315 research outputs found
Belief Propagation for Linear Programming
Belief Propagation (BP) is a popular, distributed heuristic for performing
MAP computations in Graphical Models. BP can be interpreted, from a variational
perspective, as minimizing the Bethe Free Energy (BFE). BP can also be used to
solve a special class of Linear Programming (LP) problems. For this class of
problems, MAP inference can be stated as an integer LP with an LP relaxation
that coincides with minimization of the BFE at ``zero temperature". We
generalize these prior results and establish a tight characterization of the LP
problems that can be formulated as an equivalent LP relaxation of MAP
inference. Moreover, we suggest an efficient, iterative annealing BP algorithm
for solving this broader class of LP problems. We demonstrate the algorithm's
performance on a set of weighted matching problems by using it as a cutting
plane method to solve a sequence of LPs tightened by adding ``blossom''
inequalities.Comment: To appear in ISIT 201
Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets
Spatial process models for analyzing geostatistical data entail computations
that become prohibitive as the number of spatial locations become large. This
manuscript develops a class of highly scalable Nearest Neighbor Gaussian
Process (NNGP) models to provide fully model-based inference for large
geostatistical datasets. We establish that the NNGP is a well-defined spatial
process providing legitimate finite-dimensional Gaussian densities with sparse
precision matrices. We embed the NNGP as a sparsity-inducing prior within a
rich hierarchical modeling framework and outline how computationally efficient
Markov chain Monte Carlo (MCMC) algorithms can be executed without storing or
decomposing large matrices. The floating point operations (flops) per iteration
of this algorithm is linear in the number of spatial locations, thereby
rendering substantial scalability. We illustrate the computational and
inferential benefits of the NNGP over competing methods using simulation
studies and also analyze forest biomass from a massive United States Forest
Inventory dataset at a scale that precludes alternative dimension-reducing
methods
Modeling large scale species abundance with latent spatial processes
Modeling species abundance patterns using local environmental features is an
important, current problem in ecology. The Cape Floristic Region (CFR) in South
Africa is a global hot spot of diversity and endemism, and provides a rich
class of species abundance data for such modeling. Here, we propose a
multi-stage Bayesian hierarchical model for explaining species abundance over
this region. Our model is specified at areal level, where the CFR is divided
into roughly one minute grid cells; species abundance is observed at
some locations within some cells. The abundance values are ordinally
categorized. Environmental and soil-type factors, likely to influence the
abundance pattern, are included in the model. We formulate the empirical
abundance pattern as a degraded version of the potential pattern, with the
degradation effect accomplished in two stages. First, we adjust for land use
transformation and then we adjust for measurement error, hence
misclassification error, to yield the observed abundance classifications. An
important point in this analysis is that only of the grid cells have been
sampled and that, for sampled grid cells, the number of sampled locations
ranges from one to more than one hundred. Still, we are able to develop
potential and transformed abundance surfaces over the entire region. In the
hierarchical framework, categorical abundance classifications are induced by
continuous latent surfaces. The degradation model above is built on the latent
scale. On this scale, an areal level spatial regression model was used for
modeling the dependence of species abundance on the environmental factors.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS335 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
spBayes for Large Univariate and Multivariate Point-Referenced Spatio-Temporal Data Models
In this paper we detail the reformulation and rewrite of core functions in the spBayes R package. These efforts have focused on improving computational efficiency, flexibility, and usability for point-referenced data models. Attention is given to algorithm and computing developments that result in improved sampler convergence rate and efficiency by reducing parameter space; decreased sampler run-time by avoiding expensive matrix computations, and; increased scalability to large datasets by implementing a class of predictive process models that attempt to overcome computational hurdles by representing spatial processes in terms of lower-dimensional realizations. Beyond these general computational improvements for existing model functions, we detail new functions for modeling data indexed in both space and time. These new functions implement a class of dynamic spatio-temporal models for settings where space is viewed as continuous and time is taken as discrete
Three-Dimensional Relativistic MHD Simulations of the Kelvin-Helmholtz Instability: Magnetic Field Amplification by a Turbulent Dynamo
Magnetic field strengths inferred for relativistic outflows including
gamma-ray bursts (GRB) and active galactic nuclei (AGN) are larger than naively
expected by orders of magnitude. We present three-dimensional relativistic
magnetohydrodynamics (MHD) simulations demonstrating amplification and
saturation of magnetic field by a macroscopic turbulent dynamo triggered by the
Kelvin-Helmholtz shear instability. We find rapid growth of electromagnetic
energy due to the stretching and folding of field lines in the turbulent
velocity field resulting from non-linear development of the instability. Using
conditions relevant for GRB internal shocks and late phases of GRB afterglow,
we obtain amplification of the electromagnetic energy fraction to . This value decays slowly after the shear is dissipated
and appears to be largely independent of the initial field strength. The
conditions required for operation of the dynamo are the presence of velocity
shear and some seed magnetization both of which are expected to be commonplace.
We also find that the turbulent kinetic energy spectrum for the case studied
obeys Kolmogorov's 5/3 law and that the electromagnetic energy spectrum is
essentially flat with the bulk of the electromagnetic energy at small scales.Comment: accepted for publication in ApJL; high-resolution version available
at http://cosmo.nyu.edu/~wqzhang/publications/kh.pdf; movies of simulations
available at http://cosmo.nyu.edu/~wqzhang/movies
Optical Discovery of Probable Stellar Tidal Disruption Flares
Using archival Sloan Digital Sky Survey (SDSS) multi-epoch imaging data (Stripe 82), we have searched for the tidal disruption of stars by supermassive black holes in non-active galaxies. Two candidate tidal disruption events (TDEs) are identified. The TDE flares have optical blackbody temperatures of 2 × 10^4 K and observed peak luminosities of M_g = –18.3 and –20.4 (νL_ν = 5 × 10^(42), 4 × 10^(43) erg s^(–1), in the rest frame); their cooling rates are very low, qualitatively consistent with expectations for tidal disruption flares. The properties of the TDE candidates are examined using (1) SDSS imaging to compare them to other flares observed in the search, (2) UV emission measured by GALEX, and (3) spectra of the hosts and of one of the flares. Our pipeline excludes optically identifiable AGN hosts, and our variability monitoring over nine years provides strong evidence that these are not flares in hidden AGNs. The spectra and color evolution of the flares are unlike any SN observed to date, their strong late-time UV emission is particularly distinctive, and they are nuclear at high resolution arguing against these being first cases of a previously unobserved class of SNe or more extreme examples of known SN types. Taken together, the observed properties are difficult to reconcile with an SN or an AGN-flare explanation, although an entirely new process specific to the inner few hundred parsecs of non-active galaxies cannot be excluded. Based on our observed rate, we infer that hundreds or thousands of TDEs will be present in current and next-generation optical synoptic surveys. Using the approach outlined here, a TDE candidate sample with O(1) purity can be selected using geometric resolution and host and flare color alone, demonstrating that a campaign to create a large sample of TDEs, with immediate and detailed multi-wavelength follow-up, is feasible. A by-product of this work is quantification of the power spectrum of extreme flares in AGNs
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