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Using side information for prediction

Presented by: 
B Y Yu [Berkeley]
Friday 11th January 2008 - 11:30 to 12:30
INI Seminar Room 1
Session Chair: 
Mike West

Extracting useful information from high-dimensional data is the focus of today's statistical research and practice. Penalized loss function minimization has been shown to be effective for this task both theoretically and empirically. With the vitues of both regularization and sparsity, the L1-penalized L2 minimization method Lasso has been popular. However, Lasso is often seen as not having enough regularization in the large p case.

In this talk, we propose two methods that take into account side information in the penalized L2 framework, in order to bring the needed extra regularization in the large p case. First, we combine different norms including L1 to to introduce the Composite Absolute Penalties (CAP) family. CAP allows the grouping and hierarchical relationships between the predictors to be expressed. It covers and goes beyond existing works including grouped lasso and elastic nets. Path following algorithms and simulation results will be presented to compare with Lasso in terms of prediction and sparsity. Second, motivated by the problem of predicting fMRI signals from input natural images, we investigate a method that uses side information in the unlabeled data for prediction. We present a theoretical result in the case of p/n -> constant and apply the method to the fMRI data problem. (It is noted that the second part is a report on on-going research.) ~

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons