Neural Ensemble Search for Uncertainty Estimation and Dataset Shift
University of Oxford（牛津大学）；University of Freiburg（弗莱堡大学）；Bosch Center for Artificial Intelligence（博世人工智能中心）
Sheheryar Zaidi, Arber Zela, Thomas Elsken, Chris Holmes, Frank Hutter, Yee Whye Teh
备注：
Accepted at NeurIPS 2021; earlier version of this work was accepted for oral presentation at ICML 2020 Workshop on Uncertainty & Robustness in Deep Learning
Ensembles of neural networks achieve superior performance compared to stand-alone networks in terms of accuracy, uncertainty calibration and robustness to dataset shift. \emph{Deep ensembles}, a state-of-the-art method for uncertainty estimation, only ensemble random initializations of a \emph{fixed} architecture. Instead, we propose two methods for automatically constructing ensembles with \emph{varying} architectures, which implicitly trade-off individual architectures' strengths against the ensemble's diversity and exploit architectural variation as a source of diversity. On a variety of classification tasks and modern architecture search spaces, we show that the resulting ensembles outperform deep ensembles not only in terms of accuracy but also uncertainty calibration and robustness to dataset shift. Our further analysis and ablation studies provide evidence of higher ensemble diversity due to architectural variation, resulting in ensembles that can outperform deep ensembles, even when having weaker average base learners. To foster reproducibility, our code is available: \url{https://github.com/automl/nes}
Deep Learning methods are known to suffer from calibration issues: they typically produce over-confident estimates. These problems are exacerbated in the low data regime. Although the calibration of probabilistic models is well studied, calibrating extremely over-parametrized models in the low-data regime presents unique challenges. We show that deep-ensembles do not necessarily lead to improved calibration properties. In fact, we show that standard ensembling methods, when used in conjunction with modern techniques such as mixup regularization, can lead to less calibrated models. This text ex…
University of Essex（埃塞克斯大学）；Ulster University（阿尔斯特大学）；Swansea University（斯旺西大学）；California State University Fresno（加州州立大学弗雷斯诺分校）
The non-stationary nature of electroencephalography (EEG) signals makes an EEG-based brain-computer interface (BCI) a dynamic system, thus improving its performance is a challenging task. In addition, it is well-known that due to non-stationarity based covariate shifts, the input data distributions of EEG-based BCI systems change during inter- and intra-session transitions, which poses great difficulty for developments of online adaptive data-driven systems. Ensemble learning approaches have been used previously to tackle this challenge. However, passive scheme based implementation leads to po…
Google Research（谷歌研究院）；Harvard University（哈佛大学）；Columbia University（哥伦比亚大学）
Ensemble learning is a standard approach to building machine learning systems that capture complex phenomena in real-world data. An important aspect of these systems is the complete and valid quantification of model uncertainty. We introduce a Bayesian nonparametric ensemble (BNE) approach that augments an existing ensemble model to account for different sources of model uncertainty. BNE augments a model's prediction and distribution functions using Bayesian nonparametric machinery. It has a theoretical guarantee in that it robustly estimates the uncertainty patterns in the data distribution, …
Yandex；HSE University（高等经济大学）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）
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 datase…
CSAIL MIT（麻省理工学院计算机科学与人工智能实验室）；Amazon Web Services（亚马逊网络服务）
The inaccuracy of neural network models on inputs that do not stem from the training data distribution is both problematic and at times unrecognized. Model uncertainty estimation can address this issue, where uncertainty estimates are often based on the variation in predictions produced by a diverse ensemble of models applied to the same input. Here we describe Maximize Overall Diversity (MOD), a straightforward approach to improve ensemble-based uncertainty estimates by encouraging larger overall diversity in ensemble predictions across all possible inputs that might be encountered in the fut…
Chalmers University of Technology（查尔姆斯理工大学）；Linköping University（林雪平大学）
Ensembles of neural networks have been shown to give better performance than single networks, both in terms of predictions and uncertainty estimation. Additionally, ensembles allow the uncertainty to be decomposed into aleatoric (data) and epistemic (model) components, giving a more complete picture of the predictive uncertainty. Ensemble distillation is the process of compressing an ensemble into a single model, often resulting in a leaner model that still outperforms the individual ensemble members. Unfortunately, standard distillation erases the natural uncertainty decomposition of the ense…
