Evolutionary algorithms for robust methods
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Date
2009-01-13T07:55:54Z
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Abstract
A drawback of robust statistical techniques is the increased computational effort often
needed compared to non robust methods. Robust estimators possessing the exact fit property, for example, are NP-hard to compute. This means that — under the widely believed assumption that the computational complexity classes NP and P are not equal — there is no hope to compute exact solutions for large high dimensional data sets. To tackle this problem, search heuristics are used to compute NP-hard estimators in high dimensions.
Here, an evolutionary algorithm that is applicable to different robust estimators
is presented. Further, variants of this evolutionary algorithm for selected estimators — most prominently least trimmed squares and least median of squares—are introduced
and shown to outperform existing popular search heuristics in difficult data situations.
The results increase the applicability of robust methods and underline the usefulness
of evolutionary computation for computational statistics.
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Keywords
Evolutionary algorithms, Least median of squares (LMS), Least quantile of squares (LQS), Least quartile difference (LQD), Least trimmed squares (LTS), Robust regression