10,107 research outputs found
Learning detectors quickly using structured covariance matrices
Computer vision is increasingly becoming interested in the rapid estimation
of object detectors. Canonical hard negative mining strategies are slow as they
require multiple passes of the large negative training set. Recent work has
demonstrated that if the distribution of negative examples is assumed to be
stationary, then Linear Discriminant Analysis (LDA) can learn comparable
detectors without ever revisiting the negative set. Even with this insight,
however, the time to learn a single object detector can still be on the order
of tens of seconds on a modern desktop computer. This paper proposes to
leverage the resulting structured covariance matrix to obtain detectors with
identical performance in orders of magnitude less time and memory. We elucidate
an important connection to the correlation filter literature, demonstrating
that these can also be trained without ever revisiting the negative set
Velocity Dealiased Spectral Estimators of Range Migrating Targets using a Single Low-PRF Wideband Waveform
Wideband radars are promising systems that may provide numerous advantages, like simultaneous detection of slow and fast moving targets, high range-velocity resolution classification, and electronic countermeasures. Unfortunately, classical processing algorithms are challenged by the range-migration phenomenon that occurs then for fast moving targets. We
propose a new approach where the range migration is used rather as an asset to retrieve information about target velocitiesand, subsequently, to obtain a velocity dealiased mode. More specifically three new complex spectral estimators are devised in case of a single low-PRF (pulse repetition frequency) wideband waveform. The new estimation schemes enable one to decrease the
level of sidelobes that arise at ambiguous velocities and, thus, to enhance the discrimination capability of the radar. Synthetic data and experimental data are used to assess the performance of the proposed estimators
A three domain covariance framework for EEG/MEG data
In this paper we introduce a covariance framework for the analysis of EEG and
MEG data that takes into account observed temporal stationarity on small time
scales and trial-to-trial variations. We formulate a model for the covariance
matrix, which is a Kronecker product of three components that correspond to
space, time and epochs/trials, and consider maximum likelihood estimation of
the unknown parameter values. An iterative algorithm that finds approximations
of the maximum likelihood estimates is proposed. We perform a simulation study
to assess the performance of the estimator and investigate the influence of
different assumptions about the covariance factors on the estimated covariance
matrix and on its components. Apart from that, we illustrate our method on real
EEG and MEG data sets.
The proposed covariance model is applicable in a variety of cases where
spontaneous EEG or MEG acts as source of noise and realistic noise covariance
estimates are needed for accurate dipole localization, such as in evoked
activity studies, or where the properties of spontaneous EEG or MEG are
themselves the topic of interest, such as in combined EEG/fMRI experiments in
which the correlation between EEG and fMRI signals is investigated.Comment: 25 pages, 8 figures, 1 tabl
Joint Covariance Estimation with Mutual Linear Structure
We consider the problem of joint estimation of structured covariance
matrices. Assuming the structure is unknown, estimation is achieved using
heterogeneous training sets. Namely, given groups of measurements coming from
centered populations with different covariances, our aim is to determine the
mutual structure of these covariance matrices and estimate them. Supposing that
the covariances span a low dimensional affine subspace in the space of
symmetric matrices, we develop a new efficient algorithm discovering the
structure and using it to improve the estimation. Our technique is based on the
application of principal component analysis in the matrix space. We also derive
an upper performance bound of the proposed algorithm in the Gaussian scenario
and compare it with the Cramer-Rao lower bound. Numerical simulations are
presented to illustrate the performance benefits of the proposed method
Beware of commonly used approximations I: errors in forecasts
In the era of precision cosmology, establishing the correct magnitude of
statistical errors in cosmological parameters is of crucial importance.
However, widely used approximations in galaxy surveys analyses can lead to
parameter uncertainties that are grossly mis-estimated, even in a regime where
the theory is well understood (e.g., linear scales). These approximations can
be introduced at three different levels: in the form of the likelihood, in the
theoretical modelling of the observable and in the numerical computation of the
observable. Their consequences are important both in data analysis through
e.g., Markov Chain Monte Carlo parameter inference, and when survey instrument
and strategy are designed and their constraining power on cosmological
parameters is forecasted, for instance using Fisher matrix analyses. In this
work, considering the galaxy angular power spectrum as the target observable,
we report one example of approximation for each of such three categories:
neglecting off-diagonal terms in the covariance matrix, neglecting cosmic
magnification and using the Limber approximation on large scales. We show that
these commonly used approximations affect the robustness of the analysis and
lead, perhaps counter-intuitively, to unacceptably large mis-estimates of
parameters errors (from few~ up to few~) and correlations.
Furthermore, these approximations might even spoil the benefits of the nascent
multi-tracer and multi-messenger cosmology. Hence we recommend that the type of
analysis presented here should be repeated for every approximation adopted in
survey design or data analysis, to quantify how it may affect the results. To
this aim, we have developed \texttt{Multi\_CLASS}, a new extension of
\texttt{CLASS} that includes the angular power spectrum for multiple (galaxy
and other tracers such as gravitational waves) populations.Comment: 43 pages, 9 figures. Matches the published version.
\texttt{Multi\_CLASS} is now available at
https://github.com/nbellomo/Multi_CLAS
Timescale effect estimation in time-series studies of air pollution and health: A Singular Spectrum Analysis approach
A wealth of epidemiological data suggests an association between
mortality/morbidity from pulmonary and cardiovascular adverse events and air
pollution, but uncertainty remains as to the extent implied by those
associations although the abundance of the data. In this paper we describe an
SSA (Singular Spectrum Analysis) based approach in order to decompose the
time-series of particulate matter concentration into a set of exposure
variables, each one representing a different timescale. We implement our
methodology to investigate both acute and long-term effects of
exposure on morbidity from respiratory causes within the urban area of Bari,
Italy.Comment: Published in at http://dx.doi.org/10.1214/07-EJS123 the Electronic
Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Flexible Bayesian Dynamic Modeling of Correlation and Covariance Matrices
Modeling correlation (and covariance) matrices can be challenging due to the
positive-definiteness constraint and potential high-dimensionality. Our
approach is to decompose the covariance matrix into the correlation and
variance matrices and propose a novel Bayesian framework based on modeling the
correlations as products of unit vectors. By specifying a wide range of
distributions on a sphere (e.g. the squared-Dirichlet distribution), the
proposed approach induces flexible prior distributions for covariance matrices
(that go beyond the commonly used inverse-Wishart prior). For modeling
real-life spatio-temporal processes with complex dependence structures, we
extend our method to dynamic cases and introduce unit-vector Gaussian process
priors in order to capture the evolution of correlation among components of a
multivariate time series. To handle the intractability of the resulting
posterior, we introduce the adaptive -Spherical Hamiltonian Monte
Carlo. We demonstrate the validity and flexibility of our proposed framework in
a simulation study of periodic processes and an analysis of rat's local field
potential activity in a complex sequence memory task.Comment: 49 pages, 15 figure
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