Replacement problems
Risk theory. Actuarial science
Sampling techniques
Software
Stochastic programming
Studies
Support vector machine
Uncertainty modelling
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Summary:In statistical learning problems, measurement errors in the observed data degrade the reliability of estimation. There exist several approaches to handle those uncertainties in observations. In this paper, we propose to use the conditional value-at-risk (CVaR) measure in order to depress influence of measurement errors, and investigate the relation between the resulting CVaR minimization problems and some existing approaches in the same framework. For the CVaR minimization problems which include the computation of integration, we apply Monte Carlo sampling method and obtain their approximate solutions. The approximation error bound and convergence property of the solution are proved by Vapnik and Chervonenkis theory. Numerical experiments show that the CVaR minimization problem can achieve fairly good estimation results, compared with several support vector machines, in the presence of measurement errors.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2008.07.027