It was recently shown that neural ordinary differential equation models cannot solve fundamental and seemingly straightforward tasks even with high-capacity vector field representations. This paper introduces two other fundamental tasks to the set that baseline methods cannot solve, and proposes mixtures of stochastic vector fields as a model class that is capable of solving these essential problems. Dynamic vector field selection is of critical importance for our model, and our approach is to propagate component uncertainty over the integration interval with a technique based on forward filtering. We also formalise several loss functions that encourage desirable properties on the trajectory paths, and of particular interest are those that directly encourage fewer expected function evaluations. Experimentally, we demonstrate that our model class is capable of capturing the natural dynamics of human behaviour; a notoriously volatile application area. Baseline approaches cannot model this problem.
|Title of host publication||ECAI 2020 - 24th European Conference on Artificial Intelligence, including 10th Conference on Prestigious Applications of Artificial Intelligence, PAIS 2020 - Proceedings|
|Editors||Giuseppe De Giacomo, Alejandro Catala, Bistra Dilkina, Michela Milano, Senen Barro, Alberto Bugarin, Jerome Lang|
|Number of pages||8|
|Publication status||Published - 24 Aug 2020|
|Event||24th European Conference on Artificial Intelligence, ECAI 2020, including 10th Conference on Prestigious Applications of Artificial Intelligence, PAIS 2020 - Santiago de Compostela, Online, Spain|
Duration: 29 Aug 2020 → 8 Sep 2020
|Name||Frontiers in Artificial Intelligence and Applications|
|Conference||24th European Conference on Artificial Intelligence, ECAI 2020, including 10th Conference on Prestigious Applications of Artificial Intelligence, PAIS 2020|
|City||Santiago de Compostela, Online|
|Period||29/08/20 → 8/09/20|
Bibliographical noteFunding Information:
This research was conducted under the ‘Continuous Behavioural Biomarkers of Cognitive Impairment’ project funded by the UK Medical Research Council Momentum Awards under Grant MC/PC/16029.
© 2020 The authors and IOS Press.
Copyright 2020 Elsevier B.V., All rights reserved.