2,083 research outputs found
Stochastic expansions using continuous dictionaries: L\'{e}vy adaptive regression kernels
This article describes a new class of prior distributions for nonparametric
function estimation. The unknown function is modeled as a limit of weighted
sums of kernels or generator functions indexed by continuous parameters that
control local and global features such as their translation, dilation,
modulation and shape. L\'{e}vy random fields and their stochastic integrals are
employed to induce prior distributions for the unknown functions or,
equivalently, for the number of kernels and for the parameters governing their
features. Scaling, shape, and other features of the generating functions are
location-specific to allow quite different function properties in different
parts of the space, as with wavelet bases and other methods employing
overcomplete dictionaries. We provide conditions under which the stochastic
expansions converge in specified Besov or Sobolev norms. Under a Gaussian error
model, this may be viewed as a sparse regression problem, with regularization
induced via the L\'{e}vy random field prior distribution. Posterior inference
for the unknown functions is based on a reversible jump Markov chain Monte
Carlo algorithm. We compare the L\'{e}vy Adaptive Regression Kernel (LARK)
method to wavelet-based methods using some of the standard test functions, and
illustrate its flexibility and adaptability in nonstationary applications.Comment: Published in at http://dx.doi.org/10.1214/11-AOS889 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Classification via local multi-resolution projections
We focus on the supervised binary classification problem, which consists in
guessing the label associated to a co-variate , given a set of
independent and identically distributed co-variates and associated labels
. We assume that the law of the random vector is unknown and
the marginal law of admits a density supported on a set \A. In the
particular case of plug-in classifiers, solving the classification problem
boils down to the estimation of the regression function \eta(X) = \Exp[Y|X].
Assuming first \A to be known, we show how it is possible to construct an
estimator of by localized projections onto a multi-resolution analysis
(MRA). In a second step, we show how this estimation procedure generalizes to
the case where \A is unknown. Interestingly, this novel estimation procedure
presents similar theoretical performances as the celebrated local-polynomial
estimator (LPE). In addition, it benefits from the lattice structure of the
underlying MRA and thus outperforms the LPE from a computational standpoint,
which turns out to be a crucial feature in many practical applications.
Finally, we prove that the associated plug-in classifier can reach super-fast
rates under a margin assumption.Comment: 38 pages, 6 figure
An oil painters recognition method based on cluster multiple kernel learning algorithm
A lot of image processing research works focus on natural images, such as in classification, clustering, and the research on the recognition of artworks (such as oil paintings), from feature extraction to classifier design, is relatively few. This paper focuses on oil painter recognition and tries to find the mobile application to recognize the painter. This paper proposes a cluster multiple kernel learning algorithm, which extracts oil painting features from three aspects: color, texture, and spatial layout, and generates multiple candidate kernels with different kernel functions. With the results of clustering numerous candidate kernels, we selected the sub-kernels with better classification performance, and use the traditional multiple kernel learning algorithm to carry out the multi-feature fusion classification. The algorithm achieves a better result on the Painting91 than using traditional multiple kernel learning directly
Multiariate Wavelet-based sahpe preserving estimation for dependant observation
We present a new approach on shape preserving estimation of probability distribution and density functions using wavelet methodology for multivariate dependent data. Our estimators preserve shape constraints such as monotonicity, positivity and integration to one, and allow for low spatial regularity of the underlying functions. As important application, we discuss conditional quantile estimation for financial time series data. We show that our methodology can be easily implemented with B-splines, and performs well in a finite sample situation, through Monte Carlo simulations.Conditional quantile; time series; shape preserving wavelet estimation; B-splines; multivariate process
Advances in pre-processing and model generation for mass spectrometric data analysis
The analysis of complex signals as obtained by mass spectrometric measurements
is complicated and needs an appropriate representation of the data. Thereby
the kind of preprocessing, feature extraction as well as the used similarity measure
are of particular importance. Focusing on biomarker analysis and taking the
functional nature of the data into account this task is even more complicated.
A new mass spectrometry tailored data preprocessing is shown, discussed and analyzed in
a clinical proteom study compared to a standard setting
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