Journal
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
Volume 35, Issue 11, Pages 2693-2705Publisher
IEEE COMPUTER SOC
DOI: 10.1109/TPAMI.2013.86
Keywords
Gaussian processes; dynamical systems; multitask learning; motion capture data; spatiotemporal covariances; differential equations
Funding
- Comunidad de Madrid (project PRO-MULTIDIS-CM) [S-0505/TIC/0233]
- Spanish government [JC2008, TEC2009-14504-C02-01, CSD2008-00010]
- Google Research Award
- EPSRC [P/F005687/1]
- EU [289434]
- Overseas Research Student Award Scheme (ORSAS)
- School of Computer Science of the University of Manchester
- Universidad Tecnologica de Pereira, Colombia
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Purely data-driven approaches for machine learning present difficulties when data are scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic approaches need to identify and specify all the interactions in the problem at hand (which may not be feasible) and still leave the issue of how to parameterize the system. In this paper, we present a hybrid approach using Gaussian processes and differential equations to combine data-driven modeling with a physical model of the system. We show how different, physically inspired, kernel functions can be developed through sensible, simple, mechanistic assumptions about the underlying system. The versatility of our approach is illustrated with three case studies from motion capture, computational biology, and geostatistics.
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