Structured variable selection in support vector machines

When applying the support vector machine (SVM) to high-dimensional classification problems, we often impose a sparse structure in the SVM to eliminate the influences of the irrelevant predictors. The lasso and other variable selection techniques have been successfully used in the SVM to perform automatic variable selection. In some problems, there is a natural hierarchical structure among the variables. Thus, in order to have an interpretable SVM classifier, it is important to respect the heredity principle when enforcing the sparsity in the SVM. Many variable selection methods, however, do not respect the heredity principle. In this paper we enforce both sparsity and the heredity principle in the SVM by using the so-called structured variable selection (SVS) framework originally proposed in Yuan, Joseph and Zou (2007). We minimize the empirical hinge loss under a set of linear inequality constraints and a lasso-type penalty. The solution always obeys the desired heredity principle and enjoys sparsity. The new SVM classifier can be efficiently fitted, because the optimization problem is a linear program. Another contribution of this work is to present a nonparametric extension of the SVS framework, and we propose nonparametric heredity SVMs. Simulated and real data are used to illustrate the merits of the proposed method.Comment: Published in at http://dx.doi.org/10.1214/07-EJS125 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

Searching Signals in Chinese Ancient Records for the 14^{14}C Increases in AD 774-775 and in AD 992-993

According to the analysis of the $^{14}$C content of two Japanese trees over a period of approximately 3000 years at high time resolution, Miyake (2012) found a rapid increase at AD 774-775 and later on at AD 992-993 (Miyake 2013). This corresponds to a high-energy event happened within one year that input $\gamma$-ray energy about 7$\times{}$10$^{24}$erg to the Earth, leaving the origin a mystery. Such strong event should have an unusual optical counterpart, and have been recorded in historical literature. We searched Chinese historical materials around AD 744-775 and AD 992-993, but no remarkable event was found except a violent thunderstorm in AD 775. However, the possibility of a thunderstorm containing so much energy is still unlikely. We conclude the event caused the $^{14}$C increase is still unclear. This event most probably has no optical counterpart, and short gamma-ray burst, giant flare of a soft gamma-ray repeater and terrestrial $\gamma$-ray flash may all be the candidates.Comment: 8 pages, 3 figure

Structured variable selection and estimation

In linear regression problems with related predictors, it is desirable to do variable selection and estimation by maintaining the hierarchical or structural relationships among predictors. In this paper we propose non-negative garrote methods that can naturally incorporate such relationships defined through effect heredity principles or marginality principles. We show that the methods are very easy to compute and enjoy nice theoretical properties. We also show that the methods can be easily extended to deal with more general regression problems such as generalized linear models. Simulations and real examples are used to illustrate the merits of the proposed methods.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS254 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Expected high energy emission from GRB 080319B and origins of the GeV emission of GRBs 080514B, 080916C and 081024B

We calculate the high energy (sub-GeV to TeV) prompt and afterglow emission of GRB 080319B that was distinguished by a naked-eye optical flash and by an unusual strong early X-ray afterglow. There are three possible sources for high energy emission: the prompt optical and $\gamma$-ray photons IC scattered by the accelerated electrons, the prompt photons IC scattered by the early external reverse-forward shock electrons, and the higher band of the synchrotron and the synchrotron self-Compton emission of the external shock. There should have been in total {hundreds} high energy photons detectable for the Large Area Telescope (LAT) onboard the Fermi satellite, and {tens} photons of those with energy $> 10$ GeV. The $> 10$ GeV emission had a duration about twice that of the soft $\gamma$-rays. AGILE could have observed these energetic signals if it was not occulted by the Earth at that moment. The physical origins of the high energy emission detected in GRB 080514B, GRB 080916C and GRB 081024B are also discussed. These observations seem to be consistent with the current high energy emission models.Comment: Accepted for publication in MNRAS, the interpretation of GRB 080916C has been extended, main conclusions are unchange

Study of Minor Actinides Transmutation in PWR MOX fuel

The management of long-lived radionuclides in spent fuel is a key issue to achieve the closed nuclear fuel cycle and the sustainable development of nuclear energy. Partitioning-Transmutation is supposed to be an efficient method to treat the long-lived radionuclides in spent fuel. Some Minor Actinides (MAs) have very long half-lives among the radionuclides in the spent fuel. Accordingly, the study of MAs transmutation is a significant work for the post-processing of spent fuel. In the present work, the transmutations in Pressurized Water Reactor (PWR) mixed oxide (MOX) fuel are investigated through the Monte Carlo based code RMC. Two kinds of MAs, $^{237}$Np and five MAs ($^{237}$Np, $^{241}$Am, $^{243}$Am, $^{244}$Cm and $^{245}$Cm) are incorporated homogeneously into the MOX fuel assembly. The transmutation of MAs is simulated with different initial MOX concentrations. The results indicate an overall nice efficiency of transmutation in both initial MOX concentrations, especially for the two kinds of MAs primarily generated in the UOX fuel, $^{237}$Np and $^{241}$Am. In addition, the inclusion of $^{237}$Np in MOX has no large influence for other MAs, while the transmutation efficiency of $^{237}$Np is excellent. The transmutation of MAs in MOX fuel depletion is expected to be a new, efficient nuclear spent fuel management method for the future nuclear power generation