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Title: On the risk of LASSO type estimators
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Abstract:

This talk attempts to address the issues of sparsity and mathematically intractable risk of LASSO estimator - by introducing a parallel LASSO-type estimator which does not rest on sparsity and whose risk is exactly computable. It offers a generalization of the classical LASSO estimator for non-orthogonal design, allowed to be of less than full rank. We compare the risk of new estimator with its shrinkage competitor, the ridge estimator.

Abstract: Analysis of deep polar ice cores has become an important tool for deriving climate information from the past. Interpretation of ice core records requires an accurate dating of the ice. The recent dating relies on models where the key element is the simulation of the individual history of ice deformation for each specific core site. We present a two-stage method for the estimation of the deformation history in polar ice using the measured anisotropy of air inclusions from deep ice cores.

Abstract: We discuss an important research problem concerning selection  of covariates that are both highly informative and correlated with each other. Most of the variable selection methods exclude the highly correlated covariates from the regression equations, which can lead investigators to overlook significant features. Especially in high dimensional settings, independence assumptions among predictors are unlikely to be fulfilled in general.