2,976 research outputs found
Inertial Stochastic PALM (iSPALM) and Applications in Machine Learning
Inertial algorithms for minimizing nonsmooth and nonconvex functions as the
inertial proximal alternating linearized minimization algorithm (iPALM) have
demonstrated their superiority with respect to computation time over their non
inertial variants. In many problems in imaging and machine learning, the
objective functions have a special form involving huge data which encourage the
application of stochastic algorithms. While algorithms based on stochastic
gradient descent are still used in the majority of applications, recently also
stochastic algorithms for minimizing nonsmooth and nonconvex functions were
proposed. In this paper, we derive an inertial variant of a stochastic PALM
algorithm with variance-reduced gradient estimator, called iSPALM, and prove
linear convergence of the algorithm under certain assumptions. Our inertial
approach can be seen as generalization of momentum methods widely used to speed
up and stabilize optimization algorithms, in particular in machine learning, to
nonsmooth problems. Numerical experiments for learning the weights of a
so-called proximal neural network and the parameters of Student-t mixture
models show that our new algorithm outperforms both stochastic PALM and its
deterministic counterparts
Coming and leaving. Internal mobility in late Imperial Austria.
The paper investigates the determinants of internal migration within late imperial Austria. In contrast to the modernization paradigm which studies onedirectional migration flows from rural to urban areas, our approach highlights that spatial mobility consisted of movements in both directions. Using data on all districts of the Austrian part of the Hapsburg Monarchy, we find that in- and outmigration rates are positively correlated, and that the modernization paradigm in migration research is consistent with our results for net-migration rates, but inconsistent with those for out-migration. (author's abstract)Series: Department of Economics Working Paper Serie
Nonlocal Myriad Filters for Cauchy Noise Removal
The contribution of this paper is two-fold. First, we introduce a generalized
myriad filter, which is a method to compute the joint maximum likelihood
estimator of the location and the scale parameter of the Cauchy distribution.
Estimating only the location parameter is known as myriad filter. We propose an
efficient algorithm to compute the generalized myriad filter and prove its
convergence. Special cases of this algorithm result in the classical myriad
filtering, respective an algorithm for estimating only the scale parameter.
Based on an asymptotic analysis, we develop a second, even faster generalized
myriad filtering technique.
Second, we use our new approaches within a nonlocal, fully unsupervised
method to denoise images corrupted by Cauchy noise. Special attention is paid
to the determination of similar patches in noisy images. Numerical examples
demonstrate the excellent performance of our algorithms which have moreover the
advantage to be robust with respect to the parameter choice
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