Maximum Entropy Property of Discrete-time Stable Spline Kernel

TL;DR

This paper investigates the maximum entropy property of the discrete-time first-order stable spline kernel, highlighting advantages of the discrete-time domain and providing a clear proof of its maximum entropy characteristic.

Contribution

It offers the first detailed analysis of the maximum entropy property of the discrete-time stable spline kernel with a self-contained proof.

Findings

The discrete-time stable spline kernel has a maximum entropy property.

Differential entropy rate is well-defined for discrete-time stochastic processes.

The paper provides a simple proof of the maximum entropy property.

Abstract

In this paper, the maximum entropy property of the discrete-time first-order stable spline kernel is studied. The advantages of studying this property in discrete-time domain instead of continuous-time domain are outlined. One of such advantages is that the differential entropy rate is well-defined for discrete-time stochastic processes. By formulating the maximum entropy problem for discrete-time stochastic processes we provide a simple and self-contained proof to show what maximum entropy property the discrete-time first-order stable spline kernel has.