Meta-Learning Stationary Stochastic Process Prediction with
Convolutional Neural Processes
- URL: http://arxiv.org/abs/2007.01332v2
- Date: Fri, 20 Nov 2020 10:52:35 GMT
- Title: Meta-Learning Stationary Stochastic Process Prediction with
Convolutional Neural Processes
- Authors: Andrew Y. K. Foong, Wessel P. Bruinsma, Jonathan Gordon, Yann Dubois,
James Requeima, Richard E. Turner
- Abstract summary: We propose ConvNP, which endows Neural Processes (NPs) with translation equivariance and extends convolutional conditional NPs to allow for dependencies in the predictive distribution.
We demonstrate the strong performance and generalization capabilities of ConvNPs on 1D, regression image completion, and various tasks with real-world-temporal data.
- Score: 32.02612871707347
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Stationary stochastic processes (SPs) are a key component of many
probabilistic models, such as those for off-the-grid spatio-temporal data. They
enable the statistical symmetry of underlying physical phenomena to be
leveraged, thereby aiding generalization. Prediction in such models can be
viewed as a translation equivariant map from observed data sets to predictive
SPs, emphasizing the intimate relationship between stationarity and
equivariance. Building on this, we propose the Convolutional Neural Process
(ConvNP), which endows Neural Processes (NPs) with translation equivariance and
extends convolutional conditional NPs to allow for dependencies in the
predictive distribution. The latter enables ConvNPs to be deployed in settings
which require coherent samples, such as Thompson sampling or conditional image
completion. Moreover, we propose a new maximum-likelihood objective to replace
the standard ELBO objective in NPs, which conceptually simplifies the framework
and empirically improves performance. We demonstrate the strong performance and
generalization capabilities of ConvNPs on 1D regression, image completion, and
various tasks with real-world spatio-temporal data.
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