Probabilistic Numeric Convolutional Neural Networks

• URL: http://arxiv.org/abs/2010.10876v1
• Date: Wed, 21 Oct 2020 10:08:21 GMT
• Title: Probabilistic Numeric Convolutional Neural Networks
• Authors: Marc Finzi, Roberto Bondesan, Max Welling
• Abstract summary: Continuous input signals like images and time series that are irregularly sampled or have missing values are challenging for existing deep learning methods. We propose Probabilistic Convolutional Neural Networks which represent features as Gaussian processes (GPs) We then define a convolutional layer as the evolution of a PDE defined on this GP, followed by a nonlinearity. In experiments we show that our approach yields a $3times$ reduction of error from the previous state of the art on the SuperPixel-MNIST dataset and competitive performance on the medical time2012 dataset PhysioNet.
• Score: 80.42120128330411
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Continuous input signals like images and time series that are irregularly sampled or have missing values are challenging for existing deep learning methods. Coherently defined feature representations must depend on the values in unobserved regions of the input. Drawing from the work in probabilistic numerics, we propose Probabilistic Numeric Convolutional Neural Networks which represent features as Gaussian processes (GPs), providing a probabilistic description of discretization error. We then define a convolutional layer as the evolution of a PDE defined on this GP, followed by a nonlinearity. This approach also naturally admits steerable equivariant convolutions under e.g. the rotation group. In experiments we show that our approach yields a $3\times$ reduction of error from the previous state of the art on the SuperPixel-MNIST dataset and competitive performance on the medical time series dataset PhysioNet2012.

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