7,303 research outputs found
A hybrid neuro--wavelet predictor for QoS control and stability
For distributed systems to properly react to peaks of requests, their
adaptation activities would benefit from the estimation of the amount of
requests. This paper proposes a solution to produce a short-term forecast based
on data characterising user behaviour of online services. We use \emph{wavelet
analysis}, providing compression and denoising on the observed time series of
the amount of past user requests; and a \emph{recurrent neural network} trained
with observed data and designed so as to provide well-timed estimations of
future requests. The said ensemble has the ability to predict the amount of
future user requests with a root mean squared error below 0.06\%. Thanks to
prediction, advance resource provision can be performed for the duration of a
request peak and for just the right amount of resources, hence avoiding
over-provisioning and associated costs. Moreover, reliable provision lets users
enjoy a level of availability of services unaffected by load variations
Sampling and Reconstruction of Sparse Signals on Circulant Graphs - An Introduction to Graph-FRI
With the objective of employing graphs toward a more generalized theory of
signal processing, we present a novel sampling framework for (wavelet-)sparse
signals defined on circulant graphs which extends basic properties of Finite
Rate of Innovation (FRI) theory to the graph domain, and can be applied to
arbitrary graphs via suitable approximation schemes. At its core, the
introduced Graph-FRI-framework states that any K-sparse signal on the vertices
of a circulant graph can be perfectly reconstructed from its
dimensionality-reduced representation in the graph spectral domain, the Graph
Fourier Transform (GFT), of minimum size 2K. By leveraging the recently
developed theory of e-splines and e-spline wavelets on graphs, one can
decompose this graph spectral transformation into the multiresolution low-pass
filtering operation with a graph e-spline filter, and subsequent transformation
to the spectral graph domain; this allows to infer a distinct sampling pattern,
and, ultimately, the structure of an associated coarsened graph, which
preserves essential properties of the original, including circularity and,
where applicable, the graph generating set.Comment: To appear in Appl. Comput. Harmon. Anal. (2017
Nonparametric methods for volatility density estimation
Stochastic volatility modelling of financial processes has become
increasingly popular. The proposed models usually contain a stationary
volatility process. We will motivate and review several nonparametric methods
for estimation of the density of the volatility process. Both models based on
discretely sampled continuous time processes and discrete time models will be
discussed.
The key insight for the analysis is a transformation of the volatility
density estimation problem to a deconvolution model for which standard methods
exist. Three type of nonparametric density estimators are reviewed: the
Fourier-type deconvolution kernel density estimator, a wavelet deconvolution
density estimator and a penalized projection estimator. The performance of
these estimators will be compared. Key words: stochastic volatility models,
deconvolution, density estimation, kernel estimator, wavelets, minimum contrast
estimation, mixin
Short-time homomorphic wavelet estimation
Successful wavelet estimation is an essential step for seismic methods like
impedance inversion, analysis of amplitude variations with offset and full
waveform inversion. Homomorphic deconvolution has long intrigued as a
potentially elegant solution to the wavelet estimation problem. Yet a
successful implementation has proven difficult. Associated disadvantages like
phase unwrapping and restrictions of sparsity in the reflectivity function
limit its application. We explore short-time homomorphic wavelet estimation as
a combination of the classical homomorphic analysis and log-spectral averaging.
The introduced method of log-spectral averaging using a short-term Fourier
transform increases the number of sample points, thus reducing estimation
variances. We apply the developed method on synthetic and real data examples
and demonstrate good performance.Comment: 13 pages, 5 figures. 2012 J. Geophys. Eng. 9 67
Adaptive variance function estimation in heteroscedastic nonparametric regression
We consider a wavelet thresholding approach to adaptive variance function
estimation in heteroscedastic nonparametric regression. A data-driven estimator
is constructed by applying wavelet thresholding to the squared first-order
differences of the observations. We show that the variance function estimator
is nearly optimally adaptive to the smoothness of both the mean and variance
functions. The estimator is shown to achieve the optimal adaptive rate of
convergence under the pointwise squared error simultaneously over a range of
smoothness classes. The estimator is also adaptively within a logarithmic
factor of the minimax risk under the global mean integrated squared error over
a collection of spatially inhomogeneous function classes. Numerical
implementation and simulation results are also discussed.Comment: Published in at http://dx.doi.org/10.1214/07-AOS509 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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