We present a simple and effective approach for posterior uncertainty quantification in deep operator networks (DeepONets); an emerging paradigm for supervised learning in function spaces. We adopt a frequentist approach based on randomized prior ensembles, and put forth an efficient vectorized implementation for fast parallel inference on accelerated hardware. Through a collection of representative examples in computational mechanics and climate modeling, we show that the merits of the proposed approach are fourfold. (1) It can provide more robust and accurate predictions when compared against deterministic DeepONets. (2) It shows great capability in providing reliable uncertainty estimates on scarce data-sets with multi-scale function pairs. (3) It can effectively detect out-of-distribution and adversarial examples. (4) It can seamlessly quantify uncertainty due to model bias, as well as noise corruption in the data. Finally, we provide an optimized JAX library called {\em UQDeepONet} that can accommodate large model architectures, large ensemble sizes, as well as large data-sets with excellent parallel performance on accelerated hardware, thereby enabling uncertainty quantification for DeepONets in realistic large-scale applications.
In this paper, we propose a novel data-driven operator learning framework referred to as the \textit{Randomized Prior Wavelet Neural Operator} (RP-WNO). The proposed RP-WNO is an extension of the recently proposed wavelet neural operator, which boasts excellent generalizing capabilities but cannot estimate the uncertainty associated with its predictions. RP-WNO, unlike the vanilla WNO, comes with inherent uncertainty quantification module and hence, is expected to be extremely useful for scientists and engineers alike. RP-WNO utilizes randomized prior networks, which can account for prior info…
Counterfactual Uncertainty Quantification of Factual Estimand of Efficacy from Before-and-After Treatment Repeated Measures Randomized Controlled Trials
Department of Mathematics, The University of Manchester；Janssen Research；Pfizer Worldwide Research \& Development；Department of Statistics, The Ohio State University
Harvard Data Science Initiative（哈佛数据科学倡议）；Harvard University（哈佛大学）
Uncertainty quantification has been a core of the statistical machine learning, but its computational bottleneck has been a serious challenge for both Bayesians and frequentists. We propose a model-based framework in quantifying uncertainty, called predictive-matching Generative Parameter Sampler (GPS). This procedure considers an Uncertainty Quantification (UQ) distribution on the targeted parameter, which matches the corresponding predictive distribution to the observed data. This framework adopts a hierarchical modeling perspective such that each observation is modeled by an individual para…
AWS（亚马逊云科技）；Amazon（亚马逊公司）；New York University（纽约大学）
We present Fortuna, an open-source library for uncertainty quantification in deep learning. Fortuna supports a range of calibration techniques, such as conformal prediction that can be applied to any trained neural network to generate reliable uncertainty estimates, and scalable Bayesian inference methods that can be applied to Flax-based deep neural networks trained from scratch for improved uncertainty quantification and accuracy. By providing a coherent framework for advanced uncertainty quantification methods, Fortuna simplifies the process of benchmarking and helps practitioners build rob…
University of Cambridge（剑桥大学）；Cancer Research UK Cambridge Centre（英国癌症研究中心剑桥中心）；Cancer Research UK Cambridge Institute（英国癌症研究中心剑桥研究所）；Danube Private University（多瑙河私立大学）；KTH Royal Institute of Technology（KTH皇家理工学院）
Uncertainty quantification in automated image analysis is highly desired in many applications. Typically, machine learning models in classification or segmentation are only developed to provide binary answers; however, quantifying the uncertainty of the models can play a critical role for example in active learning or machine human interaction. Uncertainty quantification is especially difficult when using deep learning-based models, which are the state-of-the-art in many imaging applications. The current uncertainty quantification approaches do not scale well in high-dimensional real-world pro…
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究所）；Technology Innovation Institute（技术创新研究所）；HSE University（高等经济大学）；Nuro, Inc.（Nuro公司）；Lomonosov Moscow State University（罗蒙诺索夫莫斯科国立大学）；AIRI；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）
