109,329 research outputs found
Estimation with Numerical Integration on Sparse Grids
For the estimation of many econometric models, integrals without analytical solutions have to be evaluated. Examples include limited dependent variables and nonlinear panel data models. In the case of one-dimensional integrals, Gaussian quadrature is known to work efficiently for a large class of problems. In higher dimensions, similar approaches discussed in the literature are either very specific and hard to implement or suffer from exponentially rising computational costs in the number of dimensions - a problem known as the "curse of dimensionality" of numerical integration. We propose a strategy that shares the advantages of Gaussian quadrature methods, is very general and easily implemented, and does not suffer from the curse of dimensionality. Monte Carlo experiments for the random parameters logit model indicate the superior performance of the proposed method over simulation techniques
Detecting and quantifying stellar magnetic fields -- Sparse Stokes profile approximation using orthogonal matching pursuit
In the recent years, we have seen a rapidly growing number of stellar
magnetic field detections for various types of stars. Many of these magnetic
fields are estimated from spectropolarimetric observations (Stokes V) by using
the so-called center-of-gravity (COG) method. Unfortunately, the accuracy of
this method rapidly deteriorates with increasing noise and thus calls for a
more robust procedure that combines signal detection and field estimation. We
introduce an estimation method that provides not only the effective or mean
longitudinal magnetic field from an observed Stokes V profile but also uses the
net absolute polarization of the profile to obtain an estimate of the apparent
(i.e., velocity resolved) absolute longitudinal magnetic field. By combining
the COG method with an orthogonal-matching-pursuit (OMP) approach, we were able
to decompose observed Stokes profiles with an overcomplete dictionary of
wavelet-basis functions to reliably reconstruct the observed Stokes profiles in
the presence of noise. The elementary wave functions of the sparse
reconstruction process were utilized to estimate the effective longitudinal
magnetic field and the apparent absolute longitudinal magnetic field. A
multiresolution analysis complements the OMP algorithm to provide a robust
detection and estimation method. An extensive Monte-Carlo simulation confirms
the reliability and accuracy of the magnetic OMP approach.Comment: A&A, in press, 15 pages, 14 figure
Learning Compositional Sparse Gaussian Processes with a Shrinkage Prior
Choosing a proper set of kernel functions is an important problem in learning
Gaussian Process (GP) models since each kernel structure has different model
complexity and data fitness. Recently, automatic kernel composition methods
provide not only accurate prediction but also attractive interpretability
through search-based methods. However, existing methods suffer from slow kernel
composition learning. To tackle large-scaled data, we propose a new sparse
approximate posterior for GPs, MultiSVGP, constructed from groups of inducing
points associated with individual additive kernels in compositional kernels. We
demonstrate that this approximation provides a better fit to learn
compositional kernels given empirical observations. We also provide
theoretically justification on error bound when compared to the traditional
sparse GP. In contrast to the search-based approach, we present a novel
probabilistic algorithm to learn a kernel composition by handling the sparsity
in the kernel selection with Horseshoe prior. We demonstrate that our model can
capture characteristics of time series with significant reductions in
computational time and have competitive regression performance on real-world
data sets.Comment: AAAI 202
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