Geometric Shrinkage Priors for Kählerian Signal Filters

Jaehyung Choi,Andrew Mullhaupt

doi:10.3390/e17031347

Abstract

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.

Highlights

IntroductionSignal processing is one of the most important applications
In information geometry, signal processing is one of the most important applications
One of the benefits in the Kählerian information geometry is that the simpler form of the Laplace–Beltrami operator on the Kähler manifold is beneficial to finding the Komaki priors

Summary

Introduction

Signal processing is one of the most important applications. Many practical aspects of introducing Kähler manifolds to information geometry for signal processing were reported in the same literature [7]. One of the benefits in the Kählerian information geometry is that the simpler form of the Laplace–Beltrami operator on the Kähler manifold is beneficial to finding the Komaki priors. We construct Komaki-style shrinkage priors for Kählerian signal filters. By introducing an algorithm which is based on the characteristics of Kähler manifolds, the Bayesian predictive priors outperforming the Jeffreys prior can be obtained in a more efficient and more robust way. The geometric shrinkage priors related to Kähler potential are intrinsic priors on the information manifold because the geometry is given by the Kähler potential.

Kählerian Filters

Superharmonic Priors

Geometric Shrinkage Priors

Example

Conclusion