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High-dimensional variable selection and graphs: sparsity, faithfulness and stability

Friday 11th January 2008 - 09:00 to 10:00
INI Seminar Room 1
Session Chair: 
Mike West

Over the last few years, substantial progress has been achieved on high-dimensional variable selection (and graphical modeling) using L1-penalization methods. Diametrically opposed to penalty-based schemes is the PC-algorithm, a special hierarchical multiple testing procedure, which exploits the so-called faithfulness assumption from graphical modeling. For asymptotic consistency in high-dimensional settings, the different approaches require very different "coherence" conditions, say for the design matrix in a linear model. From a conceptual aspect, the PC-algorithm allows to identify not only regression-type associations but also directed edges in a graph and causal effects (in the sense of Pearl's intervention operator). Thereby, sparsity, faithfulness and stability play a crucial role. We will discuss potential and limitations from a theory and practical point of view.

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