Controversy in mechanistic modelling with Gaussian processes
Benn Macdonald, Catherine F. Higham, Dirk Husmeier · ENLIGHTEN (Jurnal Bimbingan dan Konseling Islam) · 2016
Parameter inference in mechanistic models based on non-affine differential equations is computa-tionally onerous, and various faster alternatives based on gradient matching have been proposed. A particularly promising approach is based on nonparametric Bayesian modelling with Gaus-sian processes, which exploits the fact that a Gaussian process is closed under differentiation. However, two alternative paradigms have been proposed. The first paradigm, proposed at NIPS 2008 and AISTATS 2013, is based on a product of experts approach and a marginalization over the derivatives of the state variables. The second paradigm, proposed at ICML 2014, is based on a probabilistic generative model and a marginal-ization over the state variables. The claim has been made that this leads to better inference re-sults. In the present article, we offer a new in-terpretation of the second paradigm, which high-lights the underlying assumptions, approxima-tions and limitations. In particular, we show that the second paradigm suffers from an intrinsic identifiability problem, which the first paradigm is not affected by. 1.