{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T16:55:31Z","timestamp":1774112131251,"version":"3.50.1"},"reference-count":31,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2015,3,25]],"date-time":"2015-03-25T00:00:00Z","timestamp":1427241600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We prove the correspondence between the information geometry of a signal filter and a K\u00e4hler manifold. The information geometry of a minimum-phase linear system with a finite complex cepstrum norm is a K\u00e4hler manifold. The square of the complex cepstrum norm of the signal filter corresponds to the K\u00e4hler potential. The Hermitian structure of the K\u00e4hler manifold is explicitly emergent if and only if the impulse response function of the highest degree in z is constant in model parameters. The K\u00e4hlerian information geometry takes advantage of more efficient calculation steps for the metric tensor and the Ricci tensor. Moreover, \u03b1-generalization on the geometric tensors is linear in \u03b1 . It is also robust to find Bayesian predictive priors, such as superharmonic priors, because Laplace\u2013Beltrami operators on K\u00e4hler manifolds are in much simpler forms than those of the non-K\u00e4hler manifolds. Several time series models are studied in the K\u00e4hlerian information geometry.<\/jats:p>","DOI":"10.3390\/e17041581","type":"journal-article","created":{"date-parts":[[2015,3,25]],"date-time":"2015-03-25T11:53:17Z","timestamp":1427284397000},"page":"1581-1605","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["K\u00e4hlerian Information Geometry for Signal Processing"],"prefix":"10.3390","volume":"17","author":[{"given":"Jaehyung","family":"Choi","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics and Statistics, The State University of New York (SUNY), StonyBrook, NY 11794, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrew","family":"Mullhaupt","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Statistics, The State University of New York (SUNY), StonyBrook, NY 11794, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,3,25]]},"reference":[{"key":"ref_1","first-page":"81","article-title":"Information and accuracy attainable in the estimation of statistical parameters","volume":"37","author":"Rao","year":"1945","journal-title":"Bull. 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