Abstract Graph contrastive learning has shown great promise when labeled data is scarce, but large unlabeled datasets are available. However, it often does not take uncertainty estimation into account. We show that a variational Bayesian neural network approach can be used to improve not only the uncertainty estimates but also the downstream performance on semi-supervised node-classification tasks. Moreover, we propose a new measure of uncertainty for contrastive learning, that is based on the disagreement in likelihood due to different positive samples.

Authors Alexander Möllers, Alexander Immer, Elvin Isufi, Vincent Fortuin

Submitted AABI 2023

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Abstract The linearized-Laplace approximation (LLA) has been shown to be effective and efficient in constructing Bayesian neural networks. It is theoretically compelling since it can be seen as a Gaussian process posterior with the mean function given by the neural network's maximum-a-posteriori predictive function and the covariance function induced by the empirical neural tangent kernel. However, while its efficacy has been studied in large-scale tasks like image classification, it has not been studied in sequential decision-making problems like Bayesian optimization where Gaussian processes -- with simple mean functions and kernels such as the radial basis function -- are the de-facto surrogate models. In this work, we study the usefulness of the LLA in Bayesian optimization and highlight its strong performance and flexibility. However, we also present some pitfalls that might arise and a potential problem with the LLA when the search space is unbounded.

Authors Agustinus Kristiadi, Alexander Immer, Runa Eschenhagen, Vincent Fortuin

Submitted AABI 2023

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Abstract Deep neural networks are highly effective but suffer from a lack of interpretability due to their black-box nature. Neural additive models (NAMs) solve this by separating into additive sub-networks, revealing the interactions between features and predictions. In this paper, we approach the NAM from a Bayesian perspective in order to quantify the uncertainty in the recovered interactions. Linearized Laplace approximation enables inference of these interactions directly in function space and yields a tractable estimate of the marginal likelihood, which can be used to perform implicit feature selection through an empirical Bayes procedure. Empirically, we show that Laplace-approximated NAMs (LA-NAM) are both more robust to noise and easier to interpret than their non-Bayesian counterpart for tabular regression and classification tasks.

Authors Kouroche Bouchiat, Alexander Immer, Hugo Yèche, Gunnar Rätsch, Vincent Fortuin

Submitted AABI 2023

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Abstract Data augmentation is commonly applied to improve performance of deep learning by enforcing the knowledge that certain transformations on the input preserve the output. Currently, the used data augmentation is chosen by human effort and costly cross-validation, which makes it cumbersome to apply to new datasets. We develop a convenient gradient-based method for selecting the data augmentation without validation data and during training of a deep neural network. Our approach relies on phrasing data augmentation as an invariance in the prior distribution and learning it using Bayesian model selection, which has been shown to work in Gaussian processes, but not yet for deep neural networks. We propose a differentiable Kronecker-factored Laplace approximation to the marginal likelihood as our objective, which can be optimised without human supervision or validation data. We show that our method can successfully recover invariances present in the data, and that this improves generalisation and data efficiency on image datasets.

Authors Alexander Immer, Tycho FA van der Ouderaa, Gunnar Rätsch, Vincent Fortuin, Mark van der Wilk

Submitted NeurIPS 2022

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Abstract Pre-trained contextual representations have led to dramatic performance improvements on a range of downstream tasks. This has motivated researchers to quantify and understand the linguistic information encoded in them. In general, this is done by probing, which consists of training a supervised model to predict a linguistic property from said representations. Unfortunately, this definition of probing has been subject to extensive criticism, and can lead to paradoxical or counter-intuitive results. In this work, we present a novel framework for probing where the goal is to evaluate the inductive bias of representations for a particular task, and provide a practical avenue to do this using Bayesian inference. We apply our framework to a series of token-, arc-, and sentence-level tasks. Our results suggest that our framework solves problems of previous approaches and that fastText can offer a better inductive bias than BERT in certain situations.