Massachusetts Institute of Technology（麻省理工学院）；BITS Pilani Goa Campus（BITS Pilani果阿校区）
Understanding and quantifying uncertainty in black box Neural Networks (NNs) is critical when deployed in real-world settings such as healthcare. Recent works using Bayesian and non-Bayesian methods have shown how a unified predictive uncertainty can be modelled for NNs. Decomposing this uncertainty to disentangle the granular sources of heteroscedasticity in data provides rich information about its underlying causes. We propose a conceptually simple non-Bayesian approach, deep split ensemble, to disentangle the predictive uncertainties using a multivariate Gaussian mixture model. The NNs are …
Ensembles over neural network weights trained from different random initialization, known as deep ensembles, achieve state-of-the-art accuracy and calibration. The recently introduced batch ensembles provide a drop-in replacement that is more parameter efficient. In this paper, we design ensembles not only over weights, but over hyperparameters to improve the state of the art in both settings. For best performance independent of budget, we propose hyper-deep ensembles, a simple procedure that involves a random search over different hyperparameters, themselves stratified across multiple random …
Deep neural networks are in the limelight of machine learning with their excellent performance in many data-driven applications. However, they can lead to inaccurate predictions when queried in out-of-distribution data points, which can have detrimental effects especially in sensitive domains, such as healthcare and transportation, where erroneous predictions can be very costly and/or dangerous. Subsequently, quantifying the uncertainty of the output of a neural network is often leveraged to evaluate the confidence of its predictions, and ensemble models have proved to be effective in measurin…
German Research Center for Artificial Intelligence（德国人工智能研究中心）
Fast estimates of model uncertainty are required for many robust robotics applications. Deep Ensembles provides state of the art uncertainty without requiring Bayesian methods, but still it is computationally expensive. In this paper we propose deep sub-ensembles, an approximation to deep ensembles where the core idea is to ensemble only the layers close to the output, and not the whole model. With ResNet-20 on the CIFAR10 dataset, we obtain 1.5-2.5 speedup over a Deep Ensemble, with a small increase in error and NLL, and similarly up to 5-15 speedup with a VGG-like network on the SVHN dataset…
Machine learning algorithms have been effectively applied into various real world tasks. However, it is difficult to provide high-quality machine learning solutions to accommodate an unknown distribution of input datasets; this difficulty is called the uncertainty prediction problems. In this paper, a margin-based Pareto deep ensemble pruning (MBPEP) model is proposed. It achieves the high-quality uncertainty estimation with a small value of the prediction interval width (MPIW) and a high confidence of prediction interval coverage probability (PICP) by using deep ensemble networks. In addition…
Bayesian optimized deep ensemble for uncertainty quantification of deep neural networks: a system safety case study on sodium fast reactor thermal stratification modeling
Texas A&M University（德克萨斯农工大学）；Argonne National Laboratory（阿贡国家实验室）；Oak Ridge National Laboratory（橡树岭国家实验室）
Technical University of Denmark（丹麦技术大学）；Rigshospitalet, Copenhagen University Hospital（哥本哈根大学医院 Rigshospitalet）；University of Copenhagen（哥本哈根大学）
Data-driven methods based on machine learning have the potential to accelerate computational analysis of atomic structures. In this context, reliable uncertainty estimates are important for assessing confidence in predictions and enabling decision making. However, machine learning models can produce badly calibrated uncertainty estimates and it is therefore crucial to detect and handle uncertainty carefully. In this work we extend a message passing neural network designed specifically for predicting properties of molecules and materials with a calibrated probabilistic predictive distribution. …
Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Baidu Inc.（百度公司）；Institute for AI Industry Research, Tsinghua University（清华大学智能产业研究院）；Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）
Ensemble-based debiasing methods have been shown effective in mitigating the reliance of classifiers on specific dataset bias, by exploiting the output of a bias-only model to adjust the learning target. In this paper, we focus on the bias-only model in these ensemble-based methods, which plays an important role but has not gained much attention in the existing literature. Theoretically, we prove that the debiasing performance can be damaged by inaccurate uncertainty estimations of the bias-only model. Empirically, we show that existing bias-only models fall short in producing accurate uncerta…
