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

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

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

Spirit: A Home Automation System

Spirit is a multi device home automation system. Designed and implemented for California Polytechnic State University’s Senior Project program, this project was worked on during the duration of two school quarters from January 7, 2014 to June 13, 2014. The system consists of monitor/controllers designed to carry out everyday tasks in the average American household and an accompanying mobile application designed to receive information and control the devices. The monitor/controllers, or “Spirits”, are primarily developed using Arduino development tools and Arduino microcontroller boards. The spirits include a thermostat, named Tempus, an electrical outlet, Electrus, and a wall light switch, Luxos