Event
BIMAG Journal Club
Short summary
In this journal club session, I will cover the basics of Gaussian process(GP) and some recent advances in its application to parameter inference of coupled non-linear ODEs.
Abstract
Gaussian process(GP) is a stochastic process such that the joint distribution of arbitrary finite subset of the random variables is a multivariate normal. It plays a fundamental role in Bayesian machine learning as it can be interpreted as a prior over functions (Rasmussen and Williams, 2006), hence providing a nonparametric approach to various tasks.
In the first part, I will introduce the general framework of GP and some underlying theory, accompanied by an illustrative example of GP regression, also known as Kringing. In the second part, I will introduce some recent works on applying GP to parameter inference of coupled non-linear ODEs arising in various biological contexts.
Papers
References for GP:
- Gaussian Processes for Machine Learning (C. E. Rasmussen and C. K. I. Williams, the MIT press, 2006)
References for GP-based ODE Parameter Inference:
- Yang, S., Wong, S. W. K., Kou, S.C. (2021), “Inference of dynamic systems from noisy and sparse data via manifold-constrained Gaussian processes,” Proceedings of the National Academy of Sciences of the United States of America (PNAS), 118(15).
- Wenk, P., Gotovos, Al., Bauer, S., Gorbach, N. S., Krause, A., Buhmann, J. M. (2019), “Fast Gaussian process based gradient matching for parameter identification in systems of nonlinear ODEs,” Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics (AISTATS), 89, 1351-1360.
- Gorbach, N. S., Bauer, S., Buhmann, J. M. (2017), “Scalable Variational Inference for Dynamical Systems,” Advances in Neural Information Processing Systems (NIPS), 30.
- Macdonald, B., Higham, C., Husmeier, D. (2015), “Controversy in mechanistic modelling with Gaussian processes,” Proceedings of the 32nd International Conference on Machine Learning (ICML).
- Wang, Y., Barber, D. (2014), “Gaussian Processes for Bayesian Estimation in Ordinary Differential Equations,” Proceedings of the 31st International Conference on Machine Learning (ICML).
- Dondelinger, F., Filippone, M., Rogers, S., Husmeler, D. (2013), “ODE parameter inference using adaptive gradient matching with Gaussian processes,” Proceedings of the 16th International Conference on Artificial Intelligence and Statistics (AISTATS).
- Calderhead, B., Girolami, M., Lawrence, N. (2008), “Accelerating Bayesian Inference over Nonlinear Differential Equations with Gaussian Processes,” Advances in Neural Information Processing Systems (NIPS), 21.