Bayesian inference is used extensively to quantify the uncertainty in an inferred field given the measurement of a related field when the two are linked by a mathematical model. Despite its many applications, Bayesian inference faces challenges when inferring fields that have discrete representations of large dimension, and/or have prior distributions that are difficult to characterize mathematically. In this work we demonstrate how the approximate distribution learned by a deep generative adversarial network (GAN) may be used as a prior in a Bayesian update to address both these challenges. We demonstrate the efficacy of this approach on two distinct, and remarkably broad, classes of problems. The first class leads to supervised learning algorithms for image classification with superior out of distribution detection and accuracy, and for image inpainting with built-in variance estimation. The second class leads to unsupervised learning algorithms for image denoising and for solving physics-driven inverse problems.
This paper aims to quantify uncertainty in traffic state estimation (TSE) using the generative adversarial network based physics-informed deep learning (PIDL). The uncertainty of the focus arises from fundamental diagrams, in other words, the mapping from traffic density to velocity. To quantify uncertainty for the TSE problem is to characterize the robustness of predicted traffic states. Since its inception, generative adversarial networks (GAN) have become a popular probabilistic machine learning framework. In this paper, we will inform the GAN based predictions using stochastic traffic flow…
Rutgers University（罗格斯大学）；The University of Texas at Austin（得克萨斯大学奥斯汀分校）；Tencent YouTu Lab（腾讯优图实验室）；JD Finance America Corporation（京东金融美国公司）
Conditional generative adversarial networks have shown exceptional generation performance over the past few years. However, they require large numbers of annotations. To address this problem, we propose a novel generative adversarial network utilizing weak supervision in the form of pairwise comparisons (PC-GAN) for image attribute editing. In the light of Bayesian uncertainty estimation and noise-tolerant adversarial training, PC-GAN can estimate attribute rating efficiently and demonstrate robust performance in noise resistance. Through extensive experiments, we show both qualitatively and q…
We propose two bounded comparison metrics that may be implemented to arbitrary dimensions in regression tasks. One quantifies the structure of uncertainty and the other quantifies the distribution of uncertainty. The structure metric assesses the similarity in shape and location of uncertainty with the true error, while the distribution metric quantifies the supported magnitudes between the two. We apply these metrics to Gaussian Processes (GPs), Ensemble Deep Neural Nets (DNNs), and Ensemble Deep Neural Operators (DNOs) on high-dimensional and nonlinear test cases. We find that comparing a mo…
Deep learning models achieve high predictive accuracy across a broad spectrum of tasks, but rigorously quantifying their predictive uncertainty remains challenging. Usable estimates of predictive uncertainty should (1) cover the true prediction targets with high probability, and (2) discriminate between high- and low-confidence prediction instances. Existing methods for uncertainty quantification are based predominantly on Bayesian neural networks; these may fall short of (1) and (2) -- i.e., Bayesian credible intervals do not guarantee frequentist coverage, and approximate posterior inference…
TU Dortmund University（多特蒙德工业大学）；EPFL（洛桑联邦理工学院）；University of Wuppertal（伍珀塔尔大学）
We present an approach to quantifying both aleatoric and epistemic uncertainty for deep neural networks in image classification, based on generative adversarial networks (GANs). While most works in the literature that use GANs to generate out-of-distribution (OoD) examples only focus on the evaluation of OoD detection, we present a GAN based approach to learn a classifier that produces proper uncertainties for OoD examples as well as for false positives (FPs). Instead of shielding the entire in-distribution data with GAN generated OoD examples which is state-of-the-art, we shield each class se…
We present a method to quantify uncertainty in the predictions made by simulations of mathematical models that can be applied to a broad class of stochastic, discrete, and differential equation models. Quantifying uncertainty is crucial for determining how accurate the model predictions are and identifying which input parameters affect the outputs of interest. Most of the existing methods for uncertainty quantification require many samples to generate accurate results, are unable to differentiate where the uncertainty is coming from (e.g., parameters or model assumptions), or require a lot of …
University of Tübingen（图宾根大学）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
Image-to-image translation plays a vital role in tackling various medical imaging tasks such as attenuation correction, motion correction, undersampled reconstruction, and denoising. Generative adversarial networks have been shown to achieve the state-of-the-art in generating high fidelity images for these tasks. However, the state-of-the-art GAN-based frameworks do not estimate the uncertainty in the predictions made by the network that is essential for making informed medical decisions and subsequent revision by medical experts and has recently been shown to improve the performance and inter…
Image-to-image translation is an ill-posed problem as unique one-to-one mapping may not exist between the source and target images. Learning-based methods proposed in this context often evaluate the performance on test data that is similar to the training data, which may be impractical. This demands robust methods that can quantify uncertainty in the prediction for making informed decisions, especially for critical areas such as medical imaging. Recent works that employ conditional generative adversarial networks (GANs) have shown improved performance in learning photo-realistic image-to-image…
