Traditional Bayesian approaches for model uncertainty quantification rely on notoriously difficult processes of marginalization over each network parameter to estimate its probability density function (PDF). Our hypothesis is that internal layer outputs of a trained neural network contain all of the information related to both its mapping function (quantified by its weights) as well as the input data distribution. We therefore propose a framework for predictive uncertainty quantification of a trained neural network that explicitly estimates the PDF of its raw prediction space (before activation), p(y'|x,w), which we refer to as the model PDF, in a Gaussian reproducing kernel Hilbert space (RKHS). The Gaussian RKHS provides a localized density estimate of p(y'|x,w), which further enables us to utilize gradient based formulations of quantum physics to decompose the model PDF in terms of multiple local uncertainty moments that provide much greater resolution of the PDF than the central moments characterized by Bayesian methods. This provides the framework with a better ability to detect distributional shifts in test data away from the training data PDF learned by the model. We evaluate the framework against existing uncertainty quantification methods on benchmark datasets that have been corrupted using common perturbation techniques. The kernel framework is observed to provide model uncertainty estimates with much greater precision based on the ability to detect model prediction errors.
Manipal Institute of Technology, MAHE（马尼帕尔理工学院，马尼帕尔高等教育学院）
Most machine learning models operate under the assumption that the training, testing and deployment data is independent and identically distributed (i.i.d.). This assumption doesn't generally hold true in a natural setting. Usually, the deployment data is subject to various types of distributional shifts. The magnitude of a model's performance is proportional to this shift in the distribution of the dataset. Thus it becomes necessary to evaluate a model's uncertainty and robustness to distributional shifts to get a realistic estimate of its expected performance on real-world data. Present meth…
Estimating how uncertain an AI system is in its predictions is important to improve the safety of such systems. Uncertainty in predictive can result from uncertainty in model parameters, irreducible data uncertainty and uncertainty due to distributional mismatch between the test and training data distributions. Different actions might be taken depending on the source of the uncertainty so it is important to be able to distinguish between them. Recently, baseline tasks and metrics have been defined and several practical methods to estimate uncertainty developed. These methods, however, attempt …
The Australian National University（澳大利亚国立大学）；Data 61；Google Brain（谷歌大脑）；The University of Illinois at Chicago（伊利诺伊大学芝加哥分校）；The University of Sydney（悉尼大学）
Robust risk minimisation has several advantages: it has been studied with regards to improving the generalisation properties of models and robustness to adversarial perturbation. We bound the distributionally robust risk for a model class rich enough to include deep neural networks by a regularised empirical risk involving the Lipschitz constant of the model. This allows us to interpretand quantify the robustness properties of a deep neural network. As an application we show the distributionally robust risk upperbounds the adversarial training risk.
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…
UC Berkeley（加州大学伯克利分校）；Amazon（亚马逊）；Toyota Research Institute（丰田研究所）
Recent work has shown that the performance of machine learning models can vary substantially when models are evaluated on data drawn from a distribution that is close to but different from the training distribution. As a result, predicting model performance on unseen distributions is an important challenge. Our work connects techniques from domain adaptation and predictive uncertainty literature, and allows us to predict model accuracy on challenging unseen distributions without access to labeled data. In the context of distribution shift, distributional distances are often used to adapt model…
Deep neural networks are increasingly being used for the analysis of medical images. However, most works neglect the uncertainty in the model's prediction. We propose an uncertainty-aware deep kernel learning model which permits the estimation of the uncertainty in the prediction by a pipeline of a Convolutional Neural Network and a sparse Gaussian Process. Furthermore, we adapt different pre-training methods to investigate their impacts on the proposed model. We apply our approach to Bone Age Prediction and Lesion Localization. In most cases, the proposed model shows better performance compar…
Brown University（布朗大学）；Université de Toulouse（图卢兹大学）
Our ability to generalize beyond training data to novel, out-of-distribution, image degradations is a hallmark of primate vision. The predictive brain, exemplified by predictive coding networks (PCNs), has become a prominent neuroscience theory of neural computation. Motivated by the recent successes of variational autoencoders (VAEs) in machine learning, we rigorously derive a correspondence between PCNs and VAEs. This motivates us to consider iterative extensions of VAEs (iVAEs) as plausible variational extensions of the PCNs. We further demonstrate that iVAEs generalize to distributional sh…
Counterfactual explanations are attracting significant attention due to the flourishing applications of machine learning models in consequential domains. A counterfactual plan consists of multiple possibilities to modify a given instance so that the model's prediction will be altered. As the predictive model can be updated subject to the future arrival of new data, a counterfactual plan may become ineffective or infeasible with respect to the future values of the model parameters. In this work, we study the counterfactual plans under model uncertainty, in which the distribution of the model pa…
Generalized Conformal Predictive Systems Under Distributional Shifts
IDLab Seminar for Statistics（统计研究所研讨会）；Department of Electronics（电子系）；ETH Zurich（苏黎世联邦理工学院）；Information Systems Zurich, Switzerland（苏黎世信息系统，瑞士）；Ghent University（根特大学）