This paper proposes a fast and scalable method for uncertainty quantification of machine learning models' predictions. First, we show the principled way to measure the uncertainty of predictions for a classifier based on Nadaraya-Watson's nonparametric estimate of the conditional label distribution. Importantly, the proposed approach allows to disentangle explicitly aleatoric and epistemic uncertainties. The resulting method works directly in the feature space. However, one can apply it to any neural network by considering an embedding of the data induced by the network. We demonstrate the str…
DICOM De-Identification via Hybrid AI and Rule-Based Framework for Scalable, Uncertainty-Aware Redaction
Rowan University（罗文大学）；Moffitt Cancer Center（莫菲特癌症中心）；University of South Florida（佛罗里达州立大学）；Impact Business Information Solutions, Inc（Impact商务信息解决方案公司）
Google Brain（谷歌大脑）；Duke University（杜克大学）；University of Toronto（多伦多大学）；University of California, San Diego（加州大学圣迭戈分校）
Bayesian neural networks (BNNs) demonstrate promising success in improving the robustness and uncertainty quantification of modern deep learning. However, they generally struggle with underfitting at scale and parameter efficiency. On the other hand, deep ensembles have emerged as alternatives for uncertainty quantification that, while outperforming BNNs on certain problems, also suffer from efficiency issues. It remains unclear how to combine the strengths of these two approaches and remediate their common issues. To tackle this challenge, we propose a rank-1 parameterization of BNNs, where e…
The analysis of parametric and non-parametric uncertainties of very large dynamical systems requires the construction of a stochastic model of said system. Linear approaches relying on random matrix theory and principal componant analysis can be used when systems undergo low-frequency vibrations. In the case of fast dynamics and wave propagation, we investigate a random generator of boundary conditions for fast submodels by using machine learning. We show that the use of non-linear techniques in machine learning and data-driven methods is highly relevant. Physics-informed neural networks is a …
Cornell University（康奈尔大学）；Alibaba Group Inc.（阿里巴巴集团）
Recently smoothing deep neural network based classifiers via isotropic Gaussian perturbation is shown to be an effective and scalable way to provide state-of-the-art probabilistic robustness guarantee against $\ell_2$ norm bounded adversarial perturbations. However, how to train a good base classifier that is accurate and robust when smoothed has not been fully investigated. In this work, we derive a new regularized risk, in which the regularizer can adaptively encourage the accuracy and robustness of the smoothed counterpart when training the base classifier. It is computationally efficient a…
Uncertainty Quantification in Probabilistic Machine Learning Models: Theory, Methods, and Insights
Weill Cornell Medicine, Cornell University, New York, NY（韦尔·科恩医学中心，康奈尔大学，纽约，纽约）；Department of Electrical and Computer Engineering, Stony Brook University, Stony Brook, NY（电气与计算机工程系，史泰文斯布鲁克大学，史泰文斯布鲁克，纽约）
Scalable Bayesian uncertainty quantification with data-driven priors for radio interferometric imaging
University College London (UCL)（伦敦大学学院）；IRFU CEA Université Paris-Saclay（法国原子能和替代能源委员会 法国巴黎-萨克雷大学）；Heriot-Watt University（赫瑞瓦特大学）；Maxwell Institute for Mathematical Sciences（麦克斯韦数学研究所）；Alan Turing Institute（阿兰·图灵研究所）
Reference-state System Reliability method for scalable uncertainty quantification of coherent systems
Department of Civil and Environmental Engineering, Imperial College London, United Kingdom（帝国理工学院伦敦分校土木与环境工程系）；Department of Civil, Urban, and Environmental Engineering, Seoul National University, South Korea（首尔国立大学土木、城市与环境工程系）
Interpretable Time Series Autoregression for Periodicity Quantification
Department of Urban Studies and Planning, Massachusetts Institute of Technology（城市研究与规划系，麻省理工学院）；Questrom School of Business, Boston University（questrom商学院，波士顿大学）；Department of Mathematics at the University of California, San Diego（加州大学圣地亚哥分校数学系）
Epistemic Uncertainty Quantification for Pre-trained VLMs via Riemannian Flow Matching
Department of Information Technology, Uppsala University, Uppsala, Sweden（瑞典乌普萨拉大学信息科技系）；Science for Life Laboratory, Uppsala University, Uppsala, Sweden（瑞典乌普萨拉大学生命科学实验室）
Scalable Gaussian Process methods are computationally attractive, yet introduce modeling biases that require rigorous study. This paper analyzes two common techniques: early truncated conjugate gradients (CG) and random Fourier features (RFF). We find that both methods introduce a systematic bias on the learned hyperparameters: CG tends to underfit while RFF tends to overfit. We address these issues using randomized truncation estimators that eliminate bias in exchange for increased variance. In the case of RFF, we show that the bias-to-variance conversion is indeed a trade-off: the additional…
California Institute of Technology（加州理工学院）；Perimeter Institute for Theoretical Physics（圆周理论物理研究所）；University of Waterloo（滑铁卢大学）；Harvard University（哈佛大学）；Center for Astrophysics — Harvard & Smithsonian（哈佛-史密森尼天体物理中心）
Inference is crucial in modern astronomical research, where hidden astrophysical features and patterns are often estimated from indirect and noisy measurements. Inferring the posterior of hidden features, conditioned on the observed measurements, is essential for understanding the uncertainty of results and downstream scientific interpretations. Traditional approaches for posterior estimation include sampling-based methods and variational inference. However, sampling-based methods are typically slow for high-dimensional inverse problems, while variational inference often lacks estimation accur…
Modeling the dependence between outputs is a fundamental challenge in multilabel classification. In this work we show that a generic regularized nonlinearity mapping independent predictions to joint predictions is sufficient to achieve state-of-the-art performance on a variety of benchmark problems. Crucially, we compute the joint predictions without ever obtaining any independent predictions, while incorporating low-rank and smoothness regularization. We achieve this by leveraging randomized algorithms for matrix decomposition and kernel approximation. Furthermore, our techniques are applicab…
We present a new certification method for image and point cloud segmentation based on randomized smoothing. The method leverages a novel scalable algorithm for prediction and certification that correctly accounts for multiple testing, necessary for ensuring statistical guarantees. The key to our approach is reliance on established multiple-testing correction mechanisms as well as the ability to abstain from classifying single pixels or points while still robustly segmenting the overall input. Our experimental evaluation on synthetic data and challenging datasets, such as Pascal Context, Citysc…
This article explores and analyzes the unsupervised clustering of large partially observed graphs. We propose a scalable and provable randomized framework for clustering graphs generated from the stochastic block model. The clustering is first applied to a sub-matrix of the graph's adjacency matrix associated with a reduced graph sketch constructed using random sampling. Then, the clusters of the full graph are inferred based on the clusters extracted from the sketch using a correlation-based retrieval step. Uniform random node sampling is shown to improve the computational complexity over clu…
Current deep learning architectures are growing larger in order to learn from complex datasets. These architectures require giant matrix multiplication operations to train millions of parameters. Conversely, there is another growing trend to bring deep learning to low-power, embedded devices. The matrix operations, associated with both training and testing of deep networks, are very expensive from a computational and energy standpoint. We present a novel hashing based technique to drastically reduce the amount of computation needed to train and test deep networks. Our approach combines recent …
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…
Imperial College London（帝国理工学院）；University of Alberta（阿尔伯塔大学）
We develop a scalable, computationally efficient method for the task of energy disaggregation for home appliance monitoring. In this problem the goal is to estimate the energy consumption of each appliance over time based on the total energy-consumption signal of a household. The current state of the art is to model the problem as inference in factorial HMMs, and use quadratic programming to find an approximate solution to the resulting quadratic integer program. Here we take a more principled approach, better suited to integer programming problems, and find an approximate optimum by combining…
The Nystrom method has been popular for generating the low-rank approximation of kernel matrices that arise in many machine learning problems. The approximation quality of the Nystrom method depends crucially on the number of selected landmark points and the selection procedure. In this paper, we present a novel algorithm to compute the optimal Nystrom low-approximation when the number of landmark points exceed the target rank. Moreover, we introduce a randomized algorithm for generating landmark points that is scalable to large-scale data sets. The proposed method performs K-means clustering …
