Probabilistic Numeric Convolutional Neural Networks

TL;DR

This paper introduces Probabilistic Numeric Convolutional Neural Networks that model features as Gaussian processes, enabling better handling of irregularly sampled data and missing values, with improved accuracy demonstrated on image and time series datasets.

Contribution

It proposes a novel convolutional layer based on Gaussian processes and PDE evolution, incorporating probabilistic discretization error and equivariance properties.

Findings

3x error reduction on SuperPixel-MNIST

Competitive performance on PhysioNet2012

Probabilistic modeling improves handling of irregular data

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.