Deep neural networks (NNs) are powerful black box predictors that have recently achieved impressive performance on a wide spectrum of tasks. Quantifying predictive uncertainty in NNs is a challenging and yet unsolved problem. Bayesian NNs, which learn a distribution over weights, are currently the state-of-the-art for estimating predictive uncertainty; however these require significant modifications to the training procedure and are computationally expensive compared to standard (non-Bayesian) NNs. We propose an alternative to Bayesian NNs that is simple to implement, readily parallelizable, r…
Deep neural networks have become the default choice for many of the machine learning tasks such as classification and regression. Dropout, a method commonly used to improve the convergence of deep neural networks, generates an ensemble of thinned networks with extensive weight sharing. Recent studies that dropout can be viewed as an approximate variational inference in Gaussian processes, and used as a practical tool to obtain uncertainty estimates of the network. We propose a novel statistical mechanics based framework to dropout and use this framework to propose a new generic algorithm that …
In machine learning, an agent needs to estimate uncertainty to efficiently explore and adapt and to make effective decisions. A common approach to uncertainty estimation maintains an ensemble of models. In recent years, several approaches have been proposed for training ensembles, and conflicting views prevail with regards to the importance of various ingredients of these approaches. In this paper, we aim to address the benefits of two ingredients -- prior functions and bootstrapping -- which have come into question. We show that prior functions can significantly improve an ensemble agent's jo…
Deep neural networks (DNNs) have made a revolution in numerous fields during the last decade. However, in tasks with high safety requirements, such as medical or autonomous driving applications, providing an assessment of the models reliability can be vital. Uncertainty estimation for DNNs has been addressed using Bayesian methods, providing mathematically founded models for reliability assessment. These model are computationally expensive and generally impractical for many real-time use cases. Recently, non-Bayesian methods were proposed to tackle uncertainty estimation more efficiently. We p…
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 abo…
Argonne National Laboratory（阿贡国家实验室）；Université Paris-Saclay（巴黎萨克雷大学）
Deep neural networks are powerful predictors for a variety of tasks. However, they do not capture uncertainty directly. Using neural network ensembles to quantify uncertainty is competitive with approaches based on Bayesian neural networks while benefiting from better computational scalability. However, building ensembles of neural networks is a challenging task because, in addition to choosing the right neural architecture or hyperparameters for each member of the ensemble, there is an added cost of training each model. We propose AutoDEUQ, an automated approach for generating an ensemble of …
Paderborn University（帕德博恩大学）；University of Munich (LMU)（慕尼黑大学）
The idea to distinguish and quantify two important types of uncertainty, often referred to as aleatoric and epistemic, has received increasing attention in machine learning research in the last couple of years. In this paper, we consider ensemble-based approaches to uncertainty quantification. Distinguishing between different types of uncertainty-aware learning algorithms, we specifically focus on Bayesian methods and approaches based on so-called credal sets, which naturally suggest themselves from an ensemble learning point of view. For both approaches, we address the question of how to quan…
National Research University Higher School of Economics（国家研究型高等经济大学）；Samsung AI Center Moscow（三星莫斯科人工智能中心）；Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究院）
Uncertainty estimation and ensembling methods go hand-in-hand. Uncertainty estimation is one of the main benchmarks for assessment of ensembling performance. At the same time, deep learning ensembles have provided state-of-the-art results in uncertainty estimation. In this work, we focus on in-domain uncertainty for image classification. We explore the standards for its quantification and point out pitfalls of existing metrics. Avoiding these pitfalls, we perform a broad study of different ensembling techniques. To provide more insight in this study, we introduce the deep ensemble equivalent s…
Prognostics or Remaining Useful Life (RUL) Estimation from multi-sensor time series data is useful to enable condition-based maintenance and ensure high operational availability of equipment. We propose a novel deep learning based approach for Prognostics with Uncertainty Quantification that is useful in scenarios where: (i) access to labeled failure data is scarce due to rarity of failures (ii) future operational conditions are unobserved and (iii) inherent noise is present in the sensor readings. All three scenarios mentioned are unavoidable sources of uncertainty in the RUL estimation proce…