University of California, Davis（加州大学戴维斯分校）；New York University（纽约大学）；University of California, Berkeley（加州大学伯克利分校）
With the widespread success of deep neural networks in science and technology, it is becoming increasingly important to quantify the uncertainty of the predictions produced by deep learning. In this paper, we introduce a new method that attaches an explicit uncertainty statement to the probabilities of classification using deep neural networks. Precisely, we view that the classification probabilities are sampled from an unknown distribution, and we propose to learn this distribution through the Dirichlet mixture that is flexible enough for approximating any continuous distribution on the simpl…
Adverse weather image translation belongs to the unsupervised image-to-image (I2I) translation task which aims to transfer adverse condition domain (eg, rainy night) to standard domain (eg, day). It is a challenging task because images from adverse domains have some artifacts and insufficient information. Recently, many studies employing Generative Adversarial Networks (GANs) have achieved notable success in I2I translation but there are still limitations in applying them to adverse weather enhancement. Symmetric architecture based on bidirectional cycle-consistency loss is adopted as a standa…
University of California, Irvine（加利福尼亚大学欧文分校）；Google Research（谷歌研究院）
Recent work has increased the performance of Generative Adversarial Networks (GANs) by enforcing a consistency cost on the discriminator. We improve on this technique in several ways. We first show that consistency regularization can introduce artifacts into the GAN samples and explain how to fix this issue. We then propose several modifications to the consistency regularization procedure designed to improve its performance. We carry out extensive experiments quantifying the benefit of our improvements. For unconditional image synthesis on CIFAR-10 and CelebA, our modifications yield the best …
Cognizant（高知特）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）
Neural Networks (NNs) have been extensively used for a wide spectrum of real-world regression tasks, where the goal is to predict a numerical outcome such as revenue, effectiveness, or a quantitative result. In many such tasks, the point prediction is not enough: the uncertainty (i.e. risk or confidence) of that prediction must also be estimated. Standard NNs, which are most often used in such tasks, do not provide uncertainty information. Existing approaches address this issue by combining Bayesian models with NNs, but these models are hard to implement, more expensive to train, and usually d…
Deep generative models have demonstrated effectiveness in learning compact and expressive design representations that significantly improve geometric design optimization. However, these models do not consider the uncertainty introduced by manufacturing or fabrication. Past work that quantifies such uncertainty often makes simplifying assumptions on geometric variations, while the "real-world", "free-form" uncertainty and its impact on design performance are difficult to quantify due to the high dimensionality. To address this issue, we propose a Generative Adversarial Network-based Design unde…
The Australian National University（澳大利亚国立大学）；Data61
Robustness to adversarial attacks is an important concern due to the fragility of deep neural networks to small perturbations and has received an abundance of attention in recent years. Distributionally Robust Optimization (DRO), a particularly promising way of addressing this challenge, studies robustness via divergence-based uncertainty sets and has provided valuable insights into robustification strategies such as regularization. In the context of machine learning, the majority of existing results have chosen $f$-divergences, Wasserstein distances and more recently, the Maximum Mean Discrep…
As a powerful technique in medical imaging, image synthesis is widely used in applications such as denoising, super resolution and modality transformation etc. Recently, the revival of deep neural networks made immense progress in the field of medical imaging. Although many deep leaning based models have been proposed to improve the image synthesis accuracy, the evaluation of the model uncertainty, which is highly important for medical applications, has been a missing part. In this work, we propose to use Bayesian conditional generative adversarial network (GAN) with concrete dropout to improv…
College of Engineering, Cornell University（康奈尔大学工程学院）
This paper presents a novel deep learning based data-driven optimization method. A novel generative adversarial network (GAN) based data-driven distributionally robust chance constrained programming framework is proposed. GAN is applied to fully extract distributional information from historical data in a nonparametric and unsupervised way without a priori approximation or assumption. Since GAN utilizes deep neural networks, complicated data distributions and modes can be learned, and it can model uncertainty efficiently and accurately. Distributionally robust chance constrained programming ta…
MIT CSAIL（麻省理工学院计算机科学与人工智能实验室）；MIT-IBM Watson AI Lab（麻省理工学院-IBM沃森人工智能实验室）；The Chinese University of Hong Kong（香港中文大学）
Despite the success of Generative Adversarial Networks (GANs), mode collapse remains a serious issue during GAN training. To date, little work has focused on understanding and quantifying which modes have been dropped by a model. In this work, we visualize mode collapse at both the distribution level and the instance level. First, we deploy a semantic segmentation network to compare the distribution of segmented objects in the generated images with the target distribution in the training set. Differences in statistics reveal object classes that are omitted by a GAN. Second, given the identifie…
University of Southern California（南加州大学）；Stanford University（斯坦福大学）
In this work, we train conditional Wasserstein generative adversarial networks to effectively sample from the posterior of physics-based Bayesian inference problems. The generator is constructed using a U-Net architecture, with the latent information injected using conditional instance normalization. The former facilitates a multiscale inverse map, while the latter enables the decoupling of the latent space dimension from the dimension of the measurement, and introduces stochasticity at all scales of the U-Net. We solve PDE-based inverse problems to demonstrate the performance of our approach …
Class imbalance is a challenging issue in practical classification problems for deep learning models as well as for traditional models. Traditionally successful countermeasures such as synthetic over-sampling have had limited success with complex, structured data handled by deep learning models. In this work, we propose to use a Generative Adversarial Network (GAN) equipped with a generator network G, a discriminator network D and a classifier network C to remove the class-imbalance in visual data sets. The generator network is initialized with auto-encoder to make it stable. The discriminator…
Data-driven methods for improving turbulence modeling in Reynolds-Averaged Navier-Stokes (RANS) simulations have gained significant interest in the computational fluid dynamics community. Modern machine learning algorithms have opened up a new area of black-box turbulence models allowing for the tuning of RANS simulations to increase their predictive accuracy. While several data-driven turbulence models have been reported, the quantification of the uncertainties introduced has mostly been neglected. Uncertainty quantification for such data-driven models is essential since their predictive capa…
Knowing the uncertainty in a prediction is critical when making expensive investment decisions and when patient safety is paramount, but machine learning (ML) models in drug discovery typically provide only a single best estimate and ignore all sources of uncertainty. Predictions from these models may therefore be over-confident, which can put patients at risk and waste resources when compounds that are destined to fail are further developed. Probabilistic predictive models (PPMs) can incorporate uncertainty in both the data and model, and return a distribution of predicted values that represe…
Northeastern University（东北大学）；risQ Inc.（risQ公司）；Bay Area Environmental Research Institute（湾区环境研究所）；NASA Ames Research Center（美国国家航空航天局艾姆斯研究中心）；NASA Advanced Supercomputing Division（美国国家航空航天局高级超级计算部）
Deep Learning (DL) methods have been transforming computer vision with innovative adaptations to other domains including climate change. For DL to pervade Science and Engineering (S&E) applications where risk management is a core component, well-characterized uncertainty estimates must accompany predictions. However, S&E observations and model-simulations often follow heavily skewed distributions and are not well modeled with DL approaches, since they usually optimize a Gaussian, or Euclidean, likelihood loss. Recent developments in Bayesian Deep Learning (BDL), which attempts to capture uncer…
Over the decades, the Markowitz framework has been used extensively in portfolio analysis though it puts too much emphasis on the analysis of the market uncertainty rather than on the trend prediction. While generative adversarial network (GAN), conditional GAN (CGAN), and autoencoding CGAN (ACGAN) have been explored to generate financial time series and extract features that can help portfolio analysis. The limitation of the CGAN or ACGAN framework stands in putting too much emphasis on generating series and finding the internal trends of the series rather than predicting the future trends. I…
Recent research has shown that controllable image generation based on pre-trained GANs can benefit a wide range of computer vision tasks. However, less attention has been devoted to 3D vision tasks. In light of this, we propose a novel image-conditioned neural implicit field, which can leverage 2D supervisions from GAN-generated multi-view images and perform the single-view reconstruction of generic objects. Firstly, a novel offline StyleGAN-based generator is presented to generate plausible pseudo images with full control over the viewpoint. Then, we propose to utilize a neural implicit funct…
Over the decades, the Markowitz framework has been used extensively in portfolio analysis though it puts too much emphasis on the analysis of the market uncertainty rather than on the trend prediction. While generative adversarial network (GAN) and conditional GAN (CGAN) have been explored to generate financial time series and extract features that can help portfolio analysis. The limitation of the CGAN framework stands in putting too much emphasis on generating series rather than keeping features that can help this generator. In this paper, we introduce an autoencoding CGAN (ACGAN) based on d…
We introduce a computational framework to statistically infer thermophysical properties of any given wall from in-situ measurements of air temperature and surface heat fluxes. The proposed framework uses these measurements, within a Bayesian calibration approach, to sequentially infer input parameters of a one-dimensional heat diffusion model that describes the thermal performance of the wall. These inputs include spatially-variable functions that characterise the thermal conductivity and the volumetric heat capacity of the wall. We encode our computational framework in an algorithm that seque…
