119,338 research outputs found
Robust Subspace Tracking Algorithms in Signal Processing: A Brief Survey
Principal component analysis (PCA) and subspace estimation (SE) are popular data analysis tools and used in a wide range of applications. The main interest in PCA/SE is for dimensionality reduction and low-rank approximation purposes. The emergence of big data streams have led to several essential issues for performing PCA/SE. Among them are (i) the size of such data streams increases over time, (ii) the underlying models may be time-dependent, and (iii) problem of dealing with the uncertainty and incompleteness in data. A robust variant of PCA/SE for such data streams, namely robust online PCA or robust subspace tracking (RST), has been introduced as a good alternative. The main goal of this paper is to provide a brief survey on recent RST algorithms in signal processing. Particularly, we begin this survey by introducing the basic ideas of the RST problem. Then, different aspects of RST are reviewed with respect to different kinds of non-Gaussian noises and sparse constraints. Our own contributions on this topic are also highlighted
Finite sample theory for high-dimensional functional/scalar time series with applications
Statistical analysis of high-dimensional functional times series arises in various applications. Under this scenario, in addition to the intrinsic infinite-dimensionality of functional data, the number of functional variables can grow with the number of serially dependent observations. In this paper, we focus on the theoretical analysis of relevant estimated cross-(auto)covariance terms between two multivariate functional time series or a mixture of multivariate functional and scalar time series beyond the Gaussianity assumption. We introduce a new perspective on dependence by proposing functional cross-spectral stability measure to characterize the effect of dependence on these estimated cross terms, which are essential in the estimates for additive functional linear regressions. With the proposed functional cross-spectral stability measure, we develop useful concentration inequalities for estimated cross-(auto)covariance matrix functions to accommodate more general sub-Gaussian functional linear processes and, furthermore, establish finite sample theory for relevant estimated terms under a commonly adopted functional principal component analysis framework. Using our derived non-asymptotic results, we investigate the convergence properties of the regularized estimates for two additive functional linear regression applications under sparsity assumptions including functional linear lagged regression and partially functional linear regression in the context of high-dimensional functional/scalar time series
Constraining Scale-Dependent Non-Gaussianity with Future Large-Scale Structure and the CMB
We forecast combined future constraints from the cosmic microwave background
and large-scale structure on the models of primordial non-Gaussianity. We study
the generalized local model of non-Gaussianity, where the parameter f_NL is
promoted to a function of scale, and present the principal component analysis
applicable to an arbitrary form of f_NL(k). We emphasize the complementarity
between the CMB and LSS by using Planck, DES and BigBOSS surveys as examples,
forecast constraints on the power-law f_NL(k) model, and introduce the figure
of merit for measurements of scale-dependent non-Gaussianity.Comment: 28 pages, 8 figures, 2 tables; v2: references update
Scale-Dependent Non-Gaussianity as a Generalization of the Local Model
We generalize the local model of primordial non-Gaussianity by promoting the
parameter fNL to a general scale-dependent function fNL(k). We calculate the
resulting bispectrum and the effect on the bias of dark matter halos, and thus
the extent to which fNL(k) can be measured from the large-scale structure
observations. By calculating the principal components of fNL(k), we identify
scales where this form of non-Gaussianity is best constrained and estimate the
overlap with previously studied local and equilateral non-Gaussian models.Comment: Accepted to JCAP. 22 pages, 4 figure
Evidence for the accelerated expansion of the Universe from weak lensing tomography with COSMOS
We present a tomographic cosmological weak lensing analysis of the HST COSMOS
Survey. Applying our lensing-optimized data reduction, principal component
interpolation for the ACS PSF, and improved modelling of charge-transfer
inefficiency, we measure a lensing signal which is consistent with pure
gravitational modes and no significant shape systematics. We carefully estimate
the statistical uncertainty from simulated COSMOS-like fields obtained from
ray-tracing through the Millennium Simulation. We test our pipeline on
simulated space-based data, recalibrate non-linear power spectrum corrections
using the ray-tracing, employ photometric redshifts to reduce potential
contamination by intrinsic galaxy alignments, and marginalize over systematic
uncertainties. We find that the lensing signal scales with redshift as expected
from General Relativity for a concordance LCDM cosmology, including the full
cross-correlations between different redshift bins. For a flat LCDM cosmology,
we measure sigma_8(Omega_m/0.3)^0.51=0.75+-0.08 from lensing, in perfect
agreement with WMAP-5, yielding joint constraints Omega_m=0.266+0.025-0.023,
sigma_8=0.802+0.028-0.029 (all 68% conf.). Dropping the assumption of flatness
and using HST Key Project and BBN priors only, we find a negative deceleration
parameter q_0 at 94.3% conf. from the tomographic lensing analysis, providing
independent evidence for the accelerated expansion of the Universe. For a flat
wCDM cosmology and prior w in [-2,0], we obtain w<-0.41 (90% conf.). Our dark
energy constraints are still relatively weak solely due to the limited area of
COSMOS. However, they provide an important demonstration for the usefulness of
tomographic weak lensing measurements from space. (abridged)Comment: 26 pages, 25 figures, matches version accepted for publication by
Astronomy and Astrophysic
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