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 …
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.…
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…
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）
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…
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…
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…
Stanford University（斯坦福大学）；Google AI Perception（谷歌人工智能感知部）；Google Brain（谷歌大脑）
We present a general-purpose method to train Markov chain Monte Carlo kernels, parameterized by deep neural networks, that converge and mix quickly to their target distribution. Our method generalizes Hamiltonian Monte Carlo and is trained to maximize expected squared jumped distance, a proxy for mixing speed. We demonstrate large empirical gains on a collection of simple but challenging distributions, for instance achieving a 106x improvement in effective sample size in one case, and mixing when standard HMC makes no measurable progress in a second. Finally, we show quantitative and qualitati…
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…
We analyze the convergence rate of gradient flows on objective functions induced by Dropout and Dropconnect, when applying them to shallow linear Neural Networks (NNs) - which can also be viewed as doing matrix factorization using a particular regularizer. Dropout algorithms such as these are thus regularization techniques that use 0,1-valued random variables to filter weights during training in order to avoid coadaptation of features. By leveraging a recent result on nonconvex optimization and conducting a careful analysis of the set of minimizers as well as the Hessian of the loss function, …
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…
Single-shot Bayesian approximation for neural networks
Elektrobit Automotive GmbH（Elektrobit汽车有限公司）；Zurich University of Applied Sciences（苏黎世应用科学大学）；University of Zurich（苏黎世大学）；Konstanz University of Applied Sciences（康斯坦茨应用科学大学）
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 m…
Hate speech is an important problem in the management of user-generated content. To remove offensive content or ban misbehaving users, content moderators need reliable hate speech detectors. Recently, deep neural networks based on the transformer architecture, such as the (multilingual) BERT model, achieve superior performance in many natural language classification tasks, including hate speech detection. So far, these methods have not been able to quantify their output in terms of reliability. We propose a Bayesian method using Monte Carlo dropout within the attention layers of the transforme…
