Probabilistic Numeric Convolutional Neural Networks
This addresses the problem of handling irregular or missing data in deep learning for researchers and practitioners in fields like medical time series analysis, though it is incremental as it builds on probabilistic numerics.
The paper tackled the challenge of processing irregularly sampled or incomplete continuous signals like images and time series by proposing Probabilistic Numeric Convolutional Neural Networks, which represent features as Gaussian processes to handle discretization error, resulting in a 3x error reduction on SuperPixel-MNIST and competitive performance on PhysioNet2012.
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.