Variable selection using MM algorithms

Variable selection is fundamental to high-dimensional statistical modeling. Many variable selection techniques may be implemented by maximum penalized likelihood using various penalty functions. Optimizing the penalized likelihood function is often challenging because it may be nondifferentiable and/or nonconcave. This article proposes a new class of algorithms for finding a maximizer of the penalized likelihood for a broad class of penalty functions. These algorithms operate by perturbing the penalty function slightly to render it differentiable, then optimizing this differentiable function using a minorize-maximize (MM) algorithm. MM algorithms are useful extensions of the well-known class of EM algorithms, a fact that allows us to analyze the local and global convergence of the proposed algorithm using some of the techniques employed for EM algorithms. In particular, we prove that when our MM algorithms converge, they must converge to a desirable point; we also discuss conditions under which this convergence may be guaranteed. We exploit the Newton-Raphson-like aspect of these algorithms to propose a sandwich estimator for the standard errors of the estimators. Our method performs well in numerical tests.Comment: Published at http://dx.doi.org/10.1214/009053605000000200 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Absolutely Continuous Representations and a Kaplansky Density Theorem for Free Semigroup Algebras

We introduce notions of absolutely continuous functionals and representations on the non-commutative disk algebra $A_n$. Absolutely continuous functionals are used to help identify the type L part of the free semigroup algebra associated to a $*$-extendible representation $\sigma$. A $*$-extendible representation of $A_n$ is ``regular'' if the absolutely continuous part coincides with the type L part. All known examples are regular. Absolutely continuous functionals are intimately related to maps which intertwine a given $*$-extendible representation with the left regular representation. A simple application of these ideas extends reflexivity and hyper-reflexivity results. Moreover the use of absolute continuity is a crucial device for establishing a density theorem which states that the unit ball of $\sigma(A_n)$ is weak-$*$ dense in the unit ball of the associated free semigroup algebra if and only if $\sigma$ is regular. We provide some explicit constructions related to the density theorem for specific representations. A notion of singular functionals is also defined, and every functional decomposes in a canonical way into the sum of its absolutely continuous and singular parts.Comment: 26 pages, prepared with LATeX2e, submitted to Journal of Functional Analysi

Empirical Bayes estimation of posterior probabilities of enrichment

To interpret differentially expressed genes or other discovered features, researchers conduct hypothesis tests to determine which biological categories such as those of the Gene Ontology (GO) are enriched in the sense of having differential representation among the discovered features. We study application of better estimators of the local false discovery rate (LFDR), a probability that the biological category has equivalent representation among the preselected features. We identified three promising estimators of the LFDR for detecting differential representation: a semiparametric estimator (SPE), a normalized maximum likelihood estimator (NMLE), and a maximum likelihood estimator (MLE). We found that the MLE performs at least as well as the SPE for on the order of 100 of GO categories even when the ideal number of components in its underlying mixture model is unknown. However, the MLE is unreliable when the number of GO categories is small compared to the number of PMM components. Thus, if the number of categories is on the order of 10, the SPE is a more reliable LFDR estimator. The NMLE depends not only on the data but also on a specified value of the prior probability of differential representation. It is therefore an appropriate LFDR estimator only when the number of GO categories is too small for application of the other methods. For enrichment detection, we recommend estimating the LFDR by the MLE given at least a medium number (~100) of GO categories, by the SPE given a small number of GO categories (~10), and by the NMLE given a very small number (~1) of GO categories.Comment: exhaustive revision of Zhenyu Yang and David R. Bickel, "Minimum Description Length Measures of Evidence for Enrichment" (December 2010). COBRA Preprint Series. Article 76. http://biostats.bepress.com/cobra/ps/art7

Influence of crystal structure on charge carrier effective masses in BiFeO3_3

Ferroelectric-based photovoltaics have shown great promise as a source of renewable energy, thanks to their in-built charge separation capability, yet their efficiency is often limited by low charge carrier mobilities. In this work, we compare the photovoltaic prospects of various phases of the multiferroic material BiFeO$_3$ by evaluating their charge carrier effective masses using first-principles simulations. We identify a tetragonal phase with the promising combination of a large spontaneous polarisation and relatively light charge carriers. From a systematic study of the octahedral distortions present in BiFeO$_3$, we explain the relationship between structure and effective masses in terms of the changes to the orbital character and overlap at the band edges that result from changes in the geometry. The findings in this study provide some design principles to engineer desired effective masses in BiFeO$_3$ and similar materials through manipulation of their crystal structures in experimentally accessible ways.Comment: 12 pages, 10 figure

Structures of fibrils formed by α-synuclein hereditary disease mutant H50Q reveal new polymorphs.

Deposits of amyloid fibrils of α-synuclein are the histological hallmarks of Parkinson's disease, dementia with Lewy bodies and multiple system atrophy, with hereditary mutations in α-synuclein linked to the first two of these conditions. Seeing the changes to the structures of amyloid fibrils bearing these mutations may help to understand these diseases. To this end, we determined the cryo-EM structures of α-synuclein fibrils containing the H50Q hereditary mutation. We find that the H50Q mutation results in two previously unobserved polymorphs of α-synuclein: narrow and wide fibrils, formed from either one or two protofilaments, respectively. These structures recapitulate conserved features of the wild-type fold but reveal new structural elements, including a previously unobserved hydrogen-bond network and surprising new protofilament arrangements. The structures of the H50Q polymorphs help to rationalize the faster aggregation kinetics, higher seeding capacity in biosensor cells and greater cytotoxicity that we observe for H50Q compared to wild-type α-synuclein

The Coronal X-ray Spectrum of the Multiple Weak-Lined T Tauri Star System HD 98800

We present high-resolution X-ray spectra of the multiple (hierarchical quadruple) weak-lined T Tauri star system HD 98800, obtained with the High Energy Transmission Gratings Spectrograph (HETGS) aboard the Chandra X-ray Observatory (CXO). In the zeroth-order CXO/HETGS X-ray image, both principle binary components of HD 98800 (A and B, separation 0.8'') are detected; component A was observed to flare during the observation. The infrared excess (dust disk) component, HD 98800B, is a factor ~4 fainter in X-rays than the apparently ``diskless'' HD 98800A, in quiescence. The line ratios of He-like species (e.g., Ne IX, O VII) in the HD 98800A spectrum indicate that the X-ray-emitting plasma around HD 98800 is in a typical coronal density regime (log n <~ 11). We conclude that the dominant X-ray-emitting component(s) of HD 98800 is (are) coronally active. The sharp spectral differences between HD 98800 and the classical T Tauri star TW Hya demonstrate the potential utility of high-resolution X-ray spectroscopy in providing diagnostics of pre-main sequence accretion processes.Comment: 11 pages, 5 figures; to appear in the Astrophysical Journal (Letters