We often see undesirable tradeoffs in robust machine learning where out-of-distribution (OOD) accuracy is at odds with in-distribution (ID) accuracy: a robust classifier obtained via specialized techniques such as removing spurious features often has better OOD but worse ID accuracy compared to a standard classifier trained via ERM. In this paper, we find that ID-calibrated ensembles -- where we simply ensemble the standard and robust models after calibrating on only ID data -- outperforms prior state-of-the-art (based on self-training) on both ID and OOD accuracy. On eleven natural distributi…
Uncertainty quantification by ensemble learning is explored in terms of an application from computational optical form measurements. The application requires to solve a large-scale, nonlinear inverse problem. Ensemble learning is used to extend a recently developed deep learning approach for this application in order to provide an uncertainty quantification of its predicted solution to the inverse problem. By systematically inserting out-of-distribution errors as well as noisy data the reliability of the developed uncertainty quantification is explored. Results are encouraging and the proposed…
University of California, Berkeley（加州大学伯克利分校）；University of Chicago（芝加哥大学）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
Ensemble learning is widely applied in Machine Learning (ML) to improve model performance and to mitigate decision risks. In this approach, predictions from a diverse set of learners are combined to obtain a joint decision. Recently, various methods have been explored in literature for estimating decision uncertainties using ensemble learning; however, determining which metrics are a better fit for certain decision-making applications remains a challenging task. In this paper, we study the following key research question in the selection of uncertainty metrics: when does an uncertainty metric …
In this paper we experimentally compare the classification uncertainty of the randomised Decision Tree (DT) ensemble technique and the Bayesian DT technique with a restarting strategy on a synthetic dataset as well as on some datasets commonly used in the machine learning community. For quantitative evaluation of classification uncertainty, we use an Uncertainty Envelope dealing with the class posterior distribution and a given confidence probability. Counting the classifier outcomes, this technique produces feasible evaluations of the classification uncertainty. Using this technique in our ex…
Deep learning is increasingly being applied in safety-critical domains. For these scenarios it is important to know the level of uncertainty in a model's prediction to ensure appropriate decisions are made by the system. Deep ensembles are the de-facto standard approach to obtaining various measures of uncertainty. However, ensembles often significantly increase the resources required in the training and/or deployment phases. Approaches have been developed that typically address the costs in one of these phases. In this work we propose a novel training approach, self-distribution distillation …
Institute of Mathematics Polish Academy of Sciences（波兰科学院数学研究所）；Faculty of Mathematics, Informatics and Mechanics, University of Warsaw（华沙大学数学、信息学与力学学院）
We propose a reinforcement learning framework for discrete environments in which an agent makes both strategic and tactical decisions. The former manifests itself through the use of value function, while the latter is powered by a tree search planner. These tools complement each other. The planning module performs a local \textit{what-if} analysis, which allows to avoid tactical pitfalls and boost backups of the value function. The value function, being global in nature, compensates for inherent locality of the planner. In order to further solidify this synergy, we introduce an exploration mec…
Warwick Medical School, University of Warwick（华威大学华威医学院）；WMG, University of Warwick（华威大学华威制造集团）；Department of Statistics, University of Warwick（华威大学统计系）；Alan Turing Institute（艾伦·图灵研究所）
Offline reinforcement learning agents seek optimal policies from fixed data sets. With environmental interaction prohibited, agents face significant challenges in preventing errors in value estimates from compounding and subsequently causing the learning process to collapse. Uncertainty estimation using ensembles compensates for this by penalising high-variance value estimates, allowing agents to learn robust policies based on data-driven actions. However, the requirement for large ensembles to facilitate sufficient penalisation results in significant computational overhead. In this work, we e…
Gradient-based adversarial attacks on neural networks can be crafted in a variety of ways by varying either how the attack algorithm relies on the gradient, the network architecture used for crafting the attack, or both. Most recent work has focused on defending classifiers in a case where there is no uncertainty about the attacker's behavior (i.e., the attacker is expected to generate a specific attack using a specific network architecture). However, if the attacker is not guaranteed to behave in a certain way, the literature lacks methods in devising a strategic defense. We fill this gap by …
