This book comprises a collection of research contributions that were presented,
with one exception, at the International Workshop on the Perspectives on High-
Dimensional Data Analysis II, 2012 at the Centre de recherches math´ematiques
(CRM), Universit´ e de Montr´ eal, Canada. One goal of the workshop was to improve
the understanding of high-dimensional modeling from an integrative perspective
and to bridge the gap among statisticians, computer scientists and applied mathe-
maticians in understanding each other’s tools. It provided a venue for participants
to meet leading researchers of this field in a small group in order to maximize the
chance of interaction and discussion. The objectives included: (1) to highlight and
expand the breadth of existing methods in high-dimensional data analysis and their
potential to advance both mathematical and statistical sciences, (2) to identify im-
portant directions for future research in the theory of regularization methods, in
algorithmic development, and in methodology for different application areas, (3) to
facilitate collaboration between theoretical and subject-area researchers, and (4) to
provide opportunities for highly qualified personnel to meet and interact with lead-
ing researchers from countries around the world.
The discipline of statistical science is ever changing and evolving from investiga-
tion of classical finite-dimensional data to high-dimensional data analysis. Indeed,
we are commonly experiencing data sets containing huge numbers of variables where
in some cases the number of variables exceeds the number of sample observations.
Many modern scientific investigations require the analysis of enormous, complex
high-dimensional data that is beyond the classical statistical methodologies devel-
oped decades ago. For example, genomic and proteomic data, spatial-temporal
data, social network data, and many others fall into this category. Modeling and
making statistical decisions of high-dimensional data is a challenging problem. A
range of different models with increasing complexity can be considered, and a model
that is optimal in some sense needs to be selected from a set of candidate models.
Simultaneous variable selection and model parameters estimation plays a central
role in such investigations. There is a massive literature on variable selection, and
penalized regression methods are becoming increasingly popular. Many interest-
ing and useful developments have been published in recent years in scientific and
statistical journals.
The application of regression models for high-dimensional data analysis is a
challenging task. Regularization/penalization techniques have attracted much at-
tention in this arena. Penalized regression is a technique for mitigating difficulties
arising from collinearity and high dimensionality. This approach necessarily incurs
an estimation bias, while reducing the variance of the estimator. A tuning param-
eter is needed to adjust the effect of the penalization so that a balance between
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