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We prove the correspondence between the information geometry of a signal filter and a Kahler manifold. The information geometry of a minimum-phase linear system with a finite complex cepstrum norm is a Kahler manifold. The square of the complex cepstrum norm of the signal filter corresponds to the Kahler potential. The Hermitian structure of the Kahler manifold is explicitly emergent if and only if the impulse response function of the highest degree in $z$ is constant in model parameters. The Kahlerian information geometry takes advantage of more efficient calculation steps for the metric tensor and the Ricci tensor. Moreover, $alpha$-generalization on the geometric tensors is linear in $alpha$. It is also robust to find Bayesian predictive priors, such as superharmonic priors, because Laplace-Beltrami operators on Kahler manifolds are in much simpler forms than those of the non-Kahler manifolds. Several time series models are studied in the Kahlerian information geometry.
We review the information geometry of linear systems and its application to Bayesian inference, and the simplification available in the Kahler manifold case. We find conditions for the information geometry of linear systems to be Kahler, and the rela
We describe and to some extent characterize a new family of Kahler spin manifolds admitting non-trivial imaginary Kahlerian Killing spinors.
A recently introduced canonical divergence $mathcal{D}$ for a dual structure $(mathrm{g}, abla, abla^*)$ is discussed in connection to other divergence functions. Finally, open problems concerning symmetry properties are outlined.
We show that a Frobenius sturcture is equivalent to a dually flat sturcture in information geometry. We define a multiplication structure on the tangent spaces of statistical manifolds, which we call the statistical product. We also define a scalar q
Matrix scaling is a classical problem with a wide range of applications. It is known that the Sinkhorn algorithm for matrix scaling is interpreted as alternating e-projections from the viewpoint of classical information geometry. Recently, a generali