Authors Alexander Immer, Lucas Torroba Hennigen, Vincent Fortuin, Ryan Cotterell

Submitted ACL 2022

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Abstract In recent years, the transformer has established itself as a workhorse in many applications ranging from natural language processing to reinforcement learning. Similarly, Bayesian deep learning has become the gold-standard for uncertainty estimation in safety-critical applications, where robustness and calibration are crucial. Surprisingly, no successful attempts to improve transformer models in terms of predictive uncertainty using Bayesian inference exist. In this work, we study this curiously underpopulated area of Bayesian transformers. We find that weight-space inference in transformers does not work well, regardless of the approximate posterior. We also find that the prior is at least partially at fault, but that it is very hard to find well-specified weight priors for these models. We hypothesize that these problems stem from the complexity of obtaining a meaningful mapping from weight-space to function-space distributions in the transformer. Therefore, moving closer to function-space, we propose a novel method based on the implicit reparameterization of the Dirichlet distribution to apply variational inference directly to the attention weights. We find that this proposed method performs competitively with our baselines.

Authors Tristan Cinquin, Alexander Immer, Max Horn, Vincent Fortuin

Submitted AABI 2022

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Abstract Particle-based approximate Bayesian inference approaches such as Stein Variational Gradient Descent (SVGD) combine the flexibility and convergence guarantees of sampling methods with the computational benefits of variational inference. In practice, SVGD relies on the choice of an appropriate kernel function, which impacts its ability to model the target distribution -- a challenging problem with only heuristic solutions. We propose Neural Variational Gradient Descent (NVGD), which is based on parameterizing the witness function of the Stein discrepancy by a deep neural network whose parameters are learned in parallel to the inference, mitigating the necessity to make any kernel choices whatsoever. We empirically evaluate our method on popular synthetic inference problems, real-world Bayesian linear regression, and Bayesian neural network inference.

Authors Lauro Langosco di Langosco, Vincent Fortuin, Heiko Strathmann

Submitted AABI 2022

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Abstract Quantum machine learning promises great speedups over classical algorithms, but it often requires repeated computations to achieve a desired level of accuracy for its point estimates. Bayesian learning focuses more on sampling from posterior distributions than on point estimation, thus it might be more forgiving in the face of additional quantum noise. We propose a quantum algorithm for Bayesian neural network inference, drawing on recent advances in quantum deep learning, and simulate its empirical performance on several tasks. We find that already for small numbers of qubits, our algorithm approximates the true posterior well, while it does not require any repeated computations and thus fully realizes the quantum speedups.

Authors Noah Berner, Vincent Fortuin, Jonas Landman

Submitted AABI 2022

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Abstract 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.

Authors Simon Bing, Vincent Fortuin, Gunnar Rätsch

Submitted AABI 2022

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Abstract Deep ensembles have recently gained popularity in the deep learning community for their conceptual simplicity and efficiency. However, maintaining functional diversity between ensemble members that are independently trained with gradient descent is challenging. This can lead to pathologies when adding more ensemble members, such as a saturation of the ensemble performance, which converges to the performance of a single model. Moreover, this does not only affect the quality of its predictions, but even more so the uncertainty estimates of the ensemble, and thus its performance on out-of-distribution data. We hypothesize that this limitation can be overcome by discouraging different ensemble members from collapsing to the same function. To this end, we introduce a kernelized repulsive term in the update rule of the deep ensembles. We show that this simple modification not only enforces and maintains diversity among the members but, even more importantly, transforms the maximum a posteriori inference into proper Bayesian inference. Namely, we show that the training dynamics of our proposed repulsive ensembles follow a Wasserstein gradient flow of the KL divergence with the true posterior. We study repulsive terms in weight and function space and empirically compare their performance to standard ensembles and Bayesian baselines on synthetic and real-world prediction tasks.

Authors Francesco D'Angelo, Vincent Fortuin

Submitted NeurIPS 2021 (spotlight)

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Abstract Uncertainty estimation in deep learning has recently emerged as a crucial area of interest to advance reliability and robustness in safety-critical applications. While there have been many proposed methods that either focus on distance-aware model uncertainties for out-of-distribution detection or on input-dependent label uncertainties for in-distribution calibration, both of these types of uncertainty are often necessary. In this work, we propose the HetSNGP method for jointly modeling the model and data uncertainty. We show that our proposed model affords a favorable combination between these two complementary types of uncertainty and thus outperforms the baseline methods on some challenging out-of-distribution datasets, including CIFAR-100C, Imagenet-C, and Imagenet-A. Moreover, we propose HetSNGP Ensemble, an ensembled version of our method which adds an additional type of uncertainty and also outperforms other ensemble baselines.

