Isotropic Gaussian priors are the de facto standard for modern Bayesian neural network inference. However, such simplistic priors are unlikely to either accurately reflect our true beliefs about the weight distributions, or to give optimal performance. We study summary statistics of neural network weights in different networks trained using SGD. We find that fully connected networks (FCNNs) display heavytailed weight distributions, while convolutional neural network (CNN) weights display strong spatial correlations. Building these observations into the respective priors leads to improved performance on a variety of image classification datasets. Moreover, we find that these priors also mitigate the cold posterior effect in FCNNs, while in CNNs we see strong improvements at all temperatures, and hence no reduction in the cold posterior effect.

Data augmentation is a highly effective approach for improving performance in deep neural networks. The standard view is that it creates an enlarged dataset by adding synthetic data, which raises a problem when combining it with Bayesian inference: how much data are we really conditioning on? This question is particularly relevant to recent observations linking data augmentation to the cold posterior effect. We investigate various principled ways of finding a log-likelihood for augmented datasets. Our approach prescribes augmenting the same underlying image multiple times, both at test and train-time, and averaging either the logits or the predictive probabilities. Empirically, we observe the best performance with averaging probabilities. While there are interactions with the cold posterior effect, neither averaging logits or averaging probabilities eliminates it. IntroductionData augmentation (Shorten & Khoshgoftaar, 2019) is a fundamental technique for obtaining high performance in modern neural networks (NNs). In computer vision, data augmentation involves creating synthetic training examples by making small modifications, such as a rotation or crop, to the input image.At the same time, Bayesian inference allows us to reason about uncertainty in neural network weights (MacKay, 1992;Welling & Teh, 2011;Blundell et al., 2015;Fortuin, 2021) given limited data. Bayesian inference is particularly important in safety-critical settings such as self-driving cars or medical imaging where it is crucial to be able to hand over to a human when uncertainty is too large. * equal contribution † equal contributionPreprint. Under review.

Large, multi-dimensional spatio-temporal datasets are omnipresent in modern science and engineering. An effective framework for handling such data are Gaussian process deep generative models (GP-DGMs), which employ GP priors over the latent variables of DGMs. Existing approaches for performing inference in GP-DGMs do not support sparse GP approximations based on inducing points, which are essential for the computational efficiency of GPs, nor do they handle missing data -a natural occurrence in many spatio-temporal datasets -in a principled manner. We address these shortcomings with the development of the sparse Gaussian process variational autoencoder (SGP-VAE), characterised by the use of partial inference networks for parameterising sparse GP approximations. Leveraging the benefits of amortised variational inference, the SGP-VAE enables inference in multi-output sparse GPs on previously unobserved data with no additional training. The SGP-VAE is evaluated in a variety of experiments where it outperforms alternative approaches including multi-output GPs and structured VAEs.

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Clustering high-dimensional data, such as images or biological measurements, is a long-standing problem and has been studied extensively. Recently, Deep Clustering has gained popularity due to its flexibility in fitting the specific peculiarities of complex data. Here we introduce the Mixture-of-Experts Similarity Variational Autoencoder (MoE-Sim-VAE), a novel generative clustering model. The model can learn multi-modal distributions of high-dimensional data and use these to generate realistic data with high efficacy and efficiency. MoE-Sim-VAE is based on a Variational Autoencoder (VAE), where the decoder consists of a Mixture-of-Experts (MoE) architecture. This specific architecture allows for various modes of the data to be automatically learned by means of the experts. Additionally, we encourage the lower dimensional latent representation of our model to follow a Gaussian mixture distribution and to accurately represent the similarities between the data points. We assess the performance of our model on the MNIST benchmark data set and challenging real-world tasks of clustering mouse organs from single-cell RNA-sequencing measurements and defining cell subpopulations from mass cytometry (CyTOF) measurements on hundreds of different datasets. MoE-Sim-VAE exhibits superior clustering performance on all these tasks in comparison to the baselines as well as competitor methods.