In a Bayesian neural network (BNN), we specify a prior p(w) over the neural network parameters, and compute the posterior distribution over parameters conditioned on training data, p(w x, y) p(y w, x)p(w)/p(y x). This procedure should give considerable advantages for reasoning about predictive uncertainty, which is especially relevant in the small-data setting. Crucially, to perform Bayesian inference, we need to choose a prior that accurately reflects our beliefs about the parameters before seeing any data (Bayes, 1763; Gelman et al., 2013). However, the most common choice of the prior for BNN weights is the simplest one: the isotropic Gaussian. Isotropic Gaussians are used across almost all fields of Bayesian deep learning, ranging from variational inference (Blundell et al., 2015; Dusenberry et al., 2020), to sampling-based inference (Zhang et al., 2019), and even to infinite networks (Lee et al., 2017; Garriga-Alonso et al., 2019). This is troubling, since isotropic Gaussian priors are almost certainly not the best choice. Indeed, despite the progress on more accurate and efficient inference procedures, in most settings, the posterior predictive of BNNs using a Gaussian prior still leads to worse predictive performance than a baseline obtained by training the network with standard stochastic gradient descent (SGD) (e.g., Zhang et al., 2019; Heek & Kalchbrenner, 2019; Wenzel et al., 2020a). However, it has been shown that the performance of BNNs can be improved by artificially reducing posterior uncertainty using "cold posteriors" (Wenzel et al., 2020a).

Complex multivariate time series arise in many fields, ranging from computer vision to robotics or medicine. Often we are interested in the independent underlying factors that give rise to the high-dimensional data we are observing. While many models have been introduced to learn such disentangled representations, only few attempt to explicitly exploit the structure of sequential data. We investigate the disentanglement properties of Gaussian process variational autoencoders, a class of models recently introduced that have been successful in different tasks on time series data. Our model exploits the temporal structure of the data by modeling each latent channel with a GP prior and employing a structured variational distribution that can capture dependencies in time. We demonstrate the competitiveness of our approach against state-of-the-art unsupervised and weakly-supervised disentanglement methods on a benchmark task. Moreover, we provide evidence that we can learn meaningful disentangled representations on real-world medical time series data.

Stochastic gradient Markov Chain Monte Carlo algorithms are popular samplers for approximate inference, but they are generally biased. We show that many recent versions of these methods (e.g. Chen et al. (2014)) cannot be corrected using Metropolis-Hastings rejection sampling, because their acceptance probability is always zero. We can fix this by employing a sampler with realizable backwards trajectories, such as Gradient-Guided Monte Carlo (Horowitz, 1991), which generalizes stochastic gradient Langevin dynamics (Welling and Teh, 2011) and Hamiltonian Monte Carlo. We show that this sampler can be used with stochastic gradients, yielding nonzero acceptance probabilities, which can be computed even across multiple steps.

Variational autoencoders often assume isotropic Gaussian priors and mean-field posteriors, hence do not exploit structure in scenarios where we may expect similarity or consistency across latent variables. Gaussian process variational autoencoders alleviate this problem through the use of a latent Gaussian process, but lead to a cubic inference time complexity. We propose a more scalable extension of these models by leveraging the independence of the auxiliary features, which is present in many datasets. Our model factorizes the latent kernel across these features in different dimensions, leading to a significant speed-up (in theory and practice), while empirically performing comparably to existing non-scalable approaches. Moreover, our approach allows for additional modeling of global latent information and for more general extrapolation to unseen input combinations.

Large, multidimensional spatiotemporal 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 spatiotemporal 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. Increasing amounts of large, multidimensional datasets that exhibit strong spatiotemporal dependencies are arising from a wealth of domains, including earth, social and environmental sciences (Atluri et al., 2018). For example, consider modelling daily atmospheric measurements taken by weather stations situated across the globe. Such data are (1) large in number; (2) subject to strong spatiotemporal dependencies; (3) multidimensional; and (4) non-Gaussian with complex dependencies across outputs.

Meta-learning can successfully acquire useful inductive biases from data, especially when a large number of meta-tasks are available. Yet, its generalization properties to unseen tasks are poorly understood. Particularly if the number of meta-tasks is small, this raises concerns for potential overfitting. We provide a theoretical analysis using the PAC-Bayesian framework and derive novel generalization bounds for meta-learning with unbounded loss functions and Bayesian base learners. Using these bounds, we develop a class of PAC-optimal meta-learning algorithms with performance guarantees and a principled meta-regularization. When instantiating our PAC-optimal hyper-posterior (PACOH) with Gaussian processes as base learners, the resulting approach consistently outperforms several popular meta-learning methods, both in terms of predictive accuracy and the quality of its uncertainty estimates.

Clustering high-dimensional data, such as images or biological measurements, is a long-standing problem and has been studied extensively. Recently, Deep Clustering gained popularity due to the non-linearity of neural networks, which allows for 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 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 synthetic data, the MNIST benchmark data set, and a challenging real-world task of 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 and we show that the MoE architecture in the decoder reduces the computational cost of sampling specific data modes with high fidelity.

Generating visualizations and interpretations from high-dimensional data is a common problem in many fields. Two key approaches for tackling this problem are clustering and representation learning. There are very performant deep clustering models on the one hand and interpretable representation learning techniques, often relying on latent topological structures such as self-organizing maps, on the other hand. However, current methods do not yet successfully combine these two approaches. We present a new deep architecture for probabilistic clustering, VarPSOM, and its extension to time series data, VarTPSOM. We show that they achieve superior clustering performance compared to current deep clustering methods on static MNIST/Fashion-MNIST data as well as medical time series, while inducing an interpretable representation. Moreover, on the medical time series, VarTPSOM successfully predicts future trajectories in the original data space.

Metagenomic studies have increasingly utilized sequencing technologies in order to analyze DNA fragments found in environmental samples. It can provide useful insights for studying the interactions between hosts and microbes, infectious disease proliferation, and novel species discovery. One important step in this analysis is the taxonomic classification of those DNA fragments. Of particular interest is the determination of the distribution of the taxa of microbes in metagenomic samples. Recent attempts using deep learning focus on architectures that classify single DNA reads independently from each other. In this work, we attempt to solve the task of directly predicting the distribution over the taxa of whole metagenomic read sets. We formulate this task as a Multiple Instance Learning (MIL) problem. We extend architectures used in single-read taxonomic classification with two different types of permutation-invariant MIL pooling layers: a) deepsets and b) attention-based pooling. We illustrate that our architecture can exploit the co-occurrence of species in metagenomic read sets and outperforms the single-read architectures in predicting the distribution over the taxa at higher taxonomic ranks.

With a mortality rate of 5.4 million lives worldwide every year and a healthcare cost of more than 16 billion dollars in the USA alone, sepsis is one of the leading causes of hospital mortality and an increasing concern in the ageing western world. Recently, medical and technological advances have helped re-define the illness criteria of this disease, which is otherwise poorly understood by the medical society. Together with the rise of widely accessible Electronic Health Records, the advances in data mining and complex nonlinear algorithms are a promising avenue for the early detection of sepsis. This work contributes to the research effort in the field of automated sepsis detection with an open-access labelling of the medical MIMIC-III data set. Moreover, we propose MGP-AttTCN: a joint multitask Gaussian Process and attention-based deep learning model to early predict the occurrence of sepsis in an interpretable manner. We show that our model outperforms the current state-of-the-art and present evidence that different labelling heuristics lead to discrepancies in task difficulty.