20,269 research outputs found
Asymmetric Pruning for Learning Cascade Detectors
Cascade classifiers are one of the most important contributions to real-time
object detection. Nonetheless, there are many challenging problems arising in
training cascade detectors. One common issue is that the node classifier is
trained with a symmetric classifier. Having a low misclassification error rate
does not guarantee an optimal node learning goal in cascade classifiers, i.e.,
an extremely high detection rate with a moderate false positive rate. In this
work, we present a new approach to train an effective node classifier in a
cascade detector. The algorithm is based on two key observations: 1) Redundant
weak classifiers can be safely discarded; 2) The final detector should satisfy
the asymmetric learning objective of the cascade architecture. To achieve this,
we separate the classifier training into two steps: finding a pool of
discriminative weak classifiers/features and training the final classifier by
pruning weak classifiers which contribute little to the asymmetric learning
criterion (asymmetric classifier construction). Our model reduction approach
helps accelerate the learning time while achieving the pre-determined learning
objective. Experimental results on both face and car data sets verify the
effectiveness of the proposed algorithm. On the FDDB face data sets, our
approach achieves the state-of-the-art performance, which demonstrates the
advantage of our approach.Comment: 14 page
Exploring short gamma-ray bursts as gravitational-wave standard sirens
Recent observations support the hypothesis that a large fraction of
"short-hard" gamma-ray bursts (SHBs) are associated with compact binary
inspiral. Since gravitational-wave (GW) measurements of well-localized
inspiraling binaries can measure absolute source distances, simultaneous
observation of a binary's GWs and SHB would allow us to independently determine
both its luminosity distance and redshift. Such a "standard siren" (the GW
analog of a standard candle) would provide an excellent probe of the relatively
nearby universe's expansion, complementing other standard candles. In this
paper, we examine binary measurement using a Markov Chain Monte Carlo technique
to build the probability distributions describing measured parameters. We
assume that each SHB observation gives both sky position and the time of
coalescence, and we take both binary neutron stars and black hole-neutron star
coalescences as plausible SHB progenitors. We examine how well parameters
particularly distance) can be measured from GW observations of SHBs by a range
of ground-based detector networks. We find that earlier estimates overstate how
well distances can be measured, even at fairly large signal-to-noise ratio. The
fundamental limitation to determining distance proves to be a degeneracy
between distance and source inclination. Overcoming this limitation requires
that we either break this degeneracy, or measure enough sources to broadly
sample the inclination distribution. (Abridged)Comment: 19 pages, 10 figures. Accepted for publication in ApJ; this version
incorporates referee's comments and criticism
Aperture synthesis for gravitational-wave data analysis: Deterministic Sources
Gravitational wave detectors now under construction are sensitive to the
phase of the incident gravitational waves. Correspondingly, the signals from
the different detectors can be combined, in the analysis, to simulate a single
detector of greater amplitude and directional sensitivity: in short, aperture
synthesis. Here we consider the problem of aperture synthesis in the special
case of a search for a source whose waveform is known in detail: \textit{e.g.,}
compact binary inspiral. We derive the likelihood function for joint output of
several detectors as a function of the parameters that describe the signal and
find the optimal matched filter for the detection of the known signal. Our
results allow for the presence of noise that is correlated between the several
detectors. While their derivation is specialized to the case of Gaussian noise
we show that the results obtained are, in fact, appropriate in a well-defined,
information-theoretic sense even when the noise is non-Gaussian in character.
The analysis described here stands in distinction to ``coincidence
analyses'', wherein the data from each of several detectors is studied in
isolation to produce a list of candidate events, which are then compared to
search for coincidences that might indicate common origin in a gravitational
wave signal. We compare these two analyses --- optimal filtering and
coincidence --- in a series of numerical examples, showing that the optimal
filtering analysis always yields a greater detection efficiency for given false
alarm rate, even when the detector noise is strongly non-Gaussian.Comment: 39 pages, 4 figures, submitted to Phys. Rev.
Null stream analysis of Pulsar Timing Array data: localisation of resolvable gravitational wave sources
Super-massive black hole binaries are expected to produce a GW signal in the
nano-Hertz frequency band which may be detected by PTAs in the coming years.
The signal is composed of both stochastic and individually resolvable
components. Here we develop a generic Bayesian method for the analysis of
resolvable sources based on the construction of `null-streams' which cancel the
part of the signal held in common for each pulsar (the Earth-term). For an
array of pulsars there are independent null-streams that cancel the
GW signal from a particular sky location. This method is applied to the
localisation of quasi-circular binaries undergoing adiabatic inspiral. We carry
out a systematic investigation of the scaling of the localisation accuracy with
signal strength and number of pulsars in the PTA. Additionally, we find that
source sky localisation with the International PTA data release one is vastly
superior than what is achieved by its constituent regional PTAs.Comment: 13 pages, 7 figures, 1 appendix. Edited Figures 5, 6, 7 due to a bug
in the plotting script (results unchanged). Additional edit to fix a type in
equation
A learning approach to the detection of gravitational wave transients
We investigate the class of quadratic detectors (i.e., the statistic is a
bilinear function of the data) for the detection of poorly modeled
gravitational transients of short duration. We point out that all such
detection methods are equivalent to passing the signal through a filter bank
and linearly combine the output energy. Existing methods for the choice of the
filter bank and of the weight parameters rely essentially on the two following
ideas: (i) the use of the likelihood function based on a (possibly
non-informative) statistical model of the signal and the noise, (ii) the use of
Monte-Carlo simulations for the tuning of parametric filters to get the best
detection probability keeping fixed the false alarm rate. We propose a third
approach according to which the filter bank is "learned" from a set of training
data. By-products of this viewpoint are that, contrarily to previous methods,
(i) there is no requirement of an explicit description of the probability
density function of the data when the signal is present and (ii) the filters we
use are non-parametric. The learning procedure may be described as a two step
process: first, estimate the mean and covariance of the signal with the
training data; second, find the filters which maximize a contrast criterion
referred to as deflection between the "noise only" and "signal+noise"
hypothesis. The deflection is homogeneous to the signal-to-noise ratio and it
uses the quantities estimated at the first step. We apply this original method
to the problem of the detection of supernovae core collapses. We use the
catalog of waveforms provided recently by Dimmelmeier et al. to train our
algorithm. We expect such detector to have better performances on this
particular problem provided that the reference signals are reliable.Comment: 22 pages, 4 figure
The optimal search for an astrophysical gravitational-wave background
Roughly every 2-10 minutes, a pair of stellar mass black holes merge
somewhere in the Universe. A small fraction of these mergers are detected as
individually resolvable gravitational-wave events by advanced detectors such as
LIGO and Virgo. The rest contribute to a stochastic background. We derive the
statistically optimal search strategy for a background of unresolved binaries.
Our method applies Bayesian parameter estimation to all available data. Using
Monte Carlo simulations, we demonstrate that the search is both "safe" and
effective: it is not fooled by instrumental artefacts such as glitches, and it
recovers simulated stochastic signals without bias. Given realistic
assumptions, we estimate that the search can detect the binary black hole
background with about one day of design sensitivity data versus
months using the traditional cross-correlation search. This framework
independently constrains the merger rate and black hole mass distribution,
breaking a degeneracy present in the cross-correlation approach. The search
provides a unified framework for population studies of compact binaries, which
is cast in terms of hyper-parameter estimation. We discuss a number of
extensions and generalizations including: application to other sources (such as
binary neutron stars and continuous-wave sources), simultaneous estimation of a
continuous Gaussian background, and applications to pulsar timing.Comment: 16 pages, 9 figure
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