25,642 research outputs found
A Kernel Perspective for Regularizing Deep Neural Networks
We propose a new point of view for regularizing deep neural networks by using
the norm of a reproducing kernel Hilbert space (RKHS). Even though this norm
cannot be computed, it admits upper and lower approximations leading to various
practical strategies. Specifically, this perspective (i) provides a common
umbrella for many existing regularization principles, including spectral norm
and gradient penalties, or adversarial training, (ii) leads to new effective
regularization penalties, and (iii) suggests hybrid strategies combining lower
and upper bounds to get better approximations of the RKHS norm. We
experimentally show this approach to be effective when learning on small
datasets, or to obtain adversarially robust models.Comment: ICM
Advances in Hyperspectral Image Classification: Earth monitoring with statistical learning methods
Hyperspectral images show similar statistical properties to natural grayscale
or color photographic images. However, the classification of hyperspectral
images is more challenging because of the very high dimensionality of the
pixels and the small number of labeled examples typically available for
learning. These peculiarities lead to particular signal processing problems,
mainly characterized by indetermination and complex manifolds. The framework of
statistical learning has gained popularity in the last decade. New methods have
been presented to account for the spatial homogeneity of images, to include
user's interaction via active learning, to take advantage of the manifold
structure with semisupervised learning, to extract and encode invariances, or
to adapt classifiers and image representations to unseen yet similar scenes.
This tutuorial reviews the main advances for hyperspectral remote sensing image
classification through illustrative examples.Comment: IEEE Signal Processing Magazine, 201
Testing the martingale difference hypothesis using integrated regression functions
An omnibus test for testing a generalized version of the martingale difference hypothesis (MDH) is proposed. This generalized hypothesis includes the usual MDH, testing for conditional moments constancy such as conditional homoscedasticity (ARCH effects) or testing for directional predictability. A unified approach for dealing with all of these testing problems is proposed. These hypotheses are long standing problems in econometric time series analysis, and typically have been tested using the sample autocorrelations or in the spectral domain using the periodogram. Since these hypotheses cover also nonlinear predictability, tests based on those second order statistics are inconsistent against uncorrelated processes in the alternative hypothesis. In order to circumvent this problem pairwise integrated regression functions are introduced as measures of linear and nonlinear dependence. The proposed test does not require to chose a lag order depending on sample size, to smooth the data or to formulate a parametric alternative model. Moreover, the test is robust to higher order dependence, in particular to conditional heteroskedasticity. Under general dependence the asymptotic null distribution depends on the data generating process, so a bootstrap procedure is considered and a Monte Carlo study examines its finite sample performance. Then, the martingale and conditional heteroskedasticity properties of the Pound/Dollar exchange rate are investigated.Publicad
Quantile-Based Spectral Analysis in an Object-Oriented Framework and a Reference Implementation in R: The quantspec Package
Quantile-based approaches to the spectral analysis of time series have
recently attracted a lot of attention. Despite a growing literature that
contains various estimation proposals, no systematic methods for computing the
new estimators are available to date. This paper contains two main
contributions. First, an extensible framework for quantile-based spectral
analysis of time series is developed and documented using object-oriented
models. A comprehensive, open source, reference implementation of this
framework, the R package quantspec, was recently contributed to CRAN by the
author of this paper. The second contribution of the present paper is to
provide a detailed tutorial, with worked examples, to this R package. A reader
who is already familiar with quantile-based spectral analysis and whose primary
interest is not the design of the quantspec package, but how to use it, can
read the tutorial and worked examples (Sections 3 and 4) independently.Comment: 27 pages, 11 figures, R package available via CRAN
(http://cran.r-project.org/web/packages/quantspec) or GitHub
(https://github.com/tobiaskley/quantspec
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