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Abstract:
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Data produced by high-throughput genomic techniques are often high dimensional and undersampled. This is problematic for many statistical methods, because of overfitting and instability. Techniques that require inversion of covariance matrices (e.g. supervised dimension reduction, the assessment of interdependence structures based on graphical models) are obvious examples, but also techniques that don't require such inversion can behave very poorly when the data is scarce relative to the number of variables involved in the analysis. In this talk, we propose a novel approach, the augmented bootstrap (AB), which can be used to overcome undersampling and improve performance in many statistical analyses. The AB works as a computational "smoother", by simultaneously noising and multiplying data points. In this fashion, it combines the spirit of smoothed bootstrap, bagging, and shrinkage.
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