Andrey Malinin

Nataliia Molchanova, Vatsal Raina, Andrey Malinin et al.

This paper focuses on the uncertainty estimation for white matter lesions (WML) segmentation in magnetic resonance imaging (MRI). On one side, voxel-scale segmentation errors cause the erroneous delineation of the lesions; on the other side, lesion-scale detection errors lead to wrong lesion counts. Both of these factors are clinically relevant for the assessment of multiple sclerosis patients. This work aims to compare the ability of different voxel- and lesion-scale uncertainty measures to capture errors related to segmentation and lesion detection, respectively. Our main contributions are (i) proposing new measures of lesion-scale uncertainty that do not utilise voxel-scale uncertainties; (ii) extending an error retention curves analysis framework for evaluation of lesion-scale uncertainty measures. Our results obtained on the multi-center testing set of 58 patients demonstrate that the proposed lesion-scale measure achieves the best performance among the analysed measures. All code implementations are provided at https://github.com/NataliiaMolch/MS_WML_uncs

Nataliia Molchanova, Vatsal Raina, Andrey Malinin et al.

This paper explores uncertainty quantification (UQ) as an indicator of the trustworthiness of automated deep-learning (DL) tools in the context of white matter lesion (WML) segmentation from magnetic resonance imaging (MRI) scans of multiple sclerosis (MS) patients. Our study focuses on two principal aspects of uncertainty in structured output segmentation tasks. First, we postulate that a reliable uncertainty measure should indicate predictions likely to be incorrect with high uncertainty values. Second, we investigate the merit of quantifying uncertainty at different anatomical scales (voxel, lesion, or patient). We hypothesize that uncertainty at each scale is related to specific types of errors. Our study aims to confirm this relationship by conducting separate analyses for in-domain and out-of-domain settings. Our primary methodological contributions are (i) the development of novel measures for quantifying uncertainty at lesion and patient scales, derived from structural prediction discrepancies, and (ii) the extension of an error retention curve analysis framework to facilitate the evaluation of UQ performance at both lesion and patient scales. The results from a multi-centric MRI dataset of 444 patients demonstrate that our proposed measures more effectively capture model errors at the lesion and patient scales compared to measures that average voxel-scale uncertainty values. We provide the UQ protocols code at https://github.com/Medical-Image-Analysis-Laboratory/MS_WML_uncs.

Vatsal Raina, Nataliia Molchanova, Mara Graziani et al.

The development of automatic segmentation techniques for medical imaging tasks requires assessment metrics to fairly judge and rank such approaches on benchmarks. The Dice Similarity Coefficient (DSC) is a popular choice for comparing the agreement between the predicted segmentation against a ground-truth mask. However, the DSC metric has been shown to be biased to the occurrence rate of the positive class in the ground-truth, and hence should be considered in combination with other metrics. This work describes a detailed analysis of the recently proposed normalised Dice Similarity Coefficient (nDSC) for binary segmentation tasks as an adaptation of DSC which scales the precision at a fixed recall rate to tackle this bias. White matter lesion segmentation on magnetic resonance images of multiple sclerosis patients is selected as a case study task to empirically assess the suitability of nDSC. We validate the normalised DSC using two different models across 59 subject scans with a wide range of lesion loads. It is found that the nDSC is less biased than DSC with lesion load on standard white matter lesion segmentation benchmarks measured using standard rank correlation coefficients. An implementation of nDSC is made available at: https://github.com/NataliiaMolch/nDSC .

Andrey Malinin, Andreas Athanasopoulos, Muhamed Barakovic et al.

Distributional shift, or the mismatch between training and deployment data, is a significant obstacle to the usage of machine learning in high-stakes industrial applications, such as autonomous driving and medicine. This creates a need to be able to assess how robustly ML models generalize as well as the quality of their uncertainty estimates. Standard ML baseline datasets do not allow these properties to be assessed, as the training, validation and test data are often identically distributed. Recently, a range of dedicated benchmarks have appeared, featuring both distributionally matched and shifted data. Among these benchmarks, the Shifts dataset stands out in terms of the diversity of tasks as well as the data modalities it features. While most of the benchmarks are heavily dominated by 2D image classification tasks, Shifts contains tabular weather forecasting, machine translation, and vehicle motion prediction tasks. This enables the robustness properties of models to be assessed on a diverse set of industrial-scale tasks and either universal or directly applicable task-specific conclusions to be reached. In this paper, we extend the Shifts Dataset with two datasets sourced from industrial, high-risk applications of high societal importance. Specifically, we consider the tasks of segmentation of white matter Multiple Sclerosis lesions in 3D magnetic resonance brain images and the estimation of power consumption in marine cargo vessels. Both tasks feature ubiquitous distributional shifts and a strict safety requirement due to the high cost of errors. These new datasets will allow researchers to further explore robust generalization and uncertainty estimation in new situations. In this work, we provide a description of the dataset and baseline results for both tasks.

Gleb Bazhenov, Denis Kuznedelev, Andrey Malinin et al.

In reliable decision-making systems based on machine learning, models have to be robust to distributional shifts or provide the uncertainty of their predictions. In node-level problems of graph learning, distributional shifts can be especially complex since the samples are interdependent. To evaluate the performance of graph models, it is important to test them on diverse and meaningful distributional shifts. However, most graph benchmarks considering distributional shifts for node-level problems focus mainly on node features, while structural properties are also essential for graph problems. In this work, we propose a general approach for inducing diverse distributional shifts based on graph structure. We use this approach to create data splits according to several structural node properties: popularity, locality, and density. In our experiments, we thoroughly evaluate the proposed distributional shifts and show that they can be quite challenging for existing graph models. We also reveal that simple models often outperform more sophisticated methods on the considered structural shifts. Finally, our experiments provide evidence that there is a trade-off between the quality of learned representations for the base classification task under structural distributional shift and the ability to separate the nodes from different distributions using these representations.

Ivan Provilkov, Andrey Malinin

Neural Machine Translation (NMT) is known to suffer from a beam-search problem: after a certain point, increasing beam size causes an overall drop in translation quality. This effect is especially pronounced for long sentences. While much work was done analyzing this phenomenon, primarily for autoregressive NMT models, there is still no consensus on its underlying cause. In this work, we analyze errors that cause major quality degradation with large beams in NMT and Automatic Speech Recognition (ASR). We show that a factor that strongly contributes to the quality degradation with large beams is \textit{dataset length-bias} - \textit{NMT datasets are strongly biased towards short sentences}. To mitigate this issue, we propose a new data augmentation technique -- \textit{Multi-Sentence Resampling (MSR)}. This technique extends the training examples by concatenating several sentences from the original dataset to make a long training example. We demonstrate that MSR significantly reduces degradation with growing beam size and improves final translation quality on the IWSTL$15$ En-Vi, IWSTL$17$ En-Fr, and WMT$14$ En-De datasets.

Carel van Niekerk, Andrey Malinin, Christian Geishauser et al.

The ability to identify and resolve uncertainty is crucial for the robustness of a dialogue system. Indeed, this has been confirmed empirically on systems that utilise Bayesian approaches to dialogue belief tracking. However, such systems consider only confidence estimates and have difficulty scaling to more complex settings. Neural dialogue systems, on the other hand, rarely take uncertainties into account. They are therefore overconfident in their decisions and less robust. Moreover, the performance of the tracking task is often evaluated in isolation, without consideration of its effect on the downstream policy optimisation. We propose the use of different uncertainty measures in neural belief tracking. The effects of these measures on the downstream task of policy optimisation are evaluated by adding selected measures of uncertainty to the feature space of the policy and training policies through interaction with a user simulator. Both human and simulated user results show that incorporating these measures leads to improvements both of the performance and of the robustness of the downstream dialogue policy. This highlights the importance of developing neural dialogue belief trackers that take uncertainty into account.

Andrey Malinin, Neil Band, Ganshin et al.

There has been significant research done on developing methods for improving robustness to distributional shift and uncertainty estimation. In contrast, only limited work has examined developing standard datasets and benchmarks for assessing these approaches. Additionally, most work on uncertainty estimation and robustness has developed new techniques based on small-scale regression or image classification tasks. However, many tasks of practical interest have different modalities, such as tabular data, audio, text, or sensor data, which offer significant challenges involving regression and discrete or continuous structured prediction. Thus, given the current state of the field, a standardized large-scale dataset of tasks across a range of modalities affected by distributional shifts is necessary. This will enable researchers to meaningfully evaluate the plethora of recently developed uncertainty quantification methods, as well as assessment criteria and state-of-the-art baselines. In this work, we propose the Shifts Dataset for evaluation of uncertainty estimates and robustness to distributional shift. The dataset, which has been collected from industrial sources and services, is composed of three tasks, with each corresponding to a particular data modality: tabular weather prediction, machine translation, and self-driving car (SDC) vehicle motion prediction. All of these data modalities and tasks are affected by real, "in-the-wild" distributional shifts and pose interesting challenges with respect to uncertainty estimation. In this work we provide a description of the dataset and baseline results for all tasks.

Ekaterina Lobacheva, Maxim Kodryan, Nadezhda Chirkova et al.

Training neural networks with batch normalization and weight decay has become a common practice in recent years. In this work, we show that their combined use may result in a surprising periodic behavior of optimization dynamics: the training process regularly exhibits destabilizations that, however, do not lead to complete divergence but cause a new period of training. We rigorously investigate the mechanism underlying the discovered periodic behavior from both empirical and theoretical points of view and analyze the conditions in which it occurs in practice. We also demonstrate that periodic behavior can be regarded as a generalization of two previously opposing perspectives on training with batch normalization and weight decay, namely the equilibrium presumption and the instability presumption.

Max Ryabinin, Andrey Malinin, Mark Gales

Ensembles of machine learning models yield improved system performance as well as robust and interpretable uncertainty estimates; however, their inference costs may often be prohibitively high. \emph{Ensemble Distribution Distillation} is an approach that allows a single model to efficiently capture both the predictive performance and uncertainty estimates of an ensemble. For classification, this is achieved by training a Dirichlet distribution over the ensemble members' output distributions via the maximum likelihood criterion. Although theoretically principled, this criterion exhibits poor convergence when applied to large-scale tasks where the number of classes is very high. In our work, we analyze this effect and show that the Dirichlet log-likelihood criterion classes with low probability induce larger gradients than high-probability classes. This forces the model to focus on the distribution of the ensemble tail-class probabilities. We propose a new training objective that minimizes the reverse KL-divergence to a \emph{Proxy-Dirichlet} target derived from the ensemble. This loss resolves the gradient issues of Ensemble Distribution Distillation, as we demonstrate both theoretically and empirically on the ImageNet and WMT17 En-De datasets containing 1000 and 40,000 classes, respectively.

Yassir Fathullah, Mark Gales, Andrey Malinin

Ensemble approaches are commonly used techniques to improving a system by combining multiple model predictions. Additionally these schemes allow the uncertainty, as well as the source of the uncertainty, to be derived for the prediction. Unfortunately these benefits come at a computational and memory cost. To address this problem ensemble distillation (EnD) and more recently ensemble distribution distillation (EnDD) have been proposed that compress the ensemble into a single model, representing either the ensemble average prediction or prediction distribution respectively. This paper examines the application of both these distillation approaches to a sequence prediction task, grammatical error correction (GEC). This is an important application area for language learning tasks as it can yield highly useful feedback to the learner. It is, however, more challenging than the standard tasks investigated for distillation as the prediction of any grammatical correction to a word will be highly dependent on both the input sequence and the generated output history for the word. The performance of both EnD and EnDD are evaluated on both publicly available GEC tasks as well as a spoken language task.

Andrey Malinin, Sergey Chervontsev, Ivan Provilkov et al.

Prior Networks are a recently developed class of models which yield interpretable measures of uncertainty and have been shown to outperform state-of-the-art ensemble approaches on a range of tasks. They can also be used to distill an ensemble of models via Ensemble Distribution Distillation (EnD$^2$), such that its accuracy, calibration and uncertainty estimates are retained within a single model. However, Prior Networks have so far been developed only for classification tasks. This work extends Prior Networks and EnD$^2$ to regression tasks by considering the Normal-Wishart distribution. The properties of Regression Prior Networks are demonstrated on synthetic data, selected UCI datasets and a monocular depth estimation task, where they yield performance competitive with ensemble approaches.

Andrey Malinin, Liudmila Prokhorenkova, Aleksei Ustimenko

For many practical, high-risk applications, it is essential to quantify uncertainty in a model's predictions to avoid costly mistakes. While predictive uncertainty is widely studied for neural networks, the topic seems to be under-explored for models based on gradient boosting. However, gradient boosting often achieves state-of-the-art results on tabular data. This work examines a probabilistic ensemble-based framework for deriving uncertainty estimates in the predictions of gradient boosting classification and regression models. We conducted experiments on a range of synthetic and real datasets and investigated the applicability of ensemble approaches to gradient boosting models that are themselves ensembles of decision trees. Our analysis shows that ensembles of gradient boosting models successfully detect anomalous inputs while having limited ability to improve the predicted total uncertainty. Importantly, we also propose a concept of a virtual ensemble to get the benefits of an ensemble via only one gradient boosting model, which significantly reduces complexity.

Andrey Malinin, Mark Gales

Uncertainty estimation is important for ensuring safety and robustness of AI systems. While most research in the area has focused on un-structured prediction tasks, limited work has investigated general uncertainty estimation approaches for structured prediction. Thus, this work aims to investigate uncertainty estimation for autoregressive structured prediction tasks within a single unified and interpretable probabilistic ensemble-based framework. We consider: uncertainty estimation for sequence data at the token-level and complete sequence-level; interpretations for, and applications of, various measures of uncertainty; and discuss both the theoretical and practical challenges associated with obtaining them. This work also provides baselines for token-level and sequence-level error detection, and sequence-level out-of-domain input detection on the WMT'14 English-French and WMT'17 English-German translation and LibriSpeech speech recognition datasets.

Andrey Malinin, Mark Gales

Ensemble approaches for uncertainty estimation have recently been applied to the tasks of misclassification detection, out-of-distribution input detection and adversarial attack detection. Prior Networks have been proposed as an approach to efficiently \emph{emulate} an ensemble of models for classification by parameterising a Dirichlet prior distribution over output distributions. These models have been shown to outperform alternative ensemble approaches, such as Monte-Carlo Dropout, on the task of out-of-distribution input detection. However, scaling Prior Networks to complex datasets with many classes is difficult using the training criteria originally proposed. This paper makes two contributions. First, we show that the appropriate training criterion for Prior Networks is the \emph{reverse} KL-divergence between Dirichlet distributions. This addresses issues in the nature of the training data target distributions, enabling prior networks to be successfully trained on classification tasks with arbitrarily many classes, as well as improving out-of-distribution detection performance. Second, taking advantage of this new training criterion, this paper investigates using Prior Networks to detect adversarial attacks and proposes a generalized form of adversarial training. It is shown that the construction of successful \emph{adaptive} whitebox attacks, which affect the prediction and evade detection, against Prior Networks trained on CIFAR-10 and CIFAR-100 using the proposed approach requires a greater amount of computational effort than against networks defended using standard adversarial training or MC-dropout.

Andrey Malinin, Bruno Mlodozeniec, Mark Gales

Ensembles of models often yield improvements in system performance. These ensemble approaches have also been empirically shown to yield robust measures of uncertainty, and are capable of distinguishing between different \emph{forms} of uncertainty. However, ensembles come at a computational and memory cost which may be prohibitive for many applications. There has been significant work done on the distillation of an ensemble into a single model. Such approaches decrease computational cost and allow a single model to achieve an accuracy comparable to that of an ensemble. However, information about the \emph{diversity} of the ensemble, which can yield estimates of different forms of uncertainty, is lost. This work considers the novel task of \emph{Ensemble Distribution Distillation} (EnD$^2$) --- distilling the distribution of the predictions from an ensemble, rather than just the average prediction, into a single model. EnD$^2$ enables a single model to retain both the improved classification performance of ensemble distillation as well as information about the diversity of the ensemble, which is useful for uncertainty estimation. A solution for EnD$^2$ based on Prior Networks, a class of models which allow a single neural network to explicitly model a distribution over output distributions, is proposed in this work. The properties of EnD$^2$ are investigated on both an artificial dataset, and on the CIFAR-10, CIFAR-100 and TinyImageNet datasets, where it is shown that EnD$^2$ can approach the classification performance of an ensemble, and outperforms both standard DNNs and Ensemble Distillation on the tasks of misclassification and out-of-distribution input detection.

Andrey Malinin, Mark Gales

Adversarial examples are considered a serious issue for safety critical applications of AI, such as finance, autonomous vehicle control and medicinal applications. Though significant work has resulted in increased robustness of systems to these attacks, systems are still vulnerable to well-crafted attacks. To address this problem, several adversarial attack detection methods have been proposed. However, a system can still be vulnerable to adversarial samples that are designed to specifically evade these detection methods. One recent detection scheme that has shown good performance is based on uncertainty estimates derived from Monte-Carlo dropout ensembles. Prior Networks, a new method of estimating predictive uncertainty, has been shown to outperform Monte-Carlo dropout on a range of tasks. One of the advantages of this approach is that the behaviour of a Prior Network can be explicitly tuned to, for example, predict high uncertainty in regions where there are no training data samples. In this work, Prior Networks are applied to adversarial attack detection using measures of uncertainty in a similar fashion to Monte-Carlo Dropout. Detection based on measures of uncertainty derived from DNNs and Monte-Carlo dropout ensembles are used as a baseline. Prior Networks are shown to significantly out-perform these baseline approaches over a range of adversarial attacks in both detection of whitebox and blackbox configurations. Even when the adversarial attacks are constructed with full knowledge of the detection mechanism, it is shown to be highly challenging to successfully generate an adversarial sample.

Andrey Malinin, Mark Gales

Estimating how uncertain an AI system is in its predictions is important to improve the safety of such systems. Uncertainty in predictive can result from uncertainty in model parameters, irreducible data uncertainty and uncertainty due to distributional mismatch between the test and training data distributions. Different actions might be taken depending on the source of the uncertainty so it is important to be able to distinguish between them. Recently, baseline tasks and metrics have been defined and several practical methods to estimate uncertainty developed. These methods, however, attempt to model uncertainty due to distributional mismatch either implicitly through model uncertainty or as data uncertainty. This work proposes a new framework for modeling predictive uncertainty called Prior Networks (PNs) which explicitly models distributional uncertainty. PNs do this by parameterizing a prior distribution over predictive distributions. This work focuses on uncertainty for classification and evaluates PNs on the tasks of identifying out-of-distribution (OOD) samples and detecting misclassification on the MNIST dataset, where they are found to outperform previous methods. Experiments on synthetic and MNIST and CIFAR-10 data show that unlike previous non-Bayesian methods PNs are able to distinguish between data and distributional uncertainty.