Approximation of Nonnegative Systems by Finite Impulse Response Convolutions
Abstract
We pose the deterministic, nonparametric, approximation problem for scalar nonnegative input/output systems via finite impulse response convolutions, based on repeated observations of input/output signal pairs. The problem is converted into a nonnegative matrix factorization with special structure for which we use Csisz\'ar's I-divergence as the criterion of optimality. Conditions are given, on the input/output data, that guarantee the existence and uniqueness of the minimum. We propose a standard algorithm of the alternating minimization type for I-divergence minimization, and study its asymptotic behavior. We also provide a statistical version of the minimization problem and give its large sample properties.
Cite
@article{arxiv.1306.0914,
title = {Approximation of Nonnegative Systems by Finite Impulse Response Convolutions},
author = {Lorenzo Finesso and Peter Spreij},
journal= {arXiv preprint arXiv:1306.0914},
year = {2015}
}
Comments
This paper was previously posted under the name "Nonnegative Deconvolution with Repeated Measurements". The current version is slightly different