Defining dynamics via Gaussian processes



Two classic flavours together, Gaussian Processes and dynamical_systems, where the dynamics are modelled by a Gaussian process.

Here we use Gaussian processes to define the dynamics, in particular to learn nonparametric transition, observation or state densities. This is what [Turner, Deisenroth, and Rasmussen (2010);Frigola, Chen, and Rasmussen (2014);Frigola et al. (2013);EleftheriadisIdentification2017] do.

This is distinct from calculating a Gaussian process posterior via a state filter, which is another way you can combine the concepts of dynamics and Gaussian process.

c.f. Variational filters and particle filters.

Possible the same, recurrent Gaussian Processes? πŸ— (Mattos et al. 2016, 2017; FΓΆll et al. 2017).

References

Candela, J.Q., A. Girard, J. Larsen, and C.E. Rasmussen. 2003. β€œPropagation of Uncertainty in Bayesian Kernel Models - Application to Multiple-Step Ahead Forecasting.” In 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP ’03)., 2:II-701-4. Hong Kong, China: IEEE.
Eleftheriadis, Stefanos, Tom Nicholson, Marc Deisenroth, and James Hensman. 2017. β€œIdentification of Gaussian Process State Space Models.” In Advances in Neural Information Processing Systems 30, edited by I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett, 5309–19. Curran Associates, Inc.
FΓΆll, Roman, Bernard Haasdonk, Markus Hanselmann, and Holger Ulmer. 2017. β€œDeep Recurrent Gaussian Process with Variational Sparse Spectrum Approximation.” arXiv:1711.00799 [Stat], November.
Frigola, Roger, Yutian Chen, and Carl Edward Rasmussen. 2014. β€œVariational Gaussian Process State-Space Models.” In Advances in Neural Information Processing Systems 27, edited by Z. Ghahramani, M. Welling, C. Cortes, N. D. Lawrence, and K. Q. Weinberger, 3680–88. Curran Associates, Inc.
Frigola, Roger, Fredrik Lindsten, Thomas B SchΓΆn, and Carl Edward Rasmussen. 2013. β€œBayesian Inference and Learning in Gaussian Process State-Space Models with Particle MCMC.” In Advances in Neural Information Processing Systems 26, edited by C. J. C. Burges, L. Bottou, M. Welling, Z. Ghahramani, and K. Q. Weinberger, 3156–64. Curran Associates, Inc.
Huber, Marco F. 2014. β€œRecursive Gaussian Process: On-Line Regression and Learning.” Pattern Recognition Letters 45 (August): 85–91.
Mattos, CΓ©sar Lincoln C., Zhenwen Dai, Andreas Damianou, Guilherme A. Barreto, and Neil D. Lawrence. 2017. β€œDeep Recurrent Gaussian Processes for Outlier-Robust System Identification.” Journal of Process Control, DYCOPS-CAB 2016, 60 (December): 82–94.
Mattos, CΓ©sar Lincoln C., Zhenwen Dai, Andreas Damianou, Jeremy Forth, Guilherme A. Barreto, and Neil D. Lawrence. 2016. β€œRecurrent Gaussian Processes.” In Proceedings of ICLR.
Mohammadi, Hossein, Peter Challenor, and Marc Goodfellow. 2021. β€œEmulating Computationally Expensive Dynamical Simulators Using Gaussian Processes.” arXiv:2104.14987 [Stat], April.
Nickisch, Hannes, Arno Solin, and Alexander Grigorevskiy. 2018. β€œState Space Gaussian Processes with Non-Gaussian Likelihood.” In International Conference on Machine Learning, 3789–98.
Turner, Ryan, Marc Deisenroth, and Carl Rasmussen. 2010. β€œState-Space Inference and Learning with Gaussian Processes.” In Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, 868–75.
Wilkinson, William J., Paul E. Chang, Michael Riis Andersen, and Arno Solin. 2020. β€œState Space Expectation Propagation: Efficient Inference Schemes for Temporal Gaussian Processes.” In ICML.

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