Bühlmann, Peter L.
In many areas of science, data arises which are used for inference in complex models. The statistical inference problem is high-dimensional if the number of parameters in the model exceeds the number of observations in the data. While standard statistical procedures fail in such cases, sparse methods have proven to be successful for a broad spectrum of applications, including the celebrated compressed sensing methodology (Candes, Romberg and Tao, 2006; Donoho, 2006). Sparsity is beneficial for complexity regularization leading to near optimal statistical performance, for efficient computation, and it also plays a crucial role for quantifying uncertainties with statistical confidence statements. We explain the main principles, the corresponding mathematical developments (random matrix theory, concentration inequalities), and we will illustrate the methods in an application from genetics Show more
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Organisational unit03502 - Bühlmann, Peter L.
NotesLecture at Math-Colloquium at EPFL Lausanne on 13 November 2014.
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