Uncertainty Quantification of closure relationships integrated into thermal-hydraulic system codes is a critical prerequisite in applying the Best-Estimate Plus Uncertainty (BEPU) methodology for nuclear safety and licensing processes.The purpose of the CIRCE method is to estimate the (log)-Gaussian probability distribution of a multiplicative factor applied to a reference closure relationship in order to assess its uncertainty. Even though this method has been implemented with success in numerous physical scenarios, it can still suffer from substantial limitations such as the linearity assump…
Quantifying uncertainty of individualized treatment effects in right-censored survival data: A comparison of Bayesian additive regression trees and causal survival forest
Kansas State University（堪萨斯州立大学）；ETH Zurich（苏黎世联邦理工学院）
Graph Neural Networks (GNN) provide a powerful framework that elegantly integrates Graph theory with Machine learning for modeling and analysis of networked data. We consider the problem of quantifying the uncertainty in predictions of GNN stemming from modeling errors and measurement uncertainty. We consider aleatoric uncertainty in the form of probabilistic links and noise in feature vector of nodes, while epistemic uncertainty is incorporated via a probability distribution over the model parameters. We propose a unified approach to treat both sources of uncertainty in a Bayesian framework, …
As applications of deep learning (DL) continue to seep into critical scientific use-cases, the importance of performing uncertainty quantification (UQ) with DL has become more pressing than ever before. In scientific applications, it is also important to inform the learning of DL models with knowledge of physics of the problem to produce physically consistent and generalized solutions. This is referred to as the emerging field of physics-informed deep learning (PIDL). We consider the problem of developing PIDL formulations that can also perform UQ. To this end, we propose a novel physics-infor…
Virginia Tech（弗吉尼亚理工大学）；U.S. Geological Survey（美国地质调查局）
To simultaneously address the rising need of expressing uncertainties in deep learning models along with producing model outputs which are consistent with the known scientific knowledge, we propose a novel physics-guided architecture (PGA) of neural networks in the context of lake temperature modeling where the physical constraints are hard coded in the neural network architecture. This allows us to integrate such models with state of the art uncertainty estimation approaches such as Monte Carlo (MC) Dropout without sacrificing the physical consistency of our results. We demonstrate the effect…
Various real-world applications involve modeling complex systems with immense uncertainty and optimizing multiple objectives based on the uncertain model. Quantifying the impact of the model uncertainty on the given operational objectives is critical for designing optimal experiments that can most effectively reduce the uncertainty that affect the objectives pertinent to the application at hand. In this paper, we propose the concept of mean multi-objective cost of uncertainty (multi-objective MOCU) that can be used for objective-based quantification of uncertainty for complex uncertain systems…
Rule based classifiers that use the presence and absence of key sub-strings to make classification decisions have a natural mechanism for quantifying the uncertainty of their precision. For a binary classifier, the key insight is to treat partitions of the sub-string set induced by the documents as Bernoulli random variables. The mean value of each random variable is an estimate of the classifier's precision when presented with a document inducing that partition. These means can be compared, using standard statistical tests, to a desired or expected classifier precision. A set of binary classi…
Quantifying and managing uncertainties that occur when data-driven models such as those provided by AI and machine learning methods are applied is crucial. This whitepaper provides a brief motivation and first overview of the state of the art in identifying and quantifying sources of uncertainty for data-driven components as well as means for analyzing their impact.
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 …
UC San Diego（加州大学圣地亚哥分校）；University of Washington（华盛顿大学）；Northeastern University（东北大学）
Deep learning is gaining increasing popularity for spatiotemporal forecasting. However, prior works have mostly focused on point estimates without quantifying the uncertainty of the predictions. In high stakes domains, being able to generate probabilistic forecasts with confidence intervals is critical to risk assessment and decision making. Hence, a systematic study of uncertainty quantification (UQ) methods for spatiotemporal forecasting is missing in the community. In this paper, we describe two types of spatiotemporal forecasting problems: regular grid-based and graph-based. Then we analyz…
A Three-Way Testing Framework for Quantifying Epistemic Calibration Uncertainty in SBI
DEs, ICMC（数学与统计系，计算与应用数学研究所）；Federal Univ. of São Carlos（圣卡洛斯联邦大学）；Univ. of São Paulo（圣保罗大学）；Brazil（巴西）；Univ. Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；Inria（法国国家数字科学研究所）；CNRS（法国国家科学研究中心）；Grenoble INP（格勒诺布尔国立理工学院）；LJK（拉格朗日计算与分析实验室）
Recurrent neural networks (RNNs) are nonlinear dynamical models commonly used in the machine learning and dynamical systems literature to represent complex dynamical or sequential relationships between variables. More recently, as deep learning models have become more common, RNNs have been used to forecast increasingly complicated systems. Dynamical spatio-temporal processes represent a class of complex systems that can potentially benefit from these types of models. Although the RNN literature is expansive and highly developed, uncertainty quantification is often ignored. Even when considere…
