Variance Estimation Using Refitted Cross-validation in Ultrahigh Dimensional Regression

Variance estimation is a fundamental problem in statistical modeling. In ultrahigh dimensional linear regressions where the dimensionality is much larger than sample size, traditional variance estimation techniques are not applicable. Recent advances on variable selection in ultrahigh dimensional linear regressions make this problem accessible. One of the major problems in ultrahigh dimensional regression is the high spurious correlation between the unobserved realized noise and some of the predictors. As a result, the realized noises are actually predicted when extra irrelevant variables are selected, leading to serious underestimate of the noise level. In this paper, we propose a two-stage refitted procedure via a data splitting technique, called refitted cross-validation (RCV), to attenuate the influence of irrelevant variables with high spurious correlations. Our asymptotic results show that the resulting procedure performs as well as the oracle estimator, which knows in advance the mean regression function. The simulation studies lend further support to our theoretical claims. The naive two-stage estimator which fits the selected variables in the first stage and the plug-in one stage estimators using LASSO and SCAD are also studied and compared. Their performances can be improved by the proposed RCV method

Medical Image Segmentation Based on Multi-Modal Convolutional Neural Network: Study on Image Fusion Schemes

Image analysis using more than one modality (i.e. multi-modal) has been increasingly applied in the field of biomedical imaging. One of the challenges in performing the multimodal analysis is that there exist multiple schemes for fusing the information from different modalities, where such schemes are application-dependent and lack a unified framework to guide their designs. In this work we firstly propose a conceptual architecture for the image fusion schemes in supervised biomedical image analysis: fusing at the feature level, fusing at the classifier level, and fusing at the decision-making level. Further, motivated by the recent success in applying deep learning for natural image analysis, we implement the three image fusion schemes above based on the Convolutional Neural Network (CNN) with varied structures, and combined into a single framework. The proposed image segmentation framework is capable of analyzing the multi-modality images using different fusing schemes simultaneously. The framework is applied to detect the presence of soft tissue sarcoma from the combination of Magnetic Resonance Imaging (MRI), Computed Tomography (CT) and Positron Emission Tomography (PET) images. It is found from the results that while all the fusion schemes outperform the single-modality schemes, fusing at the feature level can generally achieve the best performance in terms of both accuracy and computational cost, but also suffers from the decreased robustness in the presence of large errors in any image modalities.Comment: Zhe Guo and Xiang Li contribute equally to this wor

Flavor Violating Transitions of Charged Leptons from a Seesaw Mechanism of Dimension Seven

A mechanism has been suggested recently to generate the neutrino mass out of a dimension-seven operator. This is expected to relieve the tension between the occurrence of a tiny neutrino mass and the observability of other physics effects beyond it. Such a mechanism would inevitably entail lepton flavor violating effects. We study in this work the radiative and purely leptonic transitions of the light charged leptons. In so doing we make a systematic analysis of the flavor structure by providing a convenient parametrization of the mass matrices in terms of independent physical parameters and diagonalizing them explicitly. We illustrate our numerical results by sampling over two CP phases and one Yukawa coupling which are the essential parameters in addition to the heavy lepton mass. We find that with the stringent constraints coming from the muon decays and the muon-electron conversion in nuclei taken into account the decays of the tau lepton are severely suppressed in the majority of parameter space. There exist, however, small regions in which some tau decays can reach a level that is about 2 orders of magnitude below their current bounds.Comment: v1: 25 pages, 8 figures; v2: proofread version for PRD. Included muon-electron conversion in nuclei at the referee's suggestion and added relevant refs accordingly; main conclusion not changed but bounds on tau lepton decays becoming more stringent; linguistic and editing corrections also mad

Highlights of Supersymmetric Hypercharge ±1\pm1 Triplets

The discovery of a standard model (SM)-like Higgs boson with a relatively heavy mass $m_h$ and hints of di-photon excess has deep implication to supersymmetric standard models (SSMs). We consider the SSM extended with hypercharge $\pm1$ triplets, and investigate two scenarios of it: (A) Triplets significantly couple to the Higgs doublets, which can substantially raise $m_h$ and simultaneously enhance the Higgs to di-photon rate via light chargino loops; (B) Oppositely, these couplings are quite weak and thus $m_h$ can not be raised. But the doubly-charged Higgs bosons, owing to the gauge group structure, naturally interprets why there is an excess rather than a deficient of Higgs to di-photon rate. Additionally, the pseudo Dirac triplet fermion is an inelastic non-thermal dark matter candidate. Light doubly-charged particles, especially the doubly-charged Higgs boson around 100 GeV in scenario B, are predicted. We give a preliminary discussion on their search at the LHC.Comment: JHEP version. Typos fixed, comments, references and acknowledge adde

Localized Dimension Growth in Random Network Coding: A Convolutional Approach

We propose an efficient Adaptive Random Convolutional Network Coding (ARCNC) algorithm to address the issue of field size in random network coding. ARCNC operates as a convolutional code, with the coefficients of local encoding kernels chosen randomly over a small finite field. The lengths of local encoding kernels increase with time until the global encoding kernel matrices at related sink nodes all have full rank. Instead of estimating the necessary field size a priori, ARCNC operates in a small finite field. It adapts to unknown network topologies without prior knowledge, by locally incrementing the dimensionality of the convolutional code. Because convolutional codes of different constraint lengths can coexist in different portions of the network, reductions in decoding delay and memory overheads can be achieved with ARCNC. We show through analysis that this method performs no worse than random linear network codes in general networks, and can provide significant gains in terms of average decoding delay in combination networks.Comment: 7 pages, 1 figure, submitted to IEEE ISIT 201