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