Gradient Hard Thresholding Pursuit for Sparsity-Constrained Optimization

Hard Thresholding Pursuit (HTP) is an iterative greedy selection procedure for finding sparse solutions of underdetermined linear systems. This method has been shown to have strong theoretical guarantee and impressive numerical performance. In this paper, we generalize HTP from compressive sensing to a generic problem setup of sparsity-constrained convex optimization. The proposed algorithm iterates between a standard gradient descent step and a hard thresholding step with or without debiasing. We prove that our method enjoys the strong guarantees analogous to HTP in terms of rate of convergence and parameter estimation accuracy. Numerical evidences show that our method is superior to the state-of-the-art greedy selection methods in sparse logistic regression and sparse precision matrix estimation tasks

Neutrino Masses and Heavy Triplet Leptons at the LHC: Testability of Type III Seesaw

We study LHC signatures of Type III seesaw in which SU(2)_L triplet leptons are introduced to supply the heavy seesaw masses. To detect the signals of these heavy triplet leptons, one needs to understand their decays to standard model particles which depend on how light and heavy leptons mix with each other. We concentrate on the usual solutions with small light and heavy lepton mixing of order the square root of the ratio of light and heavy masses, (m_\nu/M_{\nu_R})^{1/2}. This class of solutions can lead to a visible displaced vertex detectable at the LHC which can be used to distinguish small mixing and large mixing between light and heavy leptons. We show that, in this case, the couplings of light and heavy triplet leptons to gauge and Higgs bosons, which determine the decay widths and branching ratios, can be expressed in terms of light neutrino masses and their mixing. Using these relations, we study heavy triplet lepton decay patterns and production cross section at the LHC. If these heavy triplet leptons are below a TeV or so, they can be easily produced at the LHC due to their gauge interactions from being non-trivial representations of SU(2)_L. We consider two ideal production channels, 1) E^+E^- \to \ell^+\ell^+ \ell^-\ell^- jj (\ell=e,\mu,\tau) and 2) E^\pm N \to \ell^\pm \ell^\pm jjjj in detail. For case 1), we find that with one or two of the light leptons being \tau it can also be effectively studied. With judicious cuts at the LHC, the discovery of the heavy triplet leptons as high as a TeV can be achieved with 100 fb^{-1} integrated luminosity.Comment: 39 pages, 36 figures, accepted version by PR

Person Search with Natural Language Description

Searching persons in large-scale image databases with the query of natural language description has important applications in video surveillance. Existing methods mainly focused on searching persons with image-based or attribute-based queries, which have major limitations for a practical usage. In this paper, we study the problem of person search with natural language description. Given the textual description of a person, the algorithm of the person search is required to rank all the samples in the person database then retrieve the most relevant sample corresponding to the queried description. Since there is no person dataset or benchmark with textual description available, we collect a large-scale person description dataset with detailed natural language annotations and person samples from various sources, termed as CUHK Person Description Dataset (CUHK-PEDES). A wide range of possible models and baselines have been evaluated and compared on the person search benchmark. An Recurrent Neural Network with Gated Neural Attention mechanism (GNA-RNN) is proposed to establish the state-of-the art performance on person search