Maximum entropy properties of discrete-time first-order stable spline kernel
Abstract
The first order stable spline (SS-1) kernel is used extensively in regularized system identification. In particular, the stable spline estimator models the impulse response as a zero-mean Gaussian process whose covariance is given by the SS-1 kernel. In this paper, we discuss the maximum entropy properties of this prior. In particular, we formulate the exact maximum entropy problem solved by the SS-1 kernel without Gaussian and uniform sampling assumptions. Under general sampling schemes, we also explicitly derive the special structure underlying the SS-1 kernel (e.g. characterizing the tridiagonal nature of its inverse), also giving to it a maximum entropy covariance completion interpretation. Along the way similar maximum entropy properties of the Wiener kernel are also given.
Cite
@article{arxiv.1504.03253,
title = {Maximum entropy properties of discrete-time first-order stable spline kernel},
author = {Tianshi Chen and Tohid Ardeshiri and Francesca P. Carli and Alessandro Chiuso and Lennart Ljung and Gianluigi Pillonetto},
journal= {arXiv preprint arXiv:1504.03253},
year = {2015}
}