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 joint predictions across inputs and that bootstrapping affords additional benefits if the signal-to-noise ratio varies across inputs. Our claims are justified by both theoretical and experimental results.
Viterbi Faculty of Electrical Engineering, Technion Institute of Technology（以色列理工学院电气工程维特比学院）
Q-learning (QL), a common reinforcement learning algorithm, suffers from over-estimation bias due to the maximization term in the optimal Bellman operator. This bias may lead to sub-optimal behavior. Double-Q-learning tackles this issue by utilizing two estimators, yet results in an under-estimation bias. Similar to over-estimation in Q-learning, in certain scenarios, the under-estimation bias may degrade performance. In this work, we introduce a new bias-reduced algorithm called Ensemble Bootstrapped Q-Learning (EBQL), a natural extension of Double-Q-learning to ensembles. We analyze our meth…
Toronto Rehabilitation Institute（多伦多康复研究所）；United Arab Emirates University（阿联酋大学）；University of Toronto（多伦多大学）
Presence of missing values in a dataset can adversely affect the performance of a classifier. Single and Multiple Imputation are normally performed to fill in the missing values. In this paper, we present several variants of combining single and multiple imputation with bootstrapping to create ensembles that can model uncertainty and diversity in the data, and that are robust to high missingness in the data. We present three ensemble strategies: bootstrapping on incomplete data followed by (i) single imputation and (ii) multiple imputation, and (iii) multiple imputation ensemble without bootst…
University of South Carolina（南卡罗来纳大学）；Seoul National University（首尔大学）；Tomocube Inc（Tomocube公司）；UNIST（蔚山科学技术院）
Bootstrapping has been a primary tool for ensemble and uncertainty quantification in machine learning and statistics. However, due to its nature of multiple training and resampling, bootstrapping deep neural networks is computationally burdensome; hence it has difficulties in practical application to the uncertainty estimation and related tasks. To overcome this computational bottleneck, we propose a novel approach called \emph{Neural Bootstrapper} (NeuBoots), which learns to generate bootstrapped neural networks through single model training. NeuBoots injects the bootstrap weights into the hi…
The University of Nottingham Ningbo China（宁波诺丁汉大学）
This paper presents a novel ensemble framework to extract highly discriminative feature representation of image and its application for group-level happpiness intensity prediction in wild. In order to generate enough diversity of decisions, n convolutional neural networks are trained by bootstrapping the training set and extract n features for each image from them. A recurrent neural network (RNN) is then used to remember which network extracts better feature and generate the final feature representation for one individual image. Several group emotion models (GEM) are used to aggregate face fe…
Ensembling neural networks is an effective way to increase accuracy, and can often match the performance of individual larger models. This observation poses a natural question: given the choice between a deep ensemble and a single neural network with similar accuracy, is one preferable over the other? Recent work suggests that deep ensembles may offer distinct benefits beyond predictive power: namely, uncertainty quantification and robustness to dataset shift. In this work, we demonstrate limitations to these purported benefits, and show that a single (but larger) neural network can replicate …
PolyMicros: Bootstrapping a Foundation Model for Polycrystalline Material Structure
School of Computational Science and Engineering（计算科学与工程学院）；Georgia Institute of Technology（佐治亚理工学院）；Center for Integrated Nanotechnology（集成纳米技术中心）；Sandia National Laboratories（沙伊达国家实验室）；George W. Woodruff School of Mechanical Engineering（乔治·W·伍德鲁夫机械工程学院）
Using a model of the environment and a value function, an agent can construct many estimates of a state's value, by unrolling the model for different lengths and bootstrapping with its value function. Our key insight is that one can treat this set of value estimates as a type of ensemble, which we call an \emph{implicit value ensemble} (IVE). Consequently, the discrepancy between these estimates can be used as a proxy for the agent's epistemic uncertainty; we term this signal \emph{model-value inconsistency} or \emph{self-inconsistency} for short. Unlike prior work which estimates uncertainty …
Zenseact AB（Zenseact公司）；Chalmers University of Technology（查尔姆斯理工大学）；Scool INRIA Lille-Nord Europe（法国国家信息与自动化研究所里尔-北欧洲Scool团队）；CRIStAL, CNRS（法国国家科学研究中心CRIStAL实验室）；University of Neuchatel（纳沙泰尔大学）；University of Oslo（奥斯陆大学）
In this paper, we consider risk-sensitive sequential decision-making in Reinforcement Learning (RL). Our contributions are two-fold. First, we introduce a novel and coherent quantification of risk, namely composite risk, which quantifies the joint effect of aleatory and epistemic risk during the learning process. Existing works considered either aleatory or epistemic risk individually, or as an additive combination. We prove that the additive formulation is a particular case of the composite risk when the epistemic risk measure is replaced with expectation. Thus, the composite risk is more sen…
McGill University（麦吉尔大学）；Bosch Research North America（博世北美研究院）；Bosch Center for Artificial Intelligence (BCAI)（博世人工智能中心）；Washington State University（华盛顿州立大学）；DeepMind（深度思维）；Apple（苹果公司）