NAVER AI Lab（NAVER人工智能实验室）；Yonsei University（延世大学）
Neural network ensembles, such as Bayesian neural networks (BNNs), have shown success in the areas of uncertainty estimation and robustness. However, a crucial challenge prohibits their use in practice. BNNs require a large number of predictions to produce reliable results, leading to a significant increase in computational cost. To alleviate this issue, we propose spatial smoothing, a method that spatially ensembles neighboring feature map points of convolutional neural networks. By simply adding a few blur layers to the models, we empirically show that spatial smoothing improves accuracy, un…
Argonne National Laboratory（阿贡国家实验室）；Université Paris-Saclay（巴黎萨克雷大学）
Classical problems in computational physics such as data-driven forecasting and signal reconstruction from sparse sensors have recently seen an explosion in deep neural network (DNN) based algorithmic approaches. However, most DNN models do not provide uncertainty estimates, which are crucial for establishing the trustworthiness of these techniques in downstream decision making tasks and scenarios. In recent years, ensemble-based methods have achieved significant success for the uncertainty quantification in DNNs on a number of benchmark problems. However, their performance on real-world appli…
Deep Ensemble (DE) is an effective alternative to Bayesian neural networks for uncertainty quantification in deep learning. The uncertainty of DE is usually conveyed by the functional inconsistency among the ensemble members, say, the disagreement among their predictions. Yet, the functional inconsistency stems from unmanageable randomness and may easily collapse in specific cases. To render the uncertainty of DE reliable, we propose a refinement of DE where the functional inconsistency is explicitly characterized, and further tuned w.r.t. the training data and certain priori beliefs. Specific…
Manipal Institute of Technology（马尼帕尔理工学院）；Manipal Academy of Higher Education（马尼帕尔高等教育学院）
Deep Ensemble Convolutional Neural Networks has become a methodology of choice for analyzing medical images with a diagnostic performance comparable to a physician, including the diagnosis of Diabetic Retinopathy. However, commonly used techniques are deterministic and are therefore unable to provide any estimate of predictive uncertainty. Quantifying model uncertainty is crucial for reducing the risk of misdiagnosis. A reliable architecture should be well-calibrated to avoid over-confident predictions. To address this, we propose a UATTA-ENS: Uncertainty-Aware Test-Time Augmented Ensemble Tec…
ETH Zurich（苏黎世联邦理工学院）；LMU Munich（慕尼黑大学）；University of Zurich（苏黎世大学）
The ability to estimate epistemic uncertainty is often crucial when deploying machine learning in the real world, but modern methods often produce overconfident, uncalibrated uncertainty predictions. A common approach to quantify epistemic uncertainty, usable across a wide class of prediction models, is to train a model ensemble. In a naive implementation, the ensemble approach has high computational cost and high memory demand. This challenges in particular modern deep learning, where even a single deep network is already demanding in terms of compute and memory, and has given rise to a numbe…
Argonne National Laboratory（阿贡国家实验室）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
Deep-learning-based data-driven forecasting methods have produced impressive results for traffic forecasting. A major limitation of these methods, however, is that they provide forecasts without estimates of uncertainty, which are critical for real-time deployments. We focus on a diffusion convolutional recurrent neural network (DCRNN), a state-of-the-art method for short-term traffic forecasting. We develop a scalable deep ensemble approach to quantify uncertainties for DCRNN. Our approach uses a scalable Bayesian optimization method to perform hyperparameter optimization, selects a set of hi…
Scientific Computing and Imaging Institute（科学计算与成像研究所）；Oak Ridge National Laboratory（橡树岭国家实验室）
Visualizing the uncertainty of ensemble simulations is challenging due to the large size and multivariate and temporal features of ensemble data sets. One popular approach to studying the uncertainty of ensembles is analyzing the positional uncertainty of the level sets. Probabilistic marching cubes is a technique that performs Monte Carlo sampling of multivariate Gaussian noise distributions for positional uncertainty visualization of level sets. However, the technique suffers from high computational time, making interactive visualization and analysis impossible to achieve. This paper introdu…
Uncertainty Quantification for AI-Driven Crash Simulation Surrogates: A Comparative Study of Monte Carlo Dropout and Deep Ensemble on Open-Source Bumper Beam Benchmark
