20,223 research outputs found
Regression in random design and Bayesian warped wavelets estimators
In this paper we deal with the regression problem in a random design setting.
We investigate asymptotic optimality under minimax point of view of various
Bayesian rules based on warped wavelets and show that they nearly attain
optimal minimax rates of convergence over the Besov smoothness class
considered. Warped wavelets have been introduced recently, they offer very good
computable and easy-to-implement properties while being well adapted to the
statistical problem at hand. We particularly put emphasis on Bayesian rules
leaning on small and large variance Gaussian priors and discuss their
simulation performances comparing them with a hard thresholding procedure
Unsupervised spike detection and sorting with wavelets and superparamagnetic clustering
This study introduces a new method for detecting and sorting spikes from multiunit recordings. The method combines the wavelet transform, which localizes distinctive spike features, with superparamagnetic clustering,
which allows automatic classification of the data without assumptions such as low variance or gaussian distributions. Moreover, an improved method for setting amplitude thresholds for spike detection is proposed. We describe several criteria for implementation that render the algorithm unsupervised and fast. The algorithm is compared to other conventional methods using several simulated data sets whose characteristics closely resemble those of in vivo recordings. For these data sets, we found that
the proposed algorithm outperformed conventional methods
Slope heuristics and V-Fold model selection in heteroscedastic regression using strongly localized bases
We investigate the optimality for model selection of the so-called slope
heuristics, -fold cross-validation and -fold penalization in a
heteroscedastic with random design regression context. We consider a new class
of linear models that we call strongly localized bases and that generalize
histograms, piecewise polynomials and compactly supported wavelets. We derive
sharp oracle inequalities that prove the asymptotic optimality of the slope
heuristics---when the optimal penalty shape is known---and -fold
penalization. Furthermore, -fold cross-validation seems to be suboptimal for
a fixed value of since it recovers asymptotically the oracle learned from a
sample size equal to of the original amount of data. Our results are
based on genuine concentration inequalities for the true and empirical excess
risks that are of independent interest. We show in our experiments the good
behavior of the slope heuristics for the selection of linear wavelet models.
Furthermore, -fold cross-validation and -fold penalization have
comparable efficiency
Prioritized Data Compression using Wavelets
The volume of data and the velocity with which it is being generated by com-
putational experiments on high performance computing (HPC) systems is quickly
outpacing our ability to effectively store this information in its full
fidelity. There- fore, it is critically important to identify and study
compression methodologies that retain as much information as possible,
particularly in the most salient regions of the simulation space. In this
paper, we cast this in terms of a general decision-theoretic problem and
discuss a wavelet-based compression strategy for its solution. We pro- vide a
heuristic argument as justification and illustrate our methodology on several
examples. Finally, we will discuss how our proposed methodology may be utilized
in an HPC environment on large-scale computational experiments
- …