Further Results on the Convergence of the Pavon–Ferrante Algorithm for Spectral Estimation
TLDR
In this paper, the authors provide a detailed analysis of the global convergence properties of an extensively studied and extremely effective fixed-point algorithm for the Kullback-Leibler approximation of spectral densities, proposed by Pavon and Ferrante in their paper.Abstract:
In this paper, we provide a detailed analysis of the global convergence properties of an extensively studied and extremely effective fixed-point algorithm for the Kullback–Leibler approximation of spectral densities, proposed by Pavon and Ferrante in their paper “On the Georgiou–Lindquist approach to constrained Kullback–Leibler approximation of spectral densities.” Our main result states that the algorithm globally converges to one of its fixed points.read more
Citations
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On the Existence of a Solution to a Spectral Estimation Problem à la Byrnes–Georgiou–Lindquist
Bin Zhu,Giacomo Baggio +1 more
TL;DR: In this article, it was shown that a solution indeed exists given an arbitrary matrix-valued prior density, and the main tool in their proof is the topological degree theory, which is used in our proof.
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On the Well-Posedness of a Parametric Spectral Estimation Problem and Its Numerical Solution
TL;DR: In this article, a spectral estimation problem is formulated in a parametric fashion, and the solution parameter depends continuously on the prior function, and a smooth parametrization of admissible spectral densities is obtained.
Journal ArticleDOI
Learning Latent Variable Dynamic Graphical Models by Confidence Sets Selection
TL;DR: A new method is proposed, which accounts for the uncertainty in the estimation by computing a “confidence neighborhood” containing the true model with a prescribed probability, which allows for the presence of a small number of latent variables in order to enforce sparsity of the identified graph.
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On the Uniqueness Result of Theorem 6 in “Relative Entropy and the Multivariable Multidimensional Moment Problem”
TL;DR: In this paper, a moment map defined over a parametric family of spectral densities is shown to have a critical point, namely a point at which the Jacobian loses rank.
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