Variable selection for the multicategory SVM via adaptive sup-norm regularization

The Support Vector Machine (SVM) is a popular classification paradigm in machine learning and has achieved great success in real applications. However, the standard SVM can not select variables automatically and therefore its solution typically utilizes all the input variables without discrimination. This makes it difficult to identify important predictor variables, which is often one of the primary goals in data analysis. In this paper, we propose two novel types of regularization in the context of the multicategory SVM (MSVM) for simultaneous classification and variable selection. The MSVM generally requires estimation of multiple discriminating functions and applies the argmax rule for prediction. For each individual variable, we propose to characterize its importance by the supnorm of its coefficient vector associated with different functions, and then minimize the MSVM hinge loss function subject to a penalty on the sum of supnorms. To further improve the supnorm penalty, we propose the adaptive regularization, which allows different weights imposed on different variables according to their relative importance. Both types of regularization automate variable selection in the process of building classifiers, and lead to sparse multi-classifiers with enhanced interpretability and improved accuracy, especially for high dimensional low sample size data. One big advantage of the supnorm penalty is its easy implementation via standard linear programming. Several simulated examples and one real gene data analysis demonstrate the outstanding performance of the adaptive supnorm penalty in various data settings.Comment: Published in at http://dx.doi.org/10.1214/08-EJS122 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

A comparative study of mesoporous glass/silk and non-mesoporous glass/silk scaffolds: Physiochemistry and in vivo osteogenesis

Mesoporous bioactive glass (MBG) is a new class of biomaterials with a well-ordered nanochannel structure, whose in vitro bioactivity is far superior than that of non-mesoporous bioactive glass (BG); the material's in vivo osteogenic properties are, however, yet to be assessed. Porous silk scaffolds have been used for bone tissue engineering, but this material's osteoconductivity is far from optimal. The aims of this study were to incorporate MBG into silk scaffolds in order to improve their osteoconductivity and then to compare the effect of MBG and BG on the in vivo osteogenesis of silk scaffolds. MBG/silk and BG/silk scaffolds with a highly porous structure were prepared by a freeze-drying method. The mechanical strength, in vitro apatite mineralization, silicon ion release and pH stability of the composite scaffolds were assessed. The scaffolds were implanted into calvarial defects in SCID mice and the degree of in vivo osteogenesis was evaluated by microcomputed tomography (μCT), hematoxylin and eosin (H&E) and immunohistochemistry (type I collagen) analyses. The results showed that MBG/silk scaffolds have better physiochemical properties (mechanical strength, in vitro apatite mineralization, Si ion release and pH stability) compared to BG/silk scaffolds. MBG and BG both improved the in vivo osteogenesis of silk scaffolds. μCT and H&E analyses showed that MBG/silk scaffolds induced a slightly higher rate of new bone formation in the defects than did BG/silk scaffolds and immunohistochemical analysis showed greater synthesis of type I collagen in MBG/silk scaffolds compared to BG/silk scaffolds

Empirical Evaluation of Test Coverage for Functional Programs

The correlation between test coverage and test effectiveness is important to justify the use of coverage in practice. Existing results on imperative programs mostly show that test coverage predicates effectiveness. However, since functional programs are usually structurally different from imperative ones, it is unclear whether the same result may be derived and coverage can be used as a prediction of effectiveness on functional programs. In this paper we report the first empirical study on the correlation between test coverage and test effectiveness on functional programs. We consider four types of coverage: as input coverages, statement/branch coverage and expression coverage, and as oracle coverages, count of assertions and checked coverage. We also consider two types of effectiveness: raw effectiveness and normalized effectiveness. Our results are twofold. (1) In general the findings on imperative programs still hold on functional programs, warranting the use of coverage in practice. (2) On specific coverage criteria, the results may be unexpected or different from the imperative ones, calling for further studies on functional programs