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Neural ODE Processes: A Short Summary
Alexander Norcliffe · Cristian Bodnar · Ben Day · Jacob Moss · Pietro Lió

Tue Dec 14 06:45 AM -- 07:30 AM (PST) @ None
in The Symbiosis of Deep Learning and Differential Equations »
Event URL: https://openreview.net/forum?id=6yovcKE2LeN »

Neural Ordinary Differential Equations (NODEs) use a neural network to model the instantaneous rate of change in the state of a system. However, despite their apparent suitability for dynamics-governed time-series, NODEs present a few disadvantages. First, they are unable to adapt to incoming data-points, a fundamental requirement for real-time applications imposed by the natural direction of time. Second, time-series are often composed of a sparse set of measurements, which could be explained by many possible underlying dynamics. NODEs do not capture this uncertainty. To this end, we introduce Neural ODE Processes (NDPs), a new class of stochastic processes determined by a distribution over Neural ODEs. By maintaining an adaptive data-dependent distribution over the underlying ODE, we show that our model can successfully capture the dynamics of low-dimensional systems from just a few data-points. At the same time, we demonstrate that NDPs scale up to challenging high-dimensional time-series with unknown latent dynamics such as rotating MNIST digits. Code is available online at https://github.com/crisbodnar/ndp.

Author Information

Alexander Norcliffe (University of Cambridge)

I'm a PhD student in Machine Learning for Medicine. I am co-supervised by Mihaela Van der Schaar and Pietro Lio in the Cambridge Centre for AI in Medicine.

Cristian Bodnar (University of Cambridge)
Ben Day (University of Cambridge)
Jacob Moss (University of Cambridge)
Pietro Lió (University of Cambridge)

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