112 research outputs found
A wavelet characterization for the upper global Holder index
In this paper, we give a wavelet characterization of the upper global Holder
index, which can be seen as the irregular counterpart of the usual global
Holder index, for which a wavelet characterization is well-known
Explicit constructions of operator scaling Gaussian fields
We propose an explicit way to generate a large class of Operator scaling
Gaussian random fields (OSGRF). Such fields are anisotropic generalizations of
selfsimilar fields. More specifically, we are able to construct any Gaussian
field belonging to this class with given Hurst index and exponent. Our
construction provides - for simulations of texture as well as for detection of
anisotropies in an image - a large class of models with controlled anisotropic
geometries and structures
A weak local irregularity property in S^\nu spaces
Although it has been shown that, from the prevalence point of view, the
elements of the S^ \nu spaces are almost surely multifractal, we show here that
they also almost surely satisfy a weak uniform irregularity property
Data driven sampling of oscillating signals
The reduction of the number of samples is a key issue in signal processing
for mobile applications. We investigate the link between the smoothness
properties of a signal and the number of samples that can be obtained through a
level crossing sampling procedure. The algorithm is analyzed and an upper bound
of the number of samples is obtained in the worst case. The theoretical results
are illustrated with applications to fractional Brownian motions and the
Weierstrass function
Large scale reduction principle and application to hypothesis testing
Consider a non--linear function where is a stationary Gaussian
sequence with long--range dependence. The usual reduction principle states that
the partial sums of behave asymptotically like the partial sums of the
first term in the expansion of in Hermite polynomials. In the context of
the wavelet estimation of the long--range dependence parameter, one replaces
the partial sums of by the wavelet scalogram, namely the partial sum
of squares of the wavelet coefficients. Is there a reduction principle in the
wavelet setting, namely is the asymptotic behavior of the scalogram for
the same as that for the first term in the expansion of in Hermite
polynomial? The answer is negative in general. This paper provides a minimal
growth condition on the scales of the wavelet coefficients which ensures that
the reduction principle also holds for the scalogram. The results are applied
to testing the hypothesis that the long-range dependence parameter takes a
specific value
On a Topic Model for Sentences
Probabilistic topic models are generative models that describe the content of
documents by discovering the latent topics underlying them. However, the
structure of the textual input, and for instance the grouping of words in
coherent text spans such as sentences, contains much information which is
generally lost with these models. In this paper, we propose sentenceLDA, an
extension of LDA whose goal is to overcome this limitation by incorporating the
structure of the text in the generative and inference processes. We illustrate
the advantages of sentenceLDA by comparing it with LDA using both intrinsic
(perplexity) and extrinsic (text classification) evaluation tasks on different
text collections
Stein estimation of the intensity of a spatial homogeneous Poisson point process
In this paper, we revisit the original ideas of Stein and propose an
estimator of the intensity parameter of a homogeneous Poisson point process
defined in and observed in a bounded window. The procedure is based on a
new general integration by parts formula for Poisson point processes. We show
that our Stein estimator outperforms the maximum likelihood estimator in terms
of mean squared error. In particular, we show that in many practical situations
we have a gain larger than 30\%
Level crossing sampling of strongly monoHölder functions
http://www.eurasip.org/Proceedings/Ext/SampTA2013/papers/p193-bidegaray-fesquet.pdfInternational audienceWe address the problem of quantifying the number of samples that can be obtained through a level crossing sampling procedure for applications to mobile systems. We specially investigate the link between the smoothness properties of the signal and the number of samples, both from a theoretical and a numerical point of view
Asymptotic behavior of the quadratic variation of the sum of two Hermite processes of consecutive orders
Hermite processes are self--similar processes with stationary increments
which appear as limits of normalized sums of random variables with long range
dependence. The Hermite process of order is fractional Brownian motion and
the Hermite process of order is the Rosenblatt process. We consider here
the sum of two Hermite processes of order and and of different
Hurst parameters. We then study its quadratic variations at different scales.
This is akin to a wavelet decomposition. We study both the cases where the
Hermite processes are dependent and where they are independent. In the
dependent case, we show that the quadratic variation, suitably normalized,
converges either to a normal or to a Rosenblatt distribution, whatever the
order of the original Hermite processes
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