# A new kernel-based approach to system identification with quantized output data

arXiv: https://arxiv.org/abs/1610.00470 · HTML: https://mlsanity.com/paper/1610.00470/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Oct 2016.

## Built on by (most cited first, 4 of 4)

- [Identification and Adaptation with Binary-Valued Observations under Non-Persistent Excitation Condition](https://mlsanity.com/paper/2107.03588/) (2021)
- [Dealing with collinearity in large-scale linear system identification using Bayesian regularization](https://mlsanity.com/paper/2203.13633/) (2022)
- [Dealing with Collinearity in Large-Scale Linear System Identification Using Gaussian Regression](https://mlsanity.com/paper/2302.10959/) (2023)
- [On the stability test for reproducing kernel Hilbert spaces](https://mlsanity.com/paper/2305.02213/) (2023)

## Abstract (arXiv)

In this paper we introduce a novel method for linear system identification with quantized output data. We model the impulse response as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential stability. This serves as a starting point to cast our system identification problem into a Bayesian framework. We employ Markov Chain Monte Carlo methods to provide an estimate of the system. In particular, we design two methods based on the so-called Gibbs sampler that allow also to estimate the kernel hyperparameters by marginal likelihood maximization via the expectation-maximization method. Numerical simulations show the effectiveness of the proposed scheme, as compared to the state-of-the-art kernel-based methods when these are employed in system identification with quantized data.