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This book features research contributions fromThe Abel Symposium on Statistical Analysis for High Dimensional Data, held inNyvagar, Lofoten, Norway, in May 2014. The focus of the symposium was on statisticaland machine learning methodologies specifically developed for inference in "bigdata" situations, with particular reference to genomic applications. Thecontributors, who are among the most prominent researchers on the theory ofstatistics for high dimensional inference, present new theories and methods, aswell as challenging applications and computational solutions. Specific themesinclude, among others, variable selection and screening, penalised regression,sparsity, thresholding, low dimensional structures, computational challenges,non-convex situations, learning graphical models, sparse covariance andprecision matrices, semi- and non-parametric formulations, multiple testing,classification, factor models, clustering, and preselection. Highlighting cutting-edge researchand casting light on future research directions, the contributions will benefitgraduate students and researchers in computational biology, statistics and themachine learning community.