Geometric shrinkage priors for K\"ahlerian signal filters

We construct geometric shrinkage priors for K\"ahlerian signal filters. Based on the characteristics of K\"ahler manifolds, an efficient and robust algorithm for finding superharmonic priors which outperform the Jeffreys prior is introduced. Several ans\"atze for the Bayesian predictive priors are also suggested. In particular, the ans\"atze related to K\"ahler potential are geometrically intrinsic priors to the information manifold of which the geometry is derived from the potential. The implication of the algorithm to time series models is also provided.Comment: 10 pages, published versio

Application of K\"ahler manifold to signal processing and Bayesian inference

We review the information geometry of linear systems and its application to Bayesian inference, and the simplification available in the K\"ahler manifold case. We find conditions for the information geometry of linear systems to be K\"ahler, and the relation of the K\"ahler potential to information geometric quantities such as $\alpha$-divergence, information distance and the dual $\alpha$-connection structure. The K\"ahler structure simplifies the calculation of the metric tensor, connection, Ricci tensor and scalar curvature, and the $\alpha$-generalization of the geometric objects. The Laplace--Beltrami operator is also simplified in the K\"ahler geometry. One of the goals in information geometry is the construction of Bayesian priors outperforming the Jeffreys prior, which we use to demonstrate the utility of the K\"ahler structure.Comment: 8 pages, submitted to the Proceedings of MaxEnt 1

K\"ahlerian information geometry for signal processing

We prove the correspondence between the information geometry of a signal filter and a K\"ahler manifold. The information geometry of a minimum-phase linear system with a finite complex cepstrum norm is a K\"ahler manifold. The square of the complex cepstrum norm of the signal filter corresponds to the K\"ahler potential. The Hermitian structure of the K\"ahler 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\"ahlerian 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 K\"ahler manifolds are in much simpler forms than those of the non-K\"ahler manifolds. Several time series models are studied in the K\"ahlerian information geometry.Comment: 24 pages, published versio

End-to-end adaptation scheme for ubiquitous remote experimentation

Remote experimentation is an effective e-learning paradigm for supporting hands-on education using laboratory equipment at distance. The current trend is to enable remote experimentation in mobile and ubiquitous learning. In such a context, the remote experimentation software should enable effective telemonitoring and teleoperation, no matter the kind of device used to access the equipment. It should also be sufficiently lenient so as to handle the rapidly evolving wireless and mobile communication environment. While the current Internet bandwidth allows remote experimentation to work flawlessly on fixed connections such as LANs, mobile users suffer from both the versatile nature of wireless communications and the limitation of the mobile devices. These conditions impose that the remote experimentation software should integrate adaptation features. For effective ubiquitous remote experimentation, it should ideally be guaranteed that the information representing the state of the remote equipment is rendered (to the end user) at the same pace at which it has been acquired, yet possibly at the cost of a somewhat minimal time delay between the acquisition and rendering phases. In this respect, an end-to-end adaptation scheme is proposed that explicitly handles the inherent variability of the connection and the versatility of the mobile devices considered in ubiquitous remote experimentation. Instead of relying on a stochastic approach, the proposed adaptation scheme relies on a deterministic mass-balance equivalence model. The effectiveness of the proposed adaptation scheme is demonstrated in critical conditions corresponding to remote experimentation carried out using a PDA over a Bluetooth lin