9,527 research outputs found
Coordinate descent algorithms for nonconvex penalized regression, with applications to biological feature selection
A number of variable selection methods have been proposed involving nonconvex
penalty functions. These methods, which include the smoothly clipped absolute
deviation (SCAD) penalty and the minimax concave penalty (MCP), have been
demonstrated to have attractive theoretical properties, but model fitting is
not a straightforward task, and the resulting solutions may be unstable. Here,
we demonstrate the potential of coordinate descent algorithms for fitting these
models, establishing theoretical convergence properties and demonstrating that
they are significantly faster than competing approaches. In addition, we
demonstrate the utility of convexity diagnostics to determine regions of the
parameter space in which the objective function is locally convex, even though
the penalty is not. Our simulation study and data examples indicate that
nonconvex penalties like MCP and SCAD are worthwhile alternatives to the lasso
in many applications. In particular, our numerical results suggest that MCP is
the preferred approach among the three methods.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS388 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A Selective Review of Group Selection in High-Dimensional Models
Grouping structures arise naturally in many statistical modeling problems.
Several methods have been proposed for variable selection that respect grouping
structure in variables. Examples include the group LASSO and several concave
group selection methods. In this article, we give a selective review of group
selection concerning methodological developments, theoretical properties and
computational algorithms. We pay particular attention to group selection
methods involving concave penalties. We address both group selection and
bi-level selection methods. We describe several applications of these methods
in nonparametric additive models, semiparametric regression, seemingly
unrelated regressions, genomic data analysis and genome wide association
studies. We also highlight some issues that require further study.Comment: Published in at http://dx.doi.org/10.1214/12-STS392 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
The finite-temperature Monte Carlo method and its application to superfluid helium clusters
We review the use of the path integral Monte Carlo (PIMC) methodology to the
study of finite-size quantum clusters, with particular emphasis on recent
applications to pure and impurity-doped He clusters. We describe the principles
of PIMC, the use of the multilevel Metropolis method for sampling particle
permutations, and the methods used to accurately incorporate anisotropic
molecule-helium interactions into the path integral scheme. Applications to
spectroscopic studies of embedded atoms and molecules are summarized, with
discussion of the new concepts of local and nanoscale superfluidity that have
been generated by recent PIMC studies of the impurity-doped He clusters.Comment: P. Huang, Y. Kwon, and K. B. Whaley, in "Quantum Fluids in
Confinement", Vol. 4 of "Advances in Quantum Many-Body Theories", edited by
E. Krotscheck and J. Navarro (World Scientific, Singapore, 2002), in pres
Structure and energetics of helium adsorption on nanosurfaces
The ground and excited state properties of small helium clusters, 4He_N,
containing nanoscale (~3-10 Angstroms) planar aromatic molecules have been
studied with quantum Monte Carlo methods. Ground state structures and energies
are obtained from importance-sampled, rigid-body diffusion Monte Carlo. Excited
state energies due to helium vibrational motion are evaluated using the
projection operator, imaginary time spectral evolution technique. We examine
the adsorption of N helium atoms (N less than or equal to 24) on a series of
planar aromatic molecules (benzene, naphthalene, anthracene, tetracene,
phthalocyanine). The first layer of helium atoms is well-localized on the
molecule surface, and we find well-defined localized excitations due to
in-plane vibrational motion of helium on the molecule surface. We discuss the
implications of these confined excitations for the molecule spectroscopy.Comment: 6 pages, 2 figures, QFS 2003 Symposium, submitted to J. Low Temp.
Phy
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