This paper presents a novel trajectory tracker for autonomous quadrotor navigation in dynamic and complex environments. The proposed framework integrates a distributional Reinforcement Learning (RL) estimator for unknown aerodynamic effects into a Stochastic Model Predictive Controller (SMPC) for trajectory tracking. Aerodynamic effects derived from drag forces and moment variations are difficult to model directly and accurately. Most current quadrotor tracking systems therefore treat them as simple `disturbances' in conventional control approaches. We propose Quantile-approximation-based Dist…
Calibrated Multivariate Distributional Regression with Pre-Rank Regularization
Department of Statistics and Data Science, Mohamed Bin Zayed University of Artificial Intelligence, Abu Dhabi, UAE（统计与数据科学系，Mohamed Bin Zayed人工智能大学，阿布扎比，阿联酋）
Many reinforcement learning (RL) problems in practice are offline, learning purely from observational data. A key challenge is how to ensure the learned policy is safe, which requires quantifying the risk associated with different actions. In the online setting, distributional RL algorithms do so by learning the distribution over returns (i.e., cumulative rewards) instead of the expected return; beyond quantifying risk, they have also been shown to learn better representations for planning. We propose Conservative Offline Distributional Actor Critic (CODAC), an offline RL algorithm suitable fo…
UC, Berkeley（加州大学伯克利分校）；MILA, Université de Montréal（蒙特利尔大学MILA）；DiDi（滴滴）；UC, San Diego（加州大学圣地亚哥分校）；CIFAR（加拿大高等研究院）
Domain adaptation (DA) is a technique that transfers predictive models trained on a labeled source domain to an unlabeled target domain, with the core difficulty of resolving distributional shift between domains. Currently, most popular DA algorithms are based on distributional matching (DM). However in practice, realistic domain shifts (RDS) may violate their basic assumptions and as a result these methods will fail. In this paper, in order to devise robust DA algorithms, we first systematically analyze the limitations of DM based methods, and then build new benchmarks with more realistic dom…
School of Social Sciences（社会科学学院）；University of Mannheim（曼海姆大学）；Department of Statistics（统计学系）；LMU Munich（慕尼黑大学）
Both industry and academia have made considerable progress in developing trustworthy and responsible machine learning (ML) systems. While critical concepts like fairness and explainability are often addressed, the safety of systems is typically not sufficiently taken into account. By viewing data-driven decision systems as socio-technical systems, we draw on the uncertainty in ML literature to show how fairML systems can also be safeML systems. We posit that a fair model needs to be an uncertainty-aware model, e.g. by drawing on distributional regression. For fair decisions, we argue that a sa…
Recent work introduced the epinet as a new approach to uncertainty modeling in deep learning. An epinet is a small neural network added to traditional neural networks, which, together, can produce predictive distributions. In particular, using an epinet can greatly improve the quality of joint predictions across multiple inputs, a measure of how well a neural network knows what it does not know. In this paper, we examine whether epinets can offer similar advantages under distributional shifts. We find that, across ImageNet-A/O/C, epinets generally improve robustness metrics. Moreover, these im…
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；University of Freiburg（弗赖堡大学）
In order to anticipate rare and impactful events, we propose to quantify the worst-case risk under distributional ambiguity using a recent development in kernel methods -- the kernel mean embedding. Specifically, we formulate the generalized moment problem whose ambiguity set (i.e., the moment constraint) is described by constraints in the associated reproducing kernel Hilbert space in a nonparametric manner. We then present the tractable approximation and its theoretical justification. As a concrete application, we numerically test the proposed method in characterizing the worst-case constrai…
Decision Making under the Exponential Family: Distributionally Robust Optimisation with Bayesian Ambiguity Sets
Department of Statistics, University of Warwick, Coventry, UK（威斯敏斯特大学统计学系）；Department of Computer Science, University of Warwick, Coventry, UK（威斯敏斯特大学计算机科学系）；Department of Statistics, University College London, UK（伦敦大学学院统计学系）；The Alan Turing Institute, London, UK（艾伦·图灵研究所）
CISPA Center for Information Security（CISPA信息安全中心）
Shapley value is a classic notion from game theory, historically used to quantify the contributions of individuals within groups, and more recently applied to assign values to data points when training machine learning models. Despite its foundational role, a key limitation of the data Shapley framework is that it only provides valuations for points within a fixed data set. It does not account for statistical aspects of the data and does not give a way to reason about points outside the data set. To address these limitations, we propose a novel framework -- distributional Shapley -- where the …
AI Vulnerability Database（人工智能漏洞数据库）；Bias Buccaneers（偏见海盗）；AT&T Data Science and AI Research（美国电话电报公司数据科学与人工智能研究院）
We investigate the detection of botnet command and control (C2) hosts in massive IP traffic using machine learning methods. To this end, we use NetFlow data -- the industry standard for monitoring of IP traffic -- and ML models using two sets of features: conventional NetFlow variables and distributional features based on NetFlow variables. In addition to using static summaries of NetFlow features, we use quantiles of their IP-level distributions as input features in predictive models to predict whether an IP belongs to known botnet families. These models are used to develop intrusion detectio…
Distributional data Shapley value (DShapley) has recently been proposed as a principled framework to quantify the contribution of individual datum in machine learning. DShapley develops the foundational game theory concept of Shapley values into a statistical framework and can be applied to identify data points that are useful (or harmful) to a learning algorithm. Estimating DShapley is computationally expensive, however, and this can be a major challenge to using it in practice. Moreover, there has been little mathematical analyses of how this value depends on data characteristics. In this pa…
LMU Munich（慕尼黑大学）；Helmholtz AI（亥姆霍兹人工智能研究所）；ETH Zurich（苏黎世联邦理工学院）；University of Zurich（苏黎世大学）；Humboldt-Universität zu Berlin（柏林洪堡大学）；Helmholtz Zentrum Munich（慕尼黑亥姆霍兹中心）；Flatiron Institute（弗莱提荣研究所）
In this paper we describe the implