Understanding decisions made by neural networks is key for the deployment of intelligent systems in real world applications. However, the opaque decision making process of these systems is a disadvantage where interpretability is essential. Many feature-based explanation techniques have been introduced over the last few years in the field of machine learning to better understand decisions made by neural networks and have become an important component to verify their reasoning capabilities. However, existing methods do not allow statements to be made about the uncertainty regarding a feature's relevance for the prediction. In this paper, we introduce Monte Carlo Relevance Propagation (MCRP) for feature relevance uncertainty estimation. A simple but powerful method based on Monte Carlo estimation of the feature relevance distribution to compute feature relevance uncertainty scores that allow a deeper understanding of a neural network's perception and reasoning.
In this report, we present qualitative analysis of Monte Carlo (MC) dropout method for measuring model uncertainty in neural network (NN) models. We first consider the sources of uncertainty in NNs, and briefly review Bayesian Neural Networks (BNN), the group of Bayesian approaches to tackle uncertainties in NNs. After presenting mathematical formulation of MC dropout, we proceed to suggesting potential benefits and associated costs for using MC dropout in typical NN models, with the results from our experiments.
German Research Center for Artificial Intelligence（德国人工智能研究中心）
Estimating predictive uncertainty is crucial for many computer vision tasks, from image classification to autonomous driving systems. Hamiltonian Monte Carlo (HMC) is an sampling method for performing Bayesian inference. On the other hand, Dropout regularization has been proposed as an approximate model averaging technique that tends to improve generalization in large scale models such as deep neural networks. Although, HMC provides convergence guarantees for most standard Bayesian models, it does not handle discrete parameters arising from Dropout regularization. In this paper, we present a r…
West University of Timisoara（蒂米什瓦拉西部大学）；University of Ljubljana（卢布尔雅那大学）
Due to complex experimental settings, missing values are common in biomedical data. To handle this issue, many methods have been proposed, from ignoring incomplete instances to various data imputation approaches. With the recent rise of deep neural networks, the field of missing data imputation has oriented towards modelling of the data distribution. This paper presents an approach based on Monte Carlo dropout within (Variational) Autoencoders which offers not only very good adaptation to the distribution of the data but also allows generation of new data, adapted to each specific instance. Th…
Multi-level Monte Carlo Dropout for Efficient Uncertainty Quantification
Institute for Mathematical Innovation University of Bath, Bath, UK（数学创新研究所 英国巴斯大学）；Department of Mathematical Sciences University of Bath, Bath, UK（数学科学系 英国巴斯大学）
Among the various options to estimate uncertainty in deep neural networks, Monte-Carlo dropout is widely popular for its simplicity and effectiveness. However the quality of the uncertainty estimated through this method varies and choices in architecture design and in training procedures have to be carefully considered and tested to obtain satisfactory results. In this paper we present a study offering a different point of view on the behavior of Monte-Carlo dropout, which enables us to observe a few interesting properties of the technique to keep in mind when considering its use for uncertain…
West University of Timisoara（蒂米什瓦拉西部大学）；University of Ljubljana（卢布尔雅那大学）
For many analytical problems the challenge is to handle huge amounts of available data. However, there are data science application areas where collecting information is difficult and costly, e.g., in the study of geological phenomena, rare diseases, faults in complex systems, insurance frauds, etc. In many such cases, generators of synthetic data with the same statistical and predictive properties as the actual data allow efficient simulations and development of tools and applications. In this work, we propose the incorporation of Monte Carlo Dropout method within Autoencoder (MCD-AE) and Var…
In image classification tasks, the ability of deep CNNs to deal with complex image data has proven to be unrivalled. However, they require large amounts of labeled training data to reach their full potential. In specialised domains such as healthcare, labeled data can be difficult and expensive to obtain. Active Learning aims to alleviate this problem, by reducing the amount of labelled data needed for a specific task while delivering satisfactory performance. We propose DEBAL, a new active learning strategy designed for deep neural networks. This method improves upon the current state-of-the-…
Fraunhofer Institute for Intelligent Analysis and Information Systems IAIS（弗劳恩霍夫智能分析与信息系统研究所）；Fraunhofer Center for Machine Learning（弗劳恩霍夫机器学习中心）；Ruhr-University Bochum（波鸿鲁尔大学）
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 …
The model uncertainty obtained by variational Bayesian inference with Monte Carlo dropout is prone to miscalibration. In this paper, different logit scaling methods are extended to dropout variational inference to recalibrate model uncertainty. Expected uncertainty calibration error (UCE) is presented as a metric to measure miscalibration. The effectiveness of recalibration is evaluated on CIFAR-10/100 and SVHN for recent CNN architectures. Experimental results show that logit scaling considerably reduce miscalibration by means of UCE. Well-calibrated uncertainty enables reliable rejection of …
University of Cambridge（剑桥大学）；Microsoft Research（微软研究院）；Alan Turing Institute（艾伦·图灵研究所）；University of California, Irvine（加州大学欧文分校）
Dropout regularization of deep neural networks has been a mysterious yet effective tool to prevent overfitting. Explanations for its success range from the prevention of "co-adapted" weights to it being a form of cheap Bayesian inference. We propose a novel framework for understanding multiplicative noise in neural networks, considering continuous distributions as well as Bernoulli noise (i.e. dropout). We show that multiplicative noise induces structured shrinkage priors on a network's weights. We derive the equivalence through reparametrization properties of scale mixtures and without invoki…
Surrogate Modelling of Proton Dose with Monte Carlo Dropout Uncertainty Quantification
Institute for Mathematical Innovation University of Bath, Bath, UK（数学创新研究所 英国巴斯大学）；Department of Mathematical Sciences University of Bath, Bath, UK（数学科学系 英国巴斯大学）
Institute of Mechatronic Systems（机电系统研究所）；Leibniz University Hannover（汉诺威莱布尼茨大学）
Model uncertainty obtained by variational Bayesian inference with Monte Carlo dropout is prone to miscalibration. The uncertainty does not represent the model error well. In this paper, temperature scaling is extended to dropout variational inference to calibrate model uncertainty. Expected uncertainty calibration error (UCE) is presented as a metric to measure miscalibration of uncertainty. The effectiveness of this approach is evaluated on CIFAR-10/100 for recent CNN architectures. Experimental results show, that temperature scaling considerably reduces miscalibration by means of UCE and ena…
This paper shows that dropout training in Generalized Linear Models is the minimax solution of a two-player, zero-sum game where an adversarial nature corrupts a statistician's covariates using a multiplicative nonparametric errors-in-variables model. In this game, nature's least favorable distribution is dropout noise, where nature independently deletes entries of the covariate vector with some fixed probability $δ$. This result implies that dropout training indeed provides out-of-sample expected loss guarantees for distributions that arise from multiplicative perturbations of in-sample data.…
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 …
Indian Institute of Technology Kanpur（印度理工学院坎普尔分校）
Domain adaptation is essential to enable wide usage of deep learning based networks trained using large labeled datasets. Adversarial learning based techniques have shown their utility towards solving this problem using a discriminator that ensures source and target distributions are close. However, here we suggest that rather than using a point estimate, it would be useful if a distribution based discriminator could be used to bridge this gap. This could be achieved using multiple classifiers or using traditional ensemble methods. In contrast, we suggest that a Monte Carlo dropout based ensem…
We study batch normalisation in the context of variational inference methods in Bayesian neural networks, such as mean-field or MC Dropout. We show that batch-normalisation does not affect the optimum of the evidence lower bound (ELBO). Furthermore, we study the Monte Carlo Batch Normalisation (MCBN) algorithm, proposed as an approximate inference technique parallel to MC Dropout, and show that for larger batch sizes, MCBN fails to capture epistemic uncertainty. Finally, we provide insights into what is required to fix this failure, namely having to view the mini-batch size as a variational pa…
Uncertainty Quantification In Surface Landmines and UXO Classification Using MC Dropout
Rochester Institute of Technology, Chester F. Carlson Center for Imaging Science（罗切斯特理工学院，切斯特·F·卡森成像科学中心）；Jadavpur University, Department of Computer Science（贾梵布尔大学，计算机科学系）
We introduce a recent symplectic integration scheme derived for solving physically motivated systems with non-separable Hamiltonians. We show its relevance to Riemannian manifold Hamiltonian Monte Carlo (RMHMC) and provide an alternative to the currently used generalised leapfrog symplectic integrator, which relies on solving multiple fixed point iterations to convergence. Via this approach, we are able to reduce the number of higher-order derivative calculations per leapfrog step. We explore the implications of this integrator and demonstrate its efficacy in reducing the computational burden …
Relevance-driven Input Dropout: an Explanation-guided Regularization Technique
Fraunhofer Heinrich Hertz Institute, Department of Artificial Intelligence（弗劳恩霍夫海因里希·赫茨研究所人工智能部门）；Lehrstuhl für Angewandte Mathematik, University of Bayreuth（拜罗伊特大学应用数学研究所）；Technische Universität Berlin（柏林技术大学）；BIFOLD – Berlin Institute for the Foundations of Learning and Data（柏林学习与数据基础研究所）；Centre of eXplainable Artificial Intelligence, Technological University Dublin（解释性人工智能中心，都柏林技术大学）
Technical University Munich（慕尼黑工业大学）；Autonomous Intelligent Driving GmbH（自主智能驾驶有限公司）；Google（谷歌）
We present a sampling-free approach for computing the epistemic uncertainty of a neural network. Epistemic uncertainty is an important quantity for the deployment of deep neural networks in safety-critical applications, since it represents how much one can trust predictions on new data. Recently promising works were proposed using noise injection combined with Monte-Carlo sampling at inference time to estimate this quantity (e.g. Monte-Carlo dropout). Our main contribution is an approximation of the epistemic uncertainty estimated by these methods that does not require sampling, thus notably r…
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术学院）；Yandex；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；National Research University Higher School of Economics（俄罗斯国家研究型高等经济大学）
We explore a recently proposed Variational Dropout technique that provided an elegant Bayesian interpretation to Gaussian Dropout. We extend Variational Dropout to the case when dropout rates are unbounded, propose a way to reduce the variance of the gradient estimator and report first experimental results with individual dropout rates per weight. Interestingly, it leads to extremely sparse solutions both in fully-connected and convolutional layers. This effect is similar to automatic relevance determination effect in empirical Bayes but has a number of advantages. We reduce the number of para…
University of California, Berkeley（加州大学伯克利分校）；RWTH Aachen University（亚琛工业大学）；California Institute of Technology（加州理工学院）
The Monte Carlo dropout method has proved to be a scalable and easy-to-use approach for estimating the uncertainty of deep neural network predictions. This approach was recently applied to Fault Detection and Di-agnosis (FDD) applications to improve the classification performance on incipient faults. In this paper, we propose a novel approach of augmenting the classification model with an additional unsupervised learning task. We justify our choice of algorithm design via an information-theoretical analysis. Our experimental results on three datasets from diverse application domains show that …
Detecting and Diagnosing Incipient Building Faults Using Uncertainty Information from Deep Neural Networks
Department of EECS, University of California, Berkeley（加州大学伯克利分校电子工程与计算机科学系）；Institute of Data Science, National University of Singapore（新加坡国立大学数据科学研究所）；The Berkeley Education Alliance for Research in Singapore（新加坡伯克利教育联盟）
Fraunhofer IAIS（弗劳恩霍夫智能分析与信息系统研究所）；University of Bochum（波鸿大学）；Fraunhofer Center for Machine Learning（弗劳恩霍夫机器学习中心）；University of Bonn（波恩大学）
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 varianc…
A recurring problem when building probabilistic latent variable models is regularization and model selection, for instance, the choice of the dimensionality of the latent space. In the context of belief networks with latent variables, this problem has been adressed with Automatic Relevance Determination (ARD) employing Monte Carlo inference. We present a variational inference approach to ARD for Deep Generative Models using doubly stochastic variational inference to provide fast and scalable learning. We show empirical results on a standard dataset illustrating the effects of contracting the l…
Deep neural networks (DNNs) provide state-of-the-art results for a multitude of applications, but the approaches using DNNs for multimodal audiovisual applications do not consider predictive uncertainty associated with individual modalities. Bayesian deep learning methods provide principled confidence and quantify predictive uncertainty. Our contribution in this work is to propose an uncertainty aware multimodal Bayesian fusion framework for activity recognition. We demonstrate a novel approach that combines deterministic and variational layers to scale Bayesian DNNs to deeper architectures. O…
Monte Carlo dropout may effectively capture model uncertainty in deep learning, where a measure of uncertainty is obtained by using multiple instances of dropout at test time. However, Monte Carlo dropout is applied across the whole network and thus significantly increases the computational complexity, proportional to the number of instances. To reduce the computational complexity, at test time we enable dropout layers only near the output of the neural network and reuse the computation from prior layers while keeping, if any, other dropout layers disabled. Additionally, we leverage the side i…
Uncertainty Quantification for AI-Driven Crash Simulation Surrogates: A Comparative Study of Monte Carlo Dropout and Deep Ensemble on Open-Source Bumper Beam Benchmark
Unreliable Uncertainty Estimates with Monte Carlo Dropout
Department of Data Science, Norwegian University of Life Sciences（数据科学系，挪威生命科学大学）；SINTEF AS, Department of Mathematics and Cybernetics（SINTEF公司，数学与自动化系）
Bayesian Neural Networks with Monte Carlo Dropout for Probabilistic Electricity Price Forecasting
Faculty of Mathematics and Economics（数学与经济学学院）；Ulm University（乌尔姆大学）；Department of Mathematics, Natural and Economic Sciences（数学、自然科学与经济科学系）；Ulm University of Applied Sciences（乌尔姆应用科学大学）
In longitudinal data a response variable is measured over time, or under different conditions, for a cohort of individuals. In many situations all intended measurements are not available which results in missing values. If the missing value is never followed by an observed measurement, this leads to dropout pattern. The missing values could be in the response variable, the covariates or in both. The missingness mechanism is termed non-random when the probability of missingness depends on the missing value and may be on the observed values. In this case the missing values should be considered i…
Technical University of Berlin, Germany（柏林工业大学（德国））；Hasso Plattner Institute for Digital Engineering, University of Potsdam, Germany（波茨坦大学哈索普拉特纳数字工程研究所（德国））；Hasso Plattner Institute for Digital Health at the Icahn School of Medicine at Mount Sinai, NYC, USA（西奈山伊坎医学院哈索普拉特纳数字健康研究所（美国纽约市））
Self-supervised learning methods can be used to learn meaningful representations from unlabeled data that can be transferred to supervised downstream tasks to reduce the need for labeled data. In this paper, we propose a 3D self-supervised method that is based on the contrastive (SimCLR) method. Additionally, we show that employing Bayesian neural networks (with Monte-Carlo Dropout) during the inference phase can further enhance the results on the downstream tasks. We showcase our models on two medical imaging segmentation tasks: i) Brain Tumor Segmentation from 3D MRI, ii) Pancreas Tumor Segm…
Tampere University（坦佩雷大学）；Finnish Environment Institute（芬兰环境研究所）；Aarhus University（奥胡斯大学）；XIAOMI（小米）
Computational color constancy is a preprocessing step used in many camera systems. The main aim is to discount the effect of the illumination on the colors in the scene and restore the original colors of the objects. Recently, several deep learning-based approaches have been proposed to solve this problem and they often led to state-of-the-art performance in terms of average errors. However, for extreme samples, these methods fail and lead to high errors. In this paper, we address this limitation by proposing to aggregate different deep learning methods according to their output uncertainty. W…
University of Waterloo（滑铁卢大学）；National Research Council Canada（加拿大国家研究委员会）
Recently, there has been a significant amount of interest in satellite telemetry anomaly detection (AD) using neural networks (NN). For AD purposes, the current approaches focus on either forecasting or reconstruction of the time series, and they cannot measure the level of reliability or the probability of correct detection. Although the Bayesian neural network (BNN)-based approaches are well known for time series uncertainty estimation, they are computationally intractable. In this paper, we present a tractable approximation for BNN based on the Monte Carlo (MC) dropout method for capturing …
University of Illinois at Chicago（伊利诺伊大学芝加哥分校）；Intel（英特尔）
We propose MC-CIM, a compute-in-memory (CIM) framework for robust, yet low power, Bayesian edge intelligence. Deep neural networks (DNN) with deterministic weights cannot express their prediction uncertainties, thereby pose critical risks for applications where the consequences of mispredictions are fatal such as surgical robotics. To address this limitation, Bayesian inference of a DNN has gained attention. Using Bayesian inference, not only the prediction itself, but the prediction confidence can also be extracted for planning risk-aware actions. However, Bayesian inference of a DNN is compu…
Testing Spintronics Implemented Monte Carlo Dropout-Based Bayesian Neural Networks
Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；Univ. Grenoble Alpes, CEA, CNRS, Grenoble INP, and IRIG-Spintec（格勒诺布尔阿尔卑斯大学、法国原子能委员会、法国国家科学研究中心、格勒诺布尔国立理工学院及IRIG-Spintec）；RevoAI GmbH（RevoAI有限责任公司）
The memorization effect of deep learning hinders its performance to effectively generalize on test set when learning with noisy labels. Prior study has discovered that epistemic uncertainty techniques are robust when trained with noisy labels compared with neural networks without uncertainty estimation. They obtain prolonged memorization effect and better generalization performance under the adversarial setting of noisy labels. Due to its superior performance amongst other selected epistemic uncertainty methods under noisy labels, we focus on Monte Carlo Dropout (MCDropout) and investigate why…
Massachusetts General Hospital（麻省总医院）；Polytechnique Montreal（蒙特利尔理工学院）；Mila, Quebec AI Institute（Mila魁北克人工智能研究所）；Massachusetts Institute of Technology（麻省理工学院）；MGH and BWH Center for Clinical Data Science（麻省总医院与布莱根妇女医院临床数据科学中心）；National Cancer Institute（美国国家癌症研究所）；Oregon Health and Science University（俄勒冈健康与科学大学）
The integration of artificial intelligence into clinical workflows requires reliable and robust models. Among the main features of robustness is repeatability. Much attention is given to classification performance without assessing the model repeatability, leading to the development of models that turn out to be unusable in practice. In this work, we evaluate the repeatability of four model types on images from the same patient that were acquired during the same visit. We study the performance of binary, multi-class, ordinal, and regression models on three medical image analysis tasks: cervica…
Rethinking Inter-LoRA Orthogonality in Adapter Merging: Insights from Orthogonal Monte Carlo Dropout
University of Manchester（曼彻斯特大学）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；InstantX Team（InstantX团队）；University of Edinburgh（爱丁堡大学）；Aalto University（阿alto大学）
Emotech Labs（Emotech实验室）；University College London（伦敦大学学院）；University of Cambridge（剑桥大学）
Active inference is a Bayesian framework for understanding biological intelligence. The underlying theory brings together perception and action under one single imperative: minimizing free energy. However, despite its theoretical utility in explaining intelligence, computational implementations have been restricted to low-dimensional and idealized situations. In this paper, we present a neural architecture for building deep active inference agents operating in complex, continuous state-spaces using multiple forms of Monte-Carlo (MC) sampling. For this, we introduce a number of techniques, nove…
We investigate the properties of a sequential Monte Carlo method where the particle weight that appears in the algorithm is estimated by a positive, unbiased estimator. We present broadly-applicable convergence results, including a central limit theorem, and we discuss their relevance for applications in statistical physics. Using these results, we show that the resampling step reduces the impact of the randomness of the weights on the asymptotic variance of the estimator. In addition, we explore the limits of convergence of the sequential Monte Carlo method, with a focus on almost sure conver…
Physics-Informed Neural Networks for Methane Sorption: Cross-Gas Transfer Learning, Ensemble Collapse Under Physics Constraints, and Monte Carlo Dropout Uncertainty Quantification
Environmental Geosciences, Department of Geosciences, University of Oslo（奥斯陆大学环境地质学系）；National Key Laboratory of Petroleum Resources and Engineering, China University of Petroleum (Beijing)（中国石油大学（北京）石油资源与工程国家级重点实验室）；College of Geosciences, China University of Petroleum (Beijing)（中国石油大学（北京）地质学院）；State Key Laboratory of Coal Mine Disaster Prevention and Control, China University of Mining and Technology（中国矿业大学煤矿灾害防治控制国家重点实验室）；The Lyell Centre, Heriot-Watt University（赫瑞斯泰大学利尔中心）；Subsurface Energy Transition and Innovation Centre, Heriot-Watt University（赫瑞斯泰大学地下能源转型与创新中心）
We consider two recent suggestions for how to perform an empirically motivated Monte Carlo study to help select a treatment effect estimator under unconfoundedness. We show theoretically that neither is likely to be informative except under restrictive conditions that are unlikely to be satisfied in many contexts. To test empirical relevance, we also apply the approaches to a real-world setting where estimator performance is known. Both approaches are worse than random at selecting estimators which minimise absolute bias. They are better when selecting estimators that minimise mean squared err…
In this work, we establish $\mathrm{L}^2$-exponential convergence for a broad class of Piecewise Deterministic Markov Processes recently proposed in the context of Markov Process Monte Carlo methods and covering in particular the Randomized Hamiltonian Monte Carlo, the Zig-Zag process and the Bouncy Particle Sampler. The kernel of the symmetric part of the generator of such processes is non-trivial, and we follow the ideas recently introduced by (Dolbeault et al., 2009, 2015) to develop a rigorous framework for hypocoercivity in a fairly general and unifying set-up, while deriving tractable es…
Recently, artificial intelligence technologies and algorithms have become a major focus for advancements in treatment planning for radiation therapy. As these are starting to become incorporated into the clinical workflow, a major concern from clinicians is not whether the model is accurate, but whether the model can express to a human operator when it does not know if its answer is correct. We propose to use Monte Carlo dropout (MCDO) and the bootstrap aggregation (bagging) technique on deep learning models to produce uncertainty estimations for radiation therapy dose prediction. We show that…