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 …
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…
Q-Ensembles are a model-free approach where input images are fed into different Q-networks and exploration is driven by the assumption that uncertainty is proportional to the variance of the output Q-values obtained. They have been shown to perform relatively well compared to other exploration strategies. Further, model-based approaches, such as encoder-decoder models have been used successfully for next frame prediction given previous frames. This paper proposes to integrate the model-free Q-ensembles and model-based approaches with the hope of compounding the benefits of both and achieving s…
Universidad Carlos III de Madrid（马德里卡洛斯三世大学）；Universidad Politécnica de Cartagena（卡塔赫纳理工大学）
Ensemble methods have been widely used for improving the results of the best single classificationmodel. A large body of works have achieved better performance mainly by applying one specific ensemble method. However, very few works have explored complex fusion schemes using het-erogeneous ensembles with new aggregation strategies. This paper is three-fold: 1) It provides an overview of the most popular ensemble methods, 2) analyzes several fusion schemes using MNIST as guiding thread and 3) introduces MNIST-NET10, a complex heterogeneous fusion architecture based on a degree of certainty aggr…
Labeled data can be expensive to acquire in several application domains, including medical imaging, robotics, and computer vision. To efficiently train machine learning models under such high labeling costs, active learning (AL) judiciously selects the most informative data instances to label on-the-fly. This active sampling process can benefit from a statistical function model, that is typically captured by a Gaussian process (GP). While most GP-based AL approaches rely on a single kernel function, the present contribution advocates an ensemble of GP models with weights adapted to the labeled…
Massachusetts Institute of Technology（麻省理工学院）；Politecnico di Milano（米兰理工大学）；National Taiwan University（台湾大学）
Advances in deep neural network (DNN) based molecular property prediction have recently led to the development of models of remarkable accuracy and generalization ability, with graph convolution neural networks (GCNNs) reporting state-of-the-art performance for this task. However, some challenges remain and one of the most important that needs to be fully addressed concerns uncertainty quantification. DNN performance is affected by the volume and the quality of the training samples. Therefore, establishing when and to what extent a prediction can be considered reliable is just as important as …
The estimation of advantage is crucial for a number of reinforcement learning algorithms, as it directly influences the choices of future paths. In this work, we propose a family of estimates based on the order statistics over the path ensemble, which allows one to flexibly drive the learning process, towards or against risks. On top of this formulation, we systematically study the impacts of different methods for estimating advantages. Our findings reveal that biased estimates, when chosen appropriately, can result in significant benefits. In particular, for the environments with sparse rewar…
Federal University of São Carlos（圣卡洛斯联邦大学）；University of Waikato（怀卡托大学）
Often, machine learning applications have to cope with dynamic environments where data are collected in the form of continuous data streams with potentially infinite length and transient behavior. Compared to traditional (batch) data mining, stream processing algorithms have additional requirements regarding computational resources and adaptability to data evolution. They must process instances incrementally because the data's continuous flow prohibits storing data for multiple passes. Ensemble learning achieved remarkable predictive performance in this scenario. Implemented as a set of (sever…
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 …
Cambridge University Engineering Department（剑桥大学工程系）；Yandex（Yandex公司）
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 …
University of Southern California（南加州大学）；IBM T. J. Watson Research Center（IBM托马斯·J·沃森研究中心）
Diversity or complementarity of experts in ensemble pattern recognition and information processing systems is widely-observed by researchers to be crucial for achieving performance improvement upon fusion. Understanding this link between ensemble diversity and fusion performance is thus an important research question. However, prior works have theoretically characterized ensemble diversity and have linked it with ensemble performance in very restricted settings. We present a generalized ambiguity decomposition (GAD) theorem as a broad framework for answering these questions. The GAD theorem ap…
We investigate an algorithm named histogram transform ensembles (HTE) density estimator whose effectiveness is supported by both solid theoretical analysis and significant experimental performance. On the theoretical side, by decomposing the error term into approximation error and estimation error, we are able to conduct the following analysis: First of all, we establish the universal consistency under $L_1(μ)$-norm. Secondly, under the assumption that the underlying density function resides in the Hölder space $C^{0,α}$, we prove almost optimal convergence rates for both single and ensemble d…
