Normalizing flows, which learn a distribution by transforming the data to samples from a Gaussian base distribution, have proven powerful density approximations. But their expressive power is limited by this choice of the base distribution. We, therefore, propose to generalize the base distribution to a more elaborate copula distribution to capture the properties of the target distribution more accurately. In a first empirical analysis, we demonstrate that this replacement can dramatically improve the vanilla normalizing flows in terms of flexibility, stability, and effectivity for heavy-tailed data. Our results suggest that the improvements are related to an increased local Lipschitz-stability of the learned flow.

Quantification of uncertainty is one of the most promising approaches to establish safe machine learning. Despite its importance, it is far from being generally solved, especially for neural networks. One of the most commonly used approaches so far is Monte Carlo dropout, which is computationally cheap and easy to apply in practice. However, it can underestimate the uncertainty. We propose a new objective, referred to as second-moment loss (SML), to address this issue. While the full network is encouraged to model the mean, the dropout networks are explicitly used to optimize the model variance. We intensively study the performance of the new objective on various UCI regression datasets. Comparing to the state-of-the-art of deep ensembles, SML leads to comparable prediction accuracies and uncertainty estimates while only requiring a single model. Under distribution shift, we observe moderate improvements. As a side result, we introduce an intuitive Wasserstein distance-based uncertainty measure that is non-saturating and thus allows to resolve quality differences between any two uncertainty estimates.

Quantification of uncertainty is one of the most promising approaches to establish safe machine learning. Despite its importance, it is far from being generally solved, especially for neural networks. One of the most commonly used approaches so far is Monte Carlo dropout, which is computationally cheap and easy to apply in practice. However, it can underestimate the uncertainty. We propose a new objective, referred to as second-moment loss (SML), to address this issue. While the full network is encouraged to model the mean, the dropout networks are explicitly used to optimize the model variance. We analyze the performance of the new objective on various toy and UCI regression datasets. Comparing to the state-of-the-art of deep ensembles, SML leads to comparable prediction accuracies and uncertainty estimates while only requiring a single model. Under distribution shift, we observe moderate improvements. From a safety perspective also the study of worst-case uncertainties is crucial. In this regard we improve considerably. Finally, we show that SML can be successfully applied to SqueezeDet, a modern object detection network. We improve on its uncertainty-related scores while not deteriorating regression quality. As a side result, we introduce an intuitive Wasserstein distance-based uncertainty measure that is non-saturating and thus allows to resolve quality differences between any two uncertainty estimates.

Uncertainty quantification in neural networks gained a lot of attention in the past years. The most popular approaches, Bayesian neural networks (BNNs), Monte Carlo dropout, and deep ensembles have one thing in common: they are all based on some kind of mixture model. While the BNNs build infinite mixture models and are derived via variational inference, the latter two build finite mixtures trained with the maximum likelihood method. In this work we investigate the effect of training an infinite mixture distribution with the maximum likelihood method instead of variational inference. We find that the proposed objective leads to stochastic networks with an increased predictive variance, which improves uncertainty based identification of miss-classification and robustness against adversarial attacks in comparison to a standard BNN with equivalent network structure. The new model also displays higher entropy on out-of-distribution data.

The heterogeneity in recently published knowledge graph embedding models' implementations, training, and evaluation has made fair and thorough comparisons difficult. In order to assess the reproducibility of previously published results, we re-implemented and evaluated 19 interaction models in the PyKEEN software package. Here, we outline which results could be reproduced with their reported hyper-parameters, which could only be reproduced with alternate hyper-parameters, and which could not be reproduced at all as well as provide insight as to why this might be the case. We then performed a large-scale benchmarking on four datasets with several thousands of experiments and 21,246 GPU hours of computation time. We present insights gained as to best practices, best configurations for each model, and where improvements could be made over previously published best configurations. Our results highlight that the combination of model architecture, training approach, loss function, and the explicit modeling of inverse relations is crucial for a model's performances, and not only determined by the model architecture. We provide evidence that several architectures can obtain results competitive to the state-of-the-art when configured carefully. We have made all code, experimental configurations, results, and analyses that lead to our interpretations available at https://github.com/pykeen/pykeen and https://github.com/pykeen/benchmarking

Machine learning systems and also, specifically, automatic speech recognition (ASR) systems are vulnerable against adversarial attacks, where an attacker maliciously changes the input. In the case of ASR systems, the most interesting cases are targeted attacks, in which an attacker aims to force the system into recognizing given target transcriptions in an arbitrary audio sample. The increasing number of sophisticated, quasi imperceptible attacks raises the question of countermeasures. In this paper, we focus on hybrid ASR systems and compare four acoustic models regarding their ability to indicate uncertainty under attack: a feed-forward neural network and three neural networks specifically designed for uncertainty quantification, namely a Bayesian neural network, Monte Carlo dropout, and a deep ensemble. We employ uncertainty measures of the acoustic model to construct a simple one-class classification model for assessing whether inputs are benign or adversarial. Based on this approach, we are able to detect adversarial examples with an area under the receiving operator curve score of more than 0.99. The neural networks for uncertainty quantification simultaneously diminish the vulnerability to the attack, which is reflected in a lower recognition accuracy of the malicious target text in comparison to a standard hybrid ASR system.

Graph Neural Networks (GNN) form a class of neural network architectures specifically designed to work with graphstructured data. In our work, we focus on multi-relational graphs, where edges are labeled with different edge types. While different GNN variants have been proposed in recent literature, to the best of our knowledge, their ability to capture long-term dependencies in graph data has not been thoroughly investigated. Due to their local aggregation nature, many layers of a GNN must be used to capture long-range patterns (i.e., at least K GNN layers are needed to incorporate any information from a node that is K hops away in the graph). However, GNNs suffer from decreasing performance when the number of layers is increased.

Monte Carlo (MC) dropout is one of the state-of-the-art approaches for uncertainty estimation in neural networks (NNs). It has been interpreted as approximately performing Bayesian inference. Based on previous work on the approximation of Gaussian processes by wide and deep neural networks with random weights, we study the limiting distribution of wide untrained NNs under dropout more rigorously and prove that they as well converge to Gaussian processes for fixed sets of weights and biases. We sketch an argument that this property might also hold for infinitely wide feed-forward networks that are trained with (full-batch) gradient descent. The theory is contrasted by an empirical analysis in which we find correlations and non-Gaussian behaviour for the pre-activations of finite width NNs. We therefore investigate how (strongly) correlated pre-activations can induce non-Gaussian behavior in NNs with strongly correlated weights.

The Metropolis algorithm is arguably the most fundamental Markov chain Monte Carlo (MCMC) method. But the algorithm is not guaranteed to converge to the desired distribution in the case of multivariate binary distributions (e.g., Ising models or stochastic neural networks such as Boltzmann machines) if the variables (sites or neurons) are updated in a fixed order, a setting commonly used in practice. The reason is that the corresponding Markov chain may not be irreducible. We propose a modified Metropolis transition operator that behaves almost always identically to the standard Metropolis operator and prove that it ensures irreducibility and convergence to the limiting distribution in the multivariate binary case with fixed-order updates. The result provides an explanation for the behaviour of Metropolis MCMC in that setting and closes a long-standing theoretical gap. We experimentally studied the standard and modified Metropolis operator for models were they actually behave differently. If the standard algorithm also converges, the modified operator exhibits similar (if not better) performance in terms of convergence speed.

Question answering has emerged as an intuitive way of querying structured data sources, and has attracted significant advancements over the years. In this article, we provide an overview over these recent advancements, focusing on neural network based question answering systems over knowledge graphs. We introduce readers to the challenges in the tasks, current paradigms of approaches, discuss notable advancements, and outline the emerging trends in the field. Through this article, we aim to provide newcomers to the field with a suitable entry point, and ease their process of making informed decisions while creating their own QA system.