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Geometric Shrinkage Priors for Kählerian Signal Filters
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Entropy 2015, 17(4), 1581-1605;

Kählerian Information Geometry for Signal Processing

Department of Applied Mathematics and Statistics, The State University of New York (SUNY), StonyBrook, NY 11794, USA
This paper is an extended version of our paper published in MaxEnt 2014, Amboise, France, 21–26 September 2014.
Author to whom correspondence should be addressed.
Received: 16 January 2015 / Revised: 13 March 2015 / Accepted: 20 March 2015 / Published: 25 March 2015
(This article belongs to the Special Issue Information, Entropy and Their Geometric Structures)
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We prove the correspondence between the information geometry of a signal filter and a Kähler manifold. The information geometry of a minimum-phase linear system with a finite complex cepstrum norm is a Kähler manifold. The square of the complex cepstrum norm of the signal filter corresponds to the Kähler potential. The Hermitian structure of the Kähler manifold is explicitly emergent if and only if the impulse response function of the highest degree in z is constant in model parameters. The Kählerian information geometry takes advantage of more efficient calculation steps for the metric tensor and the Ricci tensor. Moreover, α-generalization on the geometric tensors is linear in α . It is also robust to find Bayesian predictive priors, such as superharmonic priors, because Laplace–Beltrami operators on Kähler manifolds are in much simpler forms than those of the non-Kähler manifolds. Several time series models are studied in the Kählerian information geometry. View Full-Text
Keywords: Kähler manifold; information geometry; cepstrum; time series model; Bayesian prediction; superharmonic prior Kähler manifold; information geometry; cepstrum; time series model; Bayesian prediction; superharmonic prior
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Choi, J.; Mullhaupt, A.P. Kählerian Information Geometry for Signal Processing. Entropy 2015, 17, 1581-1605.

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