The MM Alternative to EM

The EM algorithm is a special case of a more general algorithm called the MM algorithm. Specific MM algorithms often have nothing to do with missing data. The first M step of an MM algorithm creates a surrogate function that is optimized in the second M step. In minimization, MM stands for majorize--minimize; in maximization, it stands for minorize--maximize. This two-step process always drives the objective function in the right direction. Construction of MM algorithms relies on recognizing and manipulating inequalities rather than calculating conditional expectations. This survey walks the reader through the construction of several specific MM algorithms. The potential of the MM algorithm in solving high-dimensional optimization and estimation problems is its most attractive feature. Our applications to random graph models, discriminant analysis and image restoration showcase this ability.Comment: Published in at http://dx.doi.org/10.1214/08-STS264 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

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

Simplified dark matter models in the light of AMS-02 antiproton data

In this work we perform an analysis of the recent AMS-02 antiproton flux and the antiproton-to-proton ratio in the framework of simplified dark matter models. To predict the AMS-02 observables we adopt the propagation and injection parameters determined by the observed fluxes of nuclei. We assume that the dark matter particle is a Dirac fermionic dark matter, with leptophobic pseudoscalar or axialvector mediator that couples only to Standard Model quarks and dark matter particles. We find that the AMS-02 observations are consistent with the dark matter hypothesis within the uncertainties. The antiproton data prefer a dark matter (mediator) mass in the 700 GeV--5 TeV region for the annihilation with pseudoscalar mediator and greater than 700 GeV (200 GeV--1 TeV) for the annihilation with axialvector mediator, respectively, at about 68% confidence level. The AMS-02 data require an effective dark matter annihilation cross section in the region of 1x10^{-25} -- 1x10^{-24} (1x10^{-25} -- 4x10^{-24}) cm^3/s for the simplified model with pseudoscalar (axialvector) mediator. The constraints from the LHC and Fermi-LAT are also discussed.Comment: 16 pages, 6 figures, 1 table. arXiv admin note: text overlap with arXiv:1509.0221

Structure Identifiability of an NDS with LFT Parametrized Subsystems

Requirements on subsystems have been made clear in this paper for a linear time invariant (LTI) networked dynamic system (NDS), under which subsystem interconnections can be estimated from external output measurements. In this NDS, subsystems may have distinctive dynamics, and subsystem interconnections are arbitrary. It is assumed that system matrices of each subsystem depend on its (pseudo) first principle parameters (FPPs) through a linear fractional transformation (LFT). It has been proven that if in each subsystem, the transfer function matrix (TFM) from its internal inputs to its external outputs is of full normal column rank (FNCR), while the TFM from its external inputs to its internal outputs is of full normal row rank (FNRR), then the NDS is structurally identifiable. Moreover, under some particular situations like there are no direct information transmission from an internal input to an internal output in each subsystem, a necessary and sufficient condition is established for NDS structure identifiability. A matrix valued polynomial (MVP) rank based equivalent condition is further derived, which depends affinely on subsystem (pseudo) FPPs and can be independently verified for each subsystem. From this condition, some necessary conditions are obtained for both subsystem dynamics and its (pseudo) FPPs, using the Kronecker canonical form (KCF) of a matrix pencil.Comment: 16 page

Decoupling MSSM Higgs Sector and Heavy Higgs Decay

The decoupling limit in the MSSM Higgs sector is the most likely scenario in light of the Higgs discovery. This scenario is further constrained by MSSM Higgs search bounds and flavor observables. We perform a comprehensive scan of MSSM parameters and update the constraints on the decoupling MSSM Higgs sector in terms of 8 TeV LHC data. We highlight the effect of light SUSY spectrum in the heavy neutral Higgs decay in the decoupling limit. We find that the chargino and neutralino decay mode can reach at most 40% and 20% branching ratio, respectively. In particular, the invisible decay mode BR(H^0(A^0) -> \tilde{\chi}^0_1\tilde{\chi}^0_1) increases with increasing Bino LSP mass and is between 10%-15% (20%) for 30<m_{\tilde{\chi}^0_1}<100 GeV. The leading branching fraction of heavy Higgses decay into sfermions can be as large as 80% for H^0 -> \tilde{t}_1\tilde{t}_1^\ast and 60% for H^0/A^0 -> \tilde{\tau}_1\tilde{\tau}_2^\ast+\tilde{\tau}_1^\ast\tilde{\tau}_2. The branching fractions are less than 10% for H^0 -> h^0h^0 and 1% for A^0 -> h^0Z for m_A>400 GeV. The charged Higgs decays to neutralino plus chargino and sfermions with branching ratio as large as 40% and 60%, respectively. Moreover, the exclusion limit of leading MSSM Higgs search channel, namely gg,b\bar{b} -> H^0, A^0 -> tau^+ tau^-, is extrapolated to 14 TeV LHC with high luminosities. It turns out that the tau tau mode can essentially exclude regime with tan\beta>20 for L=300 fb^{-1} and tan\beta>15 for L=3000 fb^{-1}.Comment: 20 pages, 14 figure