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Tournament screening cum EBIC for feature selection with high-dimensional feature spaces. (English) Zbl 1176.62014

Summary: Feature selection characterized by relatively small sample size and an extremely high-dimensional feature space is common in many areas of contemporary statistics. The high dimensionality of the feature space causes serious difficulties: (i) the sample correlations between features become high even if the features are stochastically independent; (ii) the computations become intractable. These difficulties make conventional approaches either inapplicable or inefficient. The reduction of dimensionality of the feature space followed by low dimensional approaches appears the only feasible way to tackle this problem.
Along this line, we develop a tournament screening cum EBIC approach for feature selection with high dimensional feature space. The procedure of tournament screening mimics that of a tournament. It is shown theoretically that the tournament screening has the sure screening property, a necessary property which should be satisfied by any valid screening procedure. It is demonstrated by numerical studies that the tournament screening cum extended Bayes information criterion (EBIC) approach enjoys desirable properties such as having higher positive selection rate and lower false discovery rate than other approaches.

MSC:

62F07 Statistical ranking and selection procedures
62P10 Applications of statistics to biology and medical sciences; meta analysis
62J05 Linear regression; mixed models
65C60 Computational problems in statistics (MSC2010)
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