# Integrated Pre-Processing for Bayesian Nonlinear System Identification with Gaussian Processes

arXiv: https://arxiv.org/abs/1303.2912 · HTML: https://mlsanity.com/paper/1303.2912/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Mar 2013.

## Built on by (most cited first, 8 of 8)

- [Deep networks for system identification: a Survey](https://mlsanity.com/paper/2301.12832/) (2023)
- [Adjusting for Autocorrelated Errors in Neural Networks for Time Series](https://mlsanity.com/paper/2101.12578/) (2021)
- [A Mamba Foundation Model for Time Series Forecasting](https://mlsanity.com/paper/2411.02941/) (2024)
- [FreDo: Frequency Domain-based Long-Term Time Series Forecasting](https://mlsanity.com/paper/2205.12301/) (2022)
- [Learning Interacting Dynamical Systems with Latent Gaussian Process ODEs](https://mlsanity.com/paper/2205.11894/) (2022)
- [A Joint Time-frequency Domain Transformer for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2305.14649/) (2023)
- [Data-driven Aerodynamic Analysis of Structures using Gaussian Processes](https://mlsanity.com/paper/2103.13877/) (2021)
- [Grasping Core Rules of Time Series through Pure Models](https://mlsanity.com/paper/2208.07105/) (2022)

## Abstract (arXiv)

We introduce GP-FNARX: a new model for nonlinear system identification based on a nonlinear autoregressive exogenous model (NARX) with filtered regressors (F) where the nonlinear regression problem is tackled using sparse Gaussian processes (GP). We integrate data pre-processing with system identification into a fully automated procedure that goes from raw data to an identified model. Both pre-processing parameters and GP hyper-parameters are tuned by maximizing the marginal likelihood of the probabilistic model. We obtain a Bayesian model of the system's dynamics which is able to report its uncertainty in regions where the data is scarce. The automated approach, the modeling of uncertainty and its relatively low computational cost make of GP-FNARX a good candidate for applications in robotics and adaptive control.