APPLE: Approximate Path for Penalized Likelihood Estimators

In high-dimensional data analysis, penalized likelihood estimators are shown to provide superior results in both variable selection and parameter estimation. A new algorithm, APPLE, is proposed for calculating the Approximate Path for Penalized Likelihood Estimators. Both the convex penalty (such as LASSO) and the nonconvex penalty (such as SCAD and MCP) cases are considered. The APPLE efficiently computes the solution path for the penalized likelihood estimator using a hybrid of the modified predictor-corrector method and the coordinate-descent algorithm. APPLE is compared with several well-known packages via simulation and analysis of two gene expression data sets.Comment: 24 pages, 9 figure

How Many Communities Are There?

Stochastic blockmodels and variants thereof are among the most widely used approaches to community detection for social networks and relational data. A stochastic blockmodel partitions the nodes of a network into disjoint sets, called communities. The approach is inherently related to clustering with mixture models; and raises a similar model selection problem for the number of communities. The Bayesian information criterion (BIC) is a popular solution, however, for stochastic blockmodels, the conditional independence assumption given the communities of the endpoints among different edges is usually violated in practice. In this regard, we propose composite likelihood BIC (CL-BIC) to select the number of communities, and we show it is robust against possible misspecifications in the underlying stochastic blockmodel assumptions. We derive the requisite methodology and illustrate the approach using both simulated and real data. Supplementary materials containing the relevant computer code are available online.Comment: 26 pages, 3 figure

Euclidean Dynamical Symmetry in Nuclear Shape Phase Transitions

The Euclidean dynamical symmetry hidden in the critical region of nuclear shape phase transitions is revealed by a novel algebraic F(5) description. With a nonlinear projection, it is shown that the dynamics in the critical region of the spherical--axial deformed and the spherical--$\gamma$ soft shape phase transitions can indeed be manifested by this description, which thus provides a unified symmetry--based interpretation of the critical phenomena in the region.Comment: 5 pages, 2 figures, 2 table