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In decision-making systems, it is important to have classifiers that havecalibrated uncertainties, with an optimisation objective that can be used forautomated model selection and training. Gaussian processes (GPs) provideuncertainty estimates and a marginal likelihood objective, but their weakinductive biases lead to inferior accuracy. This has limited theirapplicability in certain tasks (e.g. image classification). We propose atranslation-insensitive convolutional kernel, which relaxes the translationinvariance constraint imposed by previous convolutional GPs. We show how we canuse the marginal likelihood to learn the degree of insensitivity. We alsoreformulate GP image-to-image convolutional mappings as multi-output GPs,leading to deep convolutional GPs. We show experimentally that our new kernelimproves performance in both single-layer and deep models. We also demonstratethat our fully Bayesian approach improves on dropout-based Bayesian deeplearning methods in terms of uncertainty and marginal likelihood estimates.

Bayesian Image Classification with Deep Convolutional Gaussian Processes