Max-Planck-Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；University of Cambridge（剑桥大学）；Carnegie Mellon University（卡内基梅隆大学）；Google Research（谷歌研究院）
Classical methods such as Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) are ubiquitous in statistics. However, these techniques are only able to reveal linear relationships in data. Although nonlinear variants of PCA and CCA have been proposed, these are computationally prohibitive in the large scale. In a separate strand of recent research, randomized methods have been proposed to construct features that help reveal nonlinear patterns in data. For basic tasks such as regression or classification, random features exhibit little or no loss in performance, while ach…
Duke University（杜克大学）；University of Michigan（密歇根大学）
Linear mixed models (LMMs) are used extensively to model dependecies of observations in linear regression and are used extensively in many application areas. Parameter estimation for LMMs can be computationally prohibitive on big data. State-of-the-art learning algorithms require computational complexity which depends at least linearly on the dimension $p$ of the covariates, and often use heuristics that do not offer theoretical guarantees. We present scalable algorithms for learning high-dimensional LMMs with sublinear computational complexity dependence on $p$. Key to our approach are novel …
We consider a team of reinforcement learning agents that concurrently operate in a common environment, and we develop an approach to efficient coordinated exploration that is suitable for problems of practical scale. Our approach builds on seed sampling (Dimakopoulou and Van Roy, 2018) and randomized value function learning (Osband et al., 2016). We demonstrate that, for simple tabular contexts, the approach is competitive with previously proposed tabular model learning methods (Dimakopoulou and Van Roy, 2018). With a higher-dimensional problem and a neural network value function representatio…
PhagoStat a scalable and interpretable end to end framework for efficient quantification of cell phagocytosis in neurodegenerative disease studies
Sorbonne University（索邦大学）；CNRS（法国国家科学研究中心）；Inserm（法国国家健康与医学研究院）；AP-HP（巴黎公共医疗集团）；Inria（法国国家信息与自动化研究所）；Paris Brain Institute - ICM（巴黎大脑研究所 - ICM）；PSL Research university（巴黎文理研究大学）；EPHE（高等研究实践学院）
The CUR matrix decomposition is an important extension of Nyström approximation to a general matrix. It approximates any data matrix in terms of a small number of its columns and rows. In this paper we propose a novel randomized CUR algorithm with an expected relative-error bound. The proposed algorithm has the advantages over the existing relative-error CUR algorithms that it possesses tighter theoretical bound and lower time complexity, and that it can avoid maintaining the whole data matrix in main memory. Finally, experiments on several real-world datasets demonstrate significant improveme…
Existing techniques for certifying the robustness of models for discrete data either work only for a small class of models or are general at the expense of efficiency or tightness. Moreover, they do not account for sparsity in the input which, as our findings show, is often essential for obtaining non-trivial guarantees. We propose a model-agnostic certificate based on the randomized smoothing framework which subsumes earlier work and is tight, efficient, and sparsity-aware. Its computational complexity does not depend on the number of discrete categories or the dimension of the input (e.g. th…
University of Granada（格拉纳达大学）；Northwestern University（西北大学）；Cardiff University（卡迪夫大学）
In the last years, crowdsourcing is transforming the way classification training sets are obtained. Instead of relying on a single expert annotator, crowdsourcing shares the labelling effort among a large number of collaborators. For instance, this is being applied to the data acquired by the laureate Laser Interferometer Gravitational Waves Observatory (LIGO), in order to detect glitches which might hinder the identification of true gravitational-waves. The crowdsourcing scenario poses new challenging difficulties, as it deals with different opinions from a heterogeneous group of annotators w…
Towards Large-Scale In-Context Reinforcement Learning by Meta-Training in Randomized Worlds
University of Science and Technology of China（中国科学技术大学）；Shenzhen Institute of Artificial Intelligence and Robotics for Society（深圳人工智能与机器人研究院）；Baidu Inc（百度公司）
