Component-wise gradient boosting and false discovery control in survival analysis with high-dimensional covariates.

MOTIVATION: Technological advances that allow routine identification of high-dimensional risk factors have led to high demand for statistical techniques that enable full utilization of these rich sources of information for genetics studies. Variable selection for censored outcome data as well as control of false discoveries (i.e. inclusion of irrelevant variables) in the presence of high-dimensional predictors present serious challenges. This article develops a computationally feasible method based on boosting and stability selection. Specifically, we modified the component-wise gradient boosting to improve the computational feasibility and introduced random permutation in stability selection for controlling false discoveries. RESULTS: We have proposed a high-dimensional variable selection method by incorporating stability selection to control false discovery. Comparisons between the proposed method and the commonly used univariate and Lasso approaches for variable selection reveal that the proposed method yields fewer false discoveries. The proposed method is applied to study the associations of 2339 common single-nucleotide polymorphisms (SNPs) with overall survival among cutaneous melanoma (CM) patients. The results have confirmed that BRCA2 pathway SNPs are likely to be associated with overall survival, as reported by previous literature. Moreover, we have identified several new Fanconi anemia (FA) pathway SNPs that are likely to modulate survival of CM patients. AVAILABILITY AND IMPLEMENTATION: The related source code and documents are freely available at https://sites.google.com/site/bestumich/issues. CONTACT: yili@umich.edu.

Accurate localized resolution of identity approach for linear-scaling hybrid density functionals and for many-body perturbation theory

© 2015 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.A key component in calculations of exchange and correlation energies is the Coulomb operator, which requires the evaluation of two-electron integrals. For localized basis sets, these four-center integrals are most efficiently evaluated with the resolution of identity (RI) technique, which expands basis-function products in an auxiliary basis. In this work we show the practical applicability of a localized RI-variant ('RI-LVL'), which expands products of basis functions only in the subset of those auxiliary basis functions which are located at the same atoms as the basis functions. We demonstrate the accuracy of RI-LVL for Hartree-Fock calculations, for the PBE0 hybrid density functional, as well as for RPA and MP2 perturbation theory. Molecular test sets used include the S22 set of weakly interacting molecules, the G3 test set, as well as the G2-1 and BH76 test sets, and heavy elements including titanium dioxide, copper and gold clusters. Our RI-LVL implementation paves the way for linear-scaling RI-based hybrid functional calculations for large systems and for all-electron many-body perturbation theory with significantly reduced computational and memory cost.

Evaluating functional network inference using simulations of complex biological systems.

MOTIVATION: Although many network inference algorithms have been presented in the bioinformatics literature, no suitable approach has been formulated for evaluating their effectiveness at recovering models of complex biological systems from limited data. To overcome this limitation, we propose an approach to evaluate network inference algorithms according to their ability to recover a complex functional network from biologically reasonable simulated data. RESULTS: We designed a simulator to generate data representing a complex biological system at multiple levels of organization: behaviour, neural anatomy, brain electrophysiology, and gene expression of songbirds. About 90% of the simulated variables are unregulated by other variables in the system and are included simply as distracters. We sampled the simulated data at intervals as one would sample from a biological system in practice, and then used the sampled data to evaluate the effectiveness of an algorithm we developed for functional network inference. We found that our algorithm is highly effective at recovering the functional network structure of the simulated system-including the irrelevance of unregulated variables-from sampled data alone. To assess the reproducibility of these results, we tested our inference algorithm on 50 separately simulated sets of data and it consistently recovered almost perfectly the complex functional network structure underlying the simulated data. To our knowledge, this is the first approach for evaluating the effectiveness of functional network inference algorithms at recovering models from limited data. Our simulation approach also enables researchers a priori to design experiments and data-collection protocols that are amenable to functional network inference.