1,313 research outputs found
A Semi-Parametric Approach to the Detection of Non-Gaussian Gravitational Wave Stochastic Backgrounds
Using a semi-parametric approach based on the fourth-order Edgeworth
expansion for the unknown signal distribution, we derive an explicit expression
for the likelihood detection statistic in the presence of non-normally
distributed gravitational wave stochastic backgrounds. Numerical likelihood
maximization exercises based on Monte-Carlo simulations for a set of large tail
symmetric non-Gaussian distributions suggest that the fourth cumulant of the
signal distribution can be estimated with reasonable precision when the ratio
between the signal and the noise variances is larger than 0.01. The estimation
of higher-order cumulants of the observed gravitational wave signal
distribution is expected to provide additional constraints on astrophysical and
cosmological models.Comment: 26 pages, 3 figures, to appear in Phys. Rev.
Rethinking LDA: moment matching for discrete ICA
We consider moment matching techniques for estimation in Latent Dirichlet
Allocation (LDA). By drawing explicit links between LDA and discrete versions
of independent component analysis (ICA), we first derive a new set of
cumulant-based tensors, with an improved sample complexity. Moreover, we reuse
standard ICA techniques such as joint diagonalization of tensors to improve
over existing methods based on the tensor power method. In an extensive set of
experiments on both synthetic and real datasets, we show that our new
combination of tensors and orthogonal joint diagonalization techniques
outperforms existing moment matching methods.Comment: 30 pages; added plate diagrams and clarifications, changed style,
corrected typos, updated figures. in Proceedings of the 29-th Conference on
Neural Information Processing Systems (NIPS), 201
Fourier PCA and Robust Tensor Decomposition
Fourier PCA is Principal Component Analysis of a matrix obtained from higher
order derivatives of the logarithm of the Fourier transform of a
distribution.We make this method algorithmic by developing a tensor
decomposition method for a pair of tensors sharing the same vectors in rank-
decompositions. Our main application is the first provably polynomial-time
algorithm for underdetermined ICA, i.e., learning an matrix
from observations where is drawn from an unknown product
distribution with arbitrary non-Gaussian components. The number of component
distributions can be arbitrarily higher than the dimension and the
columns of only need to satisfy a natural and efficiently verifiable
nondegeneracy condition. As a second application, we give an alternative
algorithm for learning mixtures of spherical Gaussians with linearly
independent means. These results also hold in the presence of Gaussian noise.Comment: Extensively revised; details added; minor errors corrected;
exposition improve
Non-Independent Components Analysis
A seminal result in the ICA literature states that for , if
the components of are independent and at most one is Gaussian,
then is identified up to sign and permutation of its rows (Comon, 1994). In
this paper we study to which extent the independence assumption can be relaxed
by replacing it with restrictions on higher order moment or cumulant tensors of
. We document new conditions that establish identification for
several non-independent component models, e.g. common variance models, and
propose efficient estimation methods based on the identification results. We
show that in situations where independence cannot be assumed the efficiency
gains can be significant relative to methods that rely on independence
Spectral estimation for mixed causal-noncausal autoregressive models
This paper investigates new ways of estimating and identifying causal,
noncausal, and mixed causal-noncausal autoregressive models driven by a
non-Gaussian error sequence. We do not assume any parametric distribution
function for the innovations. Instead, we use the information of higher-order
cumulants, combining the spectrum and the bispectrum in a minimum distance
estimation. We show how to circumvent the nonlinearity of the parameters and
the multimodality in the noncausal and mixed models by selecting the
appropriate initial values in the estimation. In addition, we propose a method
of identification using a simple comparison criterion based on the global
minimum of the estimation function. By means of a Monte Carlo study, we find
unbiased estimated parameters and a correct identification as the data depart
from normality. We propose an empirical application on eight monthly commodity
prices, finding noncausal and mixed causal-noncausal dynamics
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