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Meta-Learning Stationary Stochastic Process Prediction with Convolutional Neural Processes
Andrew Foong · Wessel Bruinsma · Jonathan Gordon · Yann Dubois · James Requeima · Richard Turner

Thu Dec 10 09:00 AM -- 11:00 AM (PST) @ Poster Session 5 #1534
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.

Author Information

Andrew Foong (University of Cambridge)

I am a PhD student in the Machine Learning Group at the University of Cambridge, supervised by Professor Richard E. Turner, and advised by Dr. José Miguel Hernández-Lobato. I started my PhD in October 2018. My research focuses on the intersection of probabilistic modelling and deep learning, with work on Bayesian neural networks, meta-learning, modelling equivariance, and PAC-Bayes.

Wessel Bruinsma (University of Cambridge and Invenia Labs)
Jonathan Gordon (University of Cambridge)
Yann Dubois (Facebook AI)
James Requeima (University of Cambridge / Invenia Labs)
Richard Turner (University of Cambridge)

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