Title: Detection of non-null effects in linear models for sparse mixtures
Authors: Annika Tillander - Linköping University (Sweden) [presenting]
Tatjana Pavlenko - KTH Royal Institute of Technology (Sweden)
Abstract: For a linear classifier to be successful in a high-dimensional setting it is often needed to select a subset of features. This is a challenging task when the informative features are rare and weak. Accounting for the relation between features, given the sparse structure, can enhance the chances. It been shown that a block-diagonal approximation of the inverse covariance matrix lead to an additive classifier with good classification accuracy. This call for block-wise feature selection. A measure of information strength and a threshold is required. For single feature selection the Higher Criticism is a well-known thresholding method that is optimally adaptive i.e. performs well without knowledge of the sparsity and weakness parameters. It is shown how this method can be extended to handle thresholding for blocks of features. However, popular method it has limitations and will be compared to other goodness-of-fit tests based on sup-functionals of weighted empirical process for thresholding. The relevance and benefits in high-dimensional classification is demonstrated using both simulation and real data.