High-dimensional Ising model selection using ℓ1{\ell_1}-regularized logistic regression

We consider the problem of estimating the graph associated with a binary Ising Markov random field. We describe a method based on $\ell_1$-regularized logistic regression, in which the neighborhood of any given node is estimated by performing logistic regression subject to an $\ell_1$-constraint. The method is analyzed under high-dimensional scaling in which both the number of nodes $p$ and maximum neighborhood size $d$ are allowed to grow as a function of the number of observations $n$. Our main results provide sufficient conditions on the triple $(n,p,d)$ and the model parameters for the method to succeed in consistently estimating the neighborhood of every node in the graph simultaneously. With coherence conditions imposed on the population Fisher information matrix, we prove that consistent neighborhood selection can be obtained for sample sizes $n=\Omega(d^3\log p)$ with exponentially decaying error. When these same conditions are imposed directly on the sample matrices, we show that a reduced sample size of $n=\Omega(d^2\log p)$ suffices for the method to estimate neighborhoods consistently. Although this paper focuses on the binary graphical models, we indicate how a generalization of the method of the paper would apply to general discrete Markov random fields.Comment: Published in at http://dx.doi.org/10.1214/09-AOS691 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Comparison of History Effects in Magnetization in Weakly pinned Crystals of high-TcT_c and low-Tc_c Superconductors

A comparison of the history effects in weakly pinned single crystals of a high $T_c$ YBa$_2$Cu$_3$O$_{7 - \delta}$ (for H $\parallel$ c) and a low $T_c$ Ca$_3$Rh$_4$Sn$_{13}$, which show anomalous variations in critical current density $J_c(H)$ are presented via tracings of the minor magnetization hysteresis loops using a vibrating sample magnetometer. The sample histories focussed are, (i) the field cooled (FC), (ii) the zero field cooled (ZFC) and (iii) an isothermal reversal of field from the normal state. An understanding of the results in terms of the modulation in the plastic deformation of the elastic vortex solid and supercooling across order-disorder transition is sought.Comment: Presented in IWCC-200

Violent Hard X-ray Variability of Mrk 421 Observed by NuSTAR in 2013 April

The well studied blazar Markarian 421 (Mrk 421, $z$=0.031) was the subject of an intensive multi-wavelength campaign when it flared in 2013 April. The recorded X-ray and very high energy (VHE, E$>$100 GeV) $\gamma$-ray fluxes are the highest ever measured from this object. At the peak of the activity, it was monitored by the hard X-ray focusing telescope {\it Nuclear Spectroscopic Telescope Array} ({\it NuSTAR}) and {\it Swift} X-Ray Telescope (XRT). In this work, we present a detailed variability analysis of {\it NuSTAR} and {\it Swift}-XRT observations of Mrk 421 during this flaring episode. We obtained the shortest flux doubling time of 14.01$\pm$5.03 minutes, which is the shortest hard X-ray (3$-$79 keV) variability ever recorded from Mrk 421 and is on the order of the light crossing time of the black hole's event horizon. A pattern of extremely fast variability events superposed on slowly varying flares is found in most of the {\it NuSTAR} observations. We suggest that these peculiar variability patterns may be explained by magnetic energy dissipation and reconnection in a fast moving compact emission region within the jet. Based on the fast variability, we derive a lower limit on the magnetic field strength of $B \ge 0.73 \delta_1^{-2/3} \, \nu_{19}^{1/3}$~G, where $\delta_1$ is the Doppler factor in units of 10, and $\nu_{19}$ is the characteristic X-ray synchrotron frequency in units of $10^{19}$~Hz.Comment: 23 pages, 5 figures, 2 tables, to appear in the Astrophysical Journa

A Voting-Based System for Ethical Decision Making

We present a general approach to automating ethical decisions, drawing on machine learning and computational social choice. In a nutshell, we propose to learn a model of societal preferences, and, when faced with a specific ethical dilemma at runtime, efficiently aggregate those preferences to identify a desirable choice. We provide a concrete algorithm that instantiates our approach; some of its crucial steps are informed by a new theory of swap-dominance efficient voting rules. Finally, we implement and evaluate a system for ethical decision making in the autonomous vehicle domain, using preference data collected from 1.3 million people through the Moral Machine website.Comment: 25 pages; paper has been reorganized, related work and discussion sections have been expande

Black Hole Mass Limits for Optically Dark X-ray Bright Sources in Elliptical Galaxies

Estimation of the black hole mass in bright X-ray sources of nearby galaxies is crucial to the understanding of these systems and their formation. However, the present allowed black hole mass range spans five order of magnitude (10Msun < M < 10^5 Msun) with the upper limit obtained from dynamical friction arguments. We show that the absence of a detectable optical counterpart for some of these sources, can provide a much more stringent upper limit. The argument is based only on the assumption that the outer regions of their accretion disks is a standard one. Moreover, such optically dark X-ray sources cannot be foreground stars or background active galactic nuclei, and hence must be accreting systems residing within their host galaxies. As a demonstration we search for candidates among the point-like X-ray sources detected with Chandra in thirteen nearby elliptical galaxies. We use a novel technique to search for faint optical counterparts in the HST images whereby we subtract the bright galaxy light based on isophotal modeling of the surface brightness. We show that for six sources with no detectable optical emission at the 3$-$sigma level, their black hole masses M_{BH} < 5000Msun. In particular, an ultra-luminous X-ray source (ULX) in NGC 4486 has M_{BH} < 1244 Msun. We discuss the potential of this method to provide stringent constraints on the black hole masses, and the implications on the physical nature of these sources.Comment: 11 Pages, 1 figure, Accepted for publication in Ap

Coreference detection of low quality objects

The problem of record linkage is a widely studied problem that aims to identify coreferent (i.e. duplicate) data in a structured data source. As indicated by Winkler, a solution to the record linkage problem is only possible if the error rate is sufficiently low. In other words, in order to succesfully deduplicate a database, the objects in the database must be of sufficient quality. However, this assumption is not always feasible. In this paper, it is investigated how merging of low quality objects into one high quality object can improve the process of record linkage. This general idea is illustrated in the context of strings comparison, where strings of low quality (i.e. with a high typographical error rate) are merged into a string of high quality by using an n-dimensional Levenshtein distance matrix and compute the optimal alignment between the dirty strings. Results are presented and possible refinements are proposed

Minimum and maximum against k lies

A neat 1972 result of Pohl asserts that [3n/2]-2 comparisons are sufficient, and also necessary in the worst case, for finding both the minimum and the maximum of an n-element totally ordered set. The set is accessed via an oracle for pairwise comparisons. More recently, the problem has been studied in the context of the Renyi-Ulam liar games, where the oracle may give up to k false answers. For large k, an upper bound due to Aigner shows that (k+O(\sqrt{k}))n comparisons suffice. We improve on this by providing an algorithm with at most (k+1+C)n+O(k^3) comparisons for some constant C. The known lower bounds are of the form (k+1+c_k)n-D, for some constant D, where c_0=0.5, c_1=23/32=0.71875, and c_k=\Omega(2^{-5k/4}) as k goes to infinity.Comment: 11 pages, 3 figure