Authors Vincent Fortuin, Mark Collier, Florian Wenzel, James Allingham, Jeremiah Liu, Dustin Tran, Balaji Lakshminarayanan, Jesse Berent, Rodolphe Jenatton, Effrosyni Kokiopoulou

Submitted arXiv Preprints

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Abstract Machine learning models based on the aggregated outputs of submodels, either at the activation or prediction levels, lead to strong performance. We study the interplay of two popular classes of such models: ensembles of neural networks and sparse mixture of experts (sparse MoEs). First, we show that these two approaches have complementary features whose combination is beneficial. Then, we present partitioned batch ensembles, an efficient ensemble of sparse MoEs that takes the best of both classes of models. Extensive experiments on fine-tuned vision transformers demonstrate the accuracy, log-likelihood, few-shot learning, robustness, and uncertainty calibration improvements of our approach over several challenging baselines. Partitioned batch ensembles not only scale to models with up to 2.7B parameters, but also provide larger performance gains for larger models.

Authors James Urquhart Allingham, Florian Wenzel, Zelda E Mariet, Basil Mustafa, Joan Puigcerver, Neil Houlsby, Ghassen Jerfel, Vincent Fortuin, Balaji Lakshminarayanan, Jasper Snoek, Dustin Tran, Carlos Riquelme Ruiz, Rodolphe Jenatton

Submitted arXiv Preprints

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Abstract Marginal-likelihood based model-selection, even though promising, is rarely used in deep learning due to estimation difficulties. Instead, most approaches rely on validation data, which may not be readily available. In this work, we present a scalable marginal-likelihood estimation method to select both hyperparameters and network architectures, based on the training data alone. Some hyperparameters can be estimated online during training, simplifying the procedure. Our marginal-likelihood estimate is based on Laplace's method and Gauss-Newton approximations to the Hessian, and it outperforms cross-validation and manual-tuning on standard regression and image classification datasets, especially in terms of calibration and out-of-distribution detection. Our work shows that marginal likelihoods can improve generalization and be useful when validation data is unavailable (e.g., in nonstationary settings).

Authors Alexander Immer, Matthias Bauer, Vincent Fortuin, Gunnar Rätsch, Mohammad Emtiyaz Khan

Submitted ICML 2021

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Abstract We propose a novel Bayesian neural network architecture that can learn invariances from data alone by inferring a posterior distribution over different weight-sharing schemes. We show that our model outperforms other non-invariant architectures, when trained on datasets that contain specific invariances. The same holds true when no data augmentation is performed.

Authors Nikolaos Mourdoukoutas, Marco Federici, Georges Pantalos, Mark van der Wilk, Vincent Fortuin

Submitted arXiv Preprints

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Abstract 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.

Authors Jonas Rothfuss, Vincent Fortuin, Martin Josifoski, Andreas Krause

Submitted ICML 2021

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Abstract 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 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 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 as well as competitor methods and we show that the MoE architecture in the decoder reduces the computational cost of sampling specific data modes with high fidelity.

Authors Andreas Kopf, Vincent Fortuin, Vignesh Ram Somnath, Manfred Claassen

Submitted PLOS Computational Biology

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Abstract Bayesian neural networks that incorporate data augmentation implicitly use a ``randomly perturbed log-likelihood [which] does not have a clean interpretation as a valid likelihood function'' (Izmailov et al. 2021). Here, we provide several approaches to developing principled Bayesian neural networks incorporating data augmentation. We introduce a ``finite orbit'' setting which allows likelihoods to be computed exactly, and give tight multi-sample bounds in the more usual ``full orbit'' setting. These models cast light on the origin of the cold posterior effect. In particular, we find that the cold posterior effect persists even in these principled models incorporating data augmentation. This suggests that the cold posterior effect cannot be dismissed as an artifact of data augmentation using incorrect likelihoods.

Authors Seth Nabarro, Stoil Ganev, Adrià Garriga-Alonso, Vincent Fortuin, Mark van der Wilk, Laurence Aitchison

Submitted arXiv Preprints

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Abstract Ensembles of deep neural networks have achieved great success recently, but they do not offer a proper Bayesian justification. Moreover, while they allow for averaging of predictions over several hypotheses, they do not provide any guarantees for their diversity, leading to redundant solutions in function space. In contrast, particle-based inference methods, such as Stein variational gradient descent (SVGD), offer a Bayesian framework, but rely on the choice of a kernel to measure the similarity between ensemble members. In this work, we study different SVGD methods operating in the weight space, function space, and in a hybrid setting. We compare the SVGD approaches to other ensembling-based methods in terms of their theoretical properties and assess their empirical performance on synthetic and real-world tasks. We find that SVGD using functional and hybrid kernels can overcome the limitations of deep ensembles. It improves on functional diversity and uncertainty estimation and approaches the true Bayesian posterior more closely. Moreover, we show that using stochastic SVGD updates, as opposed to the standard deterministic ones, can further improve the performance.

Authors Francesco D'Angelo, Vincent Fortuin, Florian Wenzel

Submitted arXiv Preprints

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Abstract Bayesian neural networks have shown great promise in many applications where calibrated uncertainty estimates are crucial and can often also lead to a higher predictive performance. However, it remains challenging to choose a good prior distribution over their weights. While isotropic Gaussian priors are often chosen in practice due to their simplicity, they do not reflect our true prior beliefs well and can lead to suboptimal performance. Our new library, BNNpriors, enables state-of-the-art Markov Chain Monte Carlo inference on Bayesian neural networks with a wide range of predefined priors, including heavy-tailed ones, hierarchical ones, and mixture priors. Moreover, it follows a modular approach that eases the design and implementation of new custom priors. It has facilitated foundational discoveries on the nature of the cold posterior effect in Bayesian neural networks and will hopefully catalyze future research as well as practical applications in this area.

Authors Vincent Fortuin, Adrià Garriga-Alonso, Mark van der Wilk, Laurence Aitchison

Submitted Software Impacts

Link DOI

Abstract 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.

Authors Margherita Rosnati, Vincent Fortuin

Submitted PLOS One

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Abstract While the choice of prior is one of the most critical parts of the Bayesian inference workflow, recent Bayesian deep learning models have often fallen back on vague priors, such as standard Gaussians. In this review, we highlight the importance of prior choices for Bayesian deep learning and present an overview of different priors that have been proposed for (deep) Gaussian processes, variational autoencoders, and Bayesian neural networks. We also outline different methods of learning priors for these models from data. We hope to motivate practitioners in Bayesian deep learning to think more carefully about the prior specification for their models and to provide them with some inspiration in this regard.

Authors Vincent Fortuin

Submitted arXiv Preprints

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Abstract Conventional variational autoencoders fail in modeling correlations between data points due to their use of factorized priors. Amortized Gaussian process inference through GP-VAEs has led to significant improvements in this regard, but is still inhibited by the intrinsic complexity of exact GP inference. We improve the scalability of these methods through principled sparse inference approaches. We propose a new scalable GP-VAE model that outperforms existing approaches in terms of runtime and memory footprint, is easy to implement, and allows for joint end-to-end optimization of all components.

Authors Metod Jazbec, Vincent Fortuin, Michael Pearce, Stephan Mandt, Gunnar Rätsch

Submitted AISTATS 2021

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Abstract Generating interpretable visualizations of multivariate time series in the intensive care unit is of great practical importance. Clinicians seek to condense complex clinical observations into intuitively understandable critical illness patterns, like failures of different organ systems. They would greatly benefit from a low-dimensional representation in which the trajectories of the patients' pathology become apparent and relevant health features are highlighted. To this end, we propose to use the latent topological structure of Self-Organizing Maps (SOMs) to achieve an interpretable latent representation of ICU time series and combine it with recent advances in deep clustering. Specifically, we (a) present a novel way to fit SOMs with probabilistic cluster assignments (PSOM), (b) propose a new deep architecture for probabilistic clustering (DPSOM) using a VAE, and (c) extend our architecture to cluster and forecast clinical states in time series (T-DPSOM). We show that our model achieves superior clustering performance compared to state-of-the-art SOM-based clustering methods while maintaining the favorable visualization properties of SOMs. On the eICU data-set, we demonstrate that T-DPSOM provides interpretable visualizations of patient state trajectories and uncertainty estimation. We show that our method rediscovers well-known clinical patient characteristics, such as a dynamic variant of the Acute Physiology And Chronic Health Evaluation (APACHE) score. Moreover, we illustrate how it can disentangle individual organ dysfunctions on disjoint regions of the two-dimensional SOM map.

Authors Laura Manduchi, Matthias Hüser, Martin Faltys, Julia Vogt, Gunnar Rätsch, Vincent Fortuin

Submitted ACM-CHIL 2021

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Abstract Isotropic Gaussian priors are the de facto standard for modern Bayesian neural network inference. However, it is unclear whether these priors accurately reflect our true beliefs about the weight distributions or give optimal performance. To find better priors, we study summary statistics of neural network weights in networks trained using SGD. We find that convolutional neural network (CNN) weights display strong spatial correlations, while fully connected networks (FCNNs) display heavy-tailed weight distributions. Building these observations into priors leads to improved performance on a variety of image classification datasets. Surprisingly, these priors mitigate the cold posterior effect in FCNNs, but slightly increase the cold posterior effect in ResNets.

Authors Vincent Fortuin, Adrià Garriga-Alonso, Florian Wenzel, Gunnar Rätsch, Richard Turner, Mark van der Wilk, Laurence Aitchison

Submitted AABI 2021

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Abstract 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.

Authors Adrià Garriga-Alonso, Vincent Fortuin

Submitted AABI 2021

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Abstract Particle based optimization algorithms have recently been developed as sampling methods that iteratively update a set of particles to approximate a target distribution. In particular Stein variational gradient descent has gained attention in the approximate inference literature for its flexibility and accuracy. We empirically explore the ability of this method to sample from multi-modal distributions and focus on two important issues: (i) the inability of the particles to escape from local modes and (ii) the inefficacy in reproducing the density of the different regions. We propose an annealing schedule to solve these issues and show, through various experiments, how this simple solution leads to significant improvements in mode coverage, without invalidating any theoretical properties of the original algorithm.

Authors Francesco D'Angelo, Vincent Fortuin

Submitted AABI 2021

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Abstract 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.

Authors Metod Jazbec, Michael Pearce, Vincent Fortuin

Submitted AABI 2021

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Abstract 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.

Authors Matthew Ashman, Jonathan So, Will Tebbutt, Vincent Fortuin, Michael Pearce, Richard E. Turner

Submitted arXiv Preprints

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Abstract Kernel methods on discrete domains have shown great promise for many challenging tasks, e.g., on biological sequence data as well as on molecular structures. Scalable kernel methods like support vector machines offer good predictive performances but they often do not provide uncertainty estimates. In contrast, probabilistic kernel methods like Gaussian Processes offer uncertainty estimates in addition to good predictive performance but fall short in terms of scalability. We present the first sparse Gaussian Process approximation framework on discrete input domains. Our framework achieves good predictive performance as well as uncertainty estimates using different discrete optimization techniques. We present competitive results comparing our framework to support vector machine and full Gaussian Process baselines on synthetic data as well as on challenging real-world DNA sequence data.

Authors Vincent Fortuin, Gideon Dresdner, Heiko Strathmann, Gunnar Rätsch

Submitted IEEE Access

Link DOI

Abstract Obtaining high-quality uncertainty estimates is essential for many applications of deep neural networks. In this paper, we theoretically justify a scheme for estimating uncertainties, based on sampling from a prior distribution. Crucially, the uncertainty estimates are shown to be conservative in the sense that they never underestimate a posterior uncertainty obtained by a hypothetical Bayesian algorithm. We also show concentration, implying that the uncertainty estimates converge to zero as we get more data. Uncertainty estimates obtained from random priors can be adapted to any deep network architecture and trained using standard supervised learning pipelines. We provide experimental evaluation of random priors on calibration and out-of-distribution detection on typical computer vision tasks, demonstrating that they outperform deep ensembles in practice.

Authors Kamil Ciosek, Vincent Fortuin, Ryota Tomioka, Katja Hofmann, Richard Turner

Submitted ICLR 2020

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Abstract Metagenomic studies have increasingly utilized sequencing technologies in order to analyze DNA fragments found in environmental samples.One important step in this analysis is the taxonomic classification of the DNA fragments. Conventional read classification methods require large databases and vast amounts of memory to run, with recent deep learning methods suffering from very large model sizes. We therefore aim to develop a more memory-efficient technique for taxonomic classification. A task of particular interest is abundance estimation in metagenomic samples. Current attempts rely on classifying single DNA reads independently from each other and are therefore agnostic to co-occurence patterns between taxa. In this work, we also attempt to take these patterns into account. We develop a novel memory-efficient read classification technique, combining deep learning and locality-sensitive hashing. We show that this approach outperforms conventional mapping-based and other deep learning methods for single-read taxonomic classification when restricting all methods to a fixed memory footprint. Moreover, we formulate the task of abundance estimation as a Multiple Instance Learning (MIL) problem and we extend current deep learning architectures with two different types of permutation-invariant MIL pooling layers: a) deepsets and b) attention-based pooling. We illustrate that our architectures can exploit the co-occurrence of species in metagenomic read sets and outperform the single-read architectures in predicting the distribution over taxa at higher taxonomic ranks.

Authors Andreas Georgiou, Vincent Fortuin, Harun Mustafa, Gunnar Rätsch

Submitted arXiv Preprints

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Abstract Multivariate time series with missing values are common in areas such as healthcare and finance, and have grown in number and complexity over the years. This raises the question whether deep learning methodologies can outperform classical data imputation methods in this domain. However, naive applications of deep learning fall short in giving reliable confidence estimates and lack interpretability. We propose a new deep sequential latent variable model for dimensionality reduction and data imputation. Our modeling assumption is simple and interpretable: the high dimensional time series has a lower-dimensional representation which evolves smoothly in time according to a Gaussian process. The non-linear dimensionality reduction in the presence of missing data is achieved using a VAE approach with a novel structured variational approximation. We demonstrate that our approach outperforms several classical and deep learning-based data imputation methods on high-dimensional data from the domains of computer vision and healthcare, while additionally improving the smoothness of the imputations and providing interpretable uncertainty estimates.

Authors Vincent Fortuin, Dmitry Baranchuk, Gunnar Rätsch, Stephan Mandt

Submitted AISTATS 2020

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Abstract When fitting Bayesian machine learning models on scarce data, the main challenge is to obtain suitable prior knowledge and encode it into the model. Recent advances in meta-learning offer powerful methods for extracting such prior knowledge from data acquired in related tasks. When it comes to meta-learning in Gaussian process models, approaches in this setting have mostly focused on learning the kernel function of the prior, but not on learning its mean function. In this work, we explore meta-learning the mean function of a Gaussian process prior. We present analytical and empirical evidence that mean function learning can be useful in the meta-learning setting, discuss the risk of overfitting, and draw connections to other meta-learning approaches, such as model agnostic meta-learning and functional PCA.

Authors Vincent Fortuin, Heiko Strathmann, Gunnar Rätsch

Submitted arXiv Preprints

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Abstract High-dimensional time series are common in many domains. Since human cognition is not optimized to work well in high-dimensional spaces, these areas could benefit from interpretable low-dimensional representations. However, most representation learning algorithms for time series data are difficult to interpret. This is due to non-intuitive mappings from data features to salient properties of the representation and non-smoothness over time. To address this problem, we propose a new representation learning framework building on ideas from interpretable discrete dimensionality reduction and deep generative modeling. This framework allows us to learn discrete representations of time series, which give rise to smooth and interpretable embeddings with superior clustering performance. We introduce a new way to overcome the non-differentiability in discrete representation learning and present a gradient-based version of the traditional self-organizing map algorithm that is more performant than the original. Furthermore, to allow for a probabilistic interpretation of our method, we integrate a Markov model in the representation space. This model uncovers the temporal transition structure, improves clustering performance even further and provides additional explanatory insights as well as a natural representation of uncertainty. We evaluate our model in terms of clustering performance and interpretability on static (Fashion-)MNIST data, a time series of linearly interpolated (Fashion-)MNIST images, a chaotic Lorenz attractor system with two macro states, as well as on a challenging real world medical time series application on the eICU data set. Our learned representations compare favorably with competitor methods and facilitate downstream tasks on the real world data.

Authors Vincent Fortuin, Matthias Hüser, Francesco Locatello, Heiko Strathmann, Gunnar Rätsch

Submitted ICLR 2019

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Abstract Neural Processes (NPs) are a class of neural latent variable models that combine desirable properties of Gaussian Processes (GPs) and neural networks. Like GPs, NPs define distributions over functions and are able to estimate the uncertainty in their predictions. Like neural networks, NPs are computationally efficient during training and prediction time. In this paper, we establish an explicit theoretical connection between NPs and GPs. In particular, we show that, under certain conditions, NPs are mathematically equivalent to GPs with deep kernels. This result further elucidates the relationship between GPs and NPs and makes previously derived theoretical insights about GPs applicable to NPs. Furthermore, it suggests a novel approach to learning expressive GP covariance functions applicable across different prediction tasks by training a deep kernel GP on a set of datasets.

Authors Tim G. J. Rudner, Vincent Fortuin, Yee Whye Teh, Yarin Gal

Submitted Bayesian Deep Learning workshop @NeurIPS 2018

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Abstract The reconstruction of gene regulatory networks from time resolved gene expression measurements is a key challenge in systems biology with applications in health and disease. While the most popular network inference methods are based on unsupervised learning approaches, supervised learning methods have proven their potential for superior reconstruction performance. However, obtaining the appropriate volume of informative training data constitutes a key limitation for the success of such methods. Here, we introduce a supervised learning approach to detect gene-gene regulation based on exclusively synthetic training data, termed surrogate learning, and show its performance for synthetic and experimental time-series. We systematically investigate different simulation configurations of biologically representative time-series of transcripts and augmentation of the data with a measurement model. We compare the resulting synthetic datasets to experimental data, and evaluate classifiers trained on them for detection of gene-gene regulation from experimental time-series. For classifiers, we consider hybrid convolutional recurrent neural networks, random forests and logistic regression, and evaluate the reconstruction performance of different simulation settings, data pre-processing and classifiers. When training and test time-courses are generated from the same distribution, we find that the largest tested neural network architecture achieves the best performance of 0.448 +/- 0.047 (mean +/- std) in maximally achievable F1 score over all datasets outperforming random forests by 32.4 % +/- 14 % (mean +/- std). Reconstruction performance is sensitive to discrepancies between synthetic training and test data, highlighting the importance of matching training and test data domains. For an experimental gene expression dataset from E.coli, we find that training data generated with measurement model, multi-gene perturbations, but without data standardization is best suited for training classifiers for network reconstruction from the experimental test data. We further demonstrate superiority to multiple unsupervised, state-of-the-art methods for networks comprising 20 genes of the experimental data from E.coli (average AUPR best supervised = 0.22 vs best unsupervised = 0.07). We expect the proposed surrogate learning approach to be broadly applicable. It alleviates the requirement for large, difficult to attain volumes of experimental training data and instead relies on easily accessible synthetic data. Successful application for new experimental conditions and other data types is only limited by the automatable and scalable process of designing simulations which generate suitable synthetic data.

Authors Stefan Ganscha, Vincent Fortuin, Max Horn, Eirini Arvaniti, Manfred Claassen

Submitted bioRxiv Preprints

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Abstract We present a novel approach to modeling stories using recurrent neural networks. Different story features are extracted using natural language processing techniques and used to encode the stories as sequences. These sequences can be learned by deep neural networks, in order to predict the next story events. The predictions can be used as an inspiration for writers who experience a writer's block. We further assist writers in their creative process by generating visualizations of the character interactions in the story. We show that suggestions from our model are rated as highly as the real scenes from a set of films and that our visualizations can help people in gaining deeper story understanding.

Authors Vincent Fortuin, Romann M. Weber, Sasha Schriber, Diana Wotruba, Markus Gross

Submitted AAAI 2018

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