69,919 research outputs found
Online Nonparametric Anomaly Detection based on Geometric Entropy Minimization
We consider the online and nonparametric detection of abrupt and persistent
anomalies, such as a change in the regular system dynamics at a time instance
due to an anomalous event (e.g., a failure, a malicious activity). Combining
the simplicity of the nonparametric Geometric Entropy Minimization (GEM) method
with the timely detection capability of the Cumulative Sum (CUSUM) algorithm we
propose a computationally efficient online anomaly detection method that is
applicable to high-dimensional datasets, and at the same time achieve a
near-optimum average detection delay performance for a given false alarm
constraint. We provide new insights to both GEM and CUSUM, including new
asymptotic analysis for GEM, which enables soft decisions for outlier
detection, and a novel interpretation of CUSUM in terms of the discrepancy
theory, which helps us generalize it to the nonparametric GEM statistic. We
numerically show, using both simulated and real datasets, that the proposed
nonparametric algorithm attains a close performance to the clairvoyant
parametric CUSUM test.Comment: to appear in IEEE International Symposium on Information Theory
(ISIT) 201
On the Reification of Global Constraints
We introduce a simple idea for deriving reified global constraints in a systematic way. It is based on
the observation that most global constraints can be reformulated as a conjunction of pure functional dependency
constraints together with a constraint that can be easily reified. We first show how the core constraints of the
Global Constraint Catalogue can be reified and we then identify several reification categories that apply to at
least 82% of the constraints in the Global Constraint Catalogue
General theory of the modified Gutenberg-Richter law for large seismic moments
The Gutenberg-Richter power law distribution of earthquake sizes is one of
the most famous example illustrating self-similarity. It is well-known that the
Gutenberg-Richter distribution has to be modified for large seismic moments,
due to energy conservation and geometrical reasons. Several models have been
proposed, either in terms of a second power law with a larger b-value beyond a
cross-over magnitude, or based on a ``hard'' magnitude cut-off or a ``soft''
magnitude cut-off using an exponential taper. Since the large scale tectonic
deformation is dominated by the very largest earthquakes and since their impact
on loss of life and properties is huge, it is of great importance to constrain
as much as possible the shape of their distribution. We present a simple and
powerful probabilistic theoretical approach that shows that the Gamma
distribution is the best model, under the two hypothesis that the
Gutenberg-Richter power law distribution holds in absence of any condition
(condition of criticality) and that one or several constraints are imposed,
either based on conservation laws or on the nature of the observations
themselves. The selection of the Gamma distribution does not depend on the
specific nature of the constraint. We illustrate the approach with two
constraints, the existence of a finite moment release rate and the observation
of the size of a maximum earthquake in a finite catalog. Our predicted ``soft''
maximum magnitudes compare favorably with those obtained by Kagan [1997] for
the Flinn-Engdahl regionalization of subduction zones, collision zones and
mid-ocean ridges.Comment: 24 pages, including 3 tables, in press in Bull. Seism. Soc. A
Bayesian emulation for optimization in multi-step portfolio decisions
We discuss the Bayesian emulation approach to computational solution of
multi-step portfolio studies in financial time series. "Bayesian emulation for
decisions" involves mapping the technical structure of a decision analysis
problem to that of Bayesian inference in a purely synthetic "emulating"
statistical model. This provides access to standard posterior analytic,
simulation and optimization methods that yield indirect solutions of the
decision problem. We develop this in time series portfolio analysis using
classes of economically and psychologically relevant multi-step ahead portfolio
utility functions. Studies with multivariate currency, commodity and stock
index time series illustrate the approach and show some of the practical
utility and benefits of the Bayesian emulation methodology.Comment: 24 pages, 7 figures, 2 table
Probing the circumgalactic baryons through cross-correlations
We study the cross-correlation of distribution of galaxies, the
Sunyaev-Zel'dovich (SZ) and X-ray power spectra of galaxies from current and
upcoming surveys and show these to be excellent probes of the nature, i.e.
extent, evolution and energetics, of the circumgalactic medium (CGM). The
SZ-galaxy cross-power spectrum, especially at large multipoles, depends on the
steepness of the pressure profile of the CGM. This property of the SZ signal
can, thus, be used to constrain the pressure profile of the CGM. The X-ray
cross power spectrum also has a similar shape. However, it is much more
sensitive to the underlying density profile. We forecast the detectability of
the cross-correlated galaxy distribution, SZ and X-ray signals by combining
South Pole Telescope-Dark Energy Survey (SPT-DES) and eROSITA-DES/eROSITA-LSST
(extended ROentgen Survey with an Imaging Telescope Array-Large Synoptic Survey
Telescope) surveys, respectively. We find that, for the SPT-DES survey, the
signal-to-noise ratio (SNR) peaks at high mass and redshift with SNR
around and for flat
density and temperature profiles. The SNR peaks at for the
eROSITA-DES (eROSITA-LSST) surveys. We also perform a Fisher matrix analysis to
find the constraint on the gas fraction in the CGM in the presence or absence
of an unknown redshift evolution of the gas fraction. Finally, we demonstrate
that the cross-correlated SZ-galaxy and X-ray-galaxy power spectrum can be used
as powerful probes of the CGM energetics and potentially discriminate between
different feedback models recently proposed in the literature; for example, one
can distinguish a `no active galactic nuclei feedback' scenario from a CGM
energized by `fixed-velocity hot winds' at greater than .Comment: 14 pages, 10 figures, 4 tables, accepted for publication in MNRA
Resummed Photon Spectra for WIMP Annihilation
We construct an effective field theory (EFT) description of the hard photon
spectrum for heavy WIMP annihilation. This facilitates precision predictions
relevant for line searches, and allows the incorporation of non-trivial energy
resolution effects. Our framework combines techniques from non-relativistic
EFTs and soft-collinear effective theory (SCET), as well as its multi-scale
extensions that have been recently introduced for studying jet substructure. We
find a number of interesting features, including the simultaneous presence of
SCET and SCET modes, as well as collinear-soft modes
at the electroweak scale. We derive a factorization formula that enables both
the resummation of the leading large Sudakov double logarithms that appear in
the perturbative spectrum, and the inclusion of Sommerfeld enhancement effects.
Consistency of this factorization is demonstrated to leading logarithmic order
through explicit calculation. Our final result contains both the exclusive and
the inclusive limits, thereby providing a unifying description of these two
previously-considered approximations. We estimate the impact on experimental
sensitivity, focusing for concreteness on an SU(2) triplet fermion dark
matter - the pure wino - where the strongest constraints are due to a search
for gamma-ray lines from the Galactic Center. We find numerically significant
corrections compared to previous results, thereby highlighting the importance
of accounting for the photon spectrum when interpreting data from current and
future indirect detection experiments.Comment: 55+25 pages, 11+2 figures; v3, updated an expression in the appendix
to make it applicable at higher order - no impact on the results in this wor
An Analysis of the Value of Information when Exploring Stochastic, Discrete Multi-Armed Bandits
In this paper, we propose an information-theoretic exploration strategy for
stochastic, discrete multi-armed bandits that achieves optimal regret. Our
strategy is based on the value of information criterion. This criterion
measures the trade-off between policy information and obtainable rewards. High
amounts of policy information are associated with exploration-dominant searches
of the space and yield high rewards. Low amounts of policy information favor
the exploitation of existing knowledge. Information, in this criterion, is
quantified by a parameter that can be varied during search. We demonstrate that
a simulated-annealing-like update of this parameter, with a sufficiently fast
cooling schedule, leads to an optimal regret that is logarithmic with respect
to the number of episodes.Comment: Entrop
Bayesian model predictive control: Efficient model exploration and regret bounds using posterior sampling
Tight performance specifications in combination with operational constraints
make model predictive control (MPC) the method of choice in various industries.
As the performance of an MPC controller depends on a sufficiently accurate
objective and prediction model of the process, a significant effort in the MPC
design procedure is dedicated to modeling and identification. Driven by the
increasing amount of available system data and advances in the field of machine
learning, data-driven MPC techniques have been developed to facilitate the MPC
controller design. While these methods are able to leverage available data,
they typically do not provide principled mechanisms to automatically trade off
exploitation of available data and exploration to improve and update the
objective and prediction model. To this end, we present a learning-based MPC
formulation using posterior sampling techniques, which provides finite-time
regret bounds on the learning performance while being simple to implement using
off-the-shelf MPC software and algorithms. The performance analysis of the
method is based on posterior sampling theory and its practical efficiency is
illustrated using a numerical example of a highly nonlinear dynamical
car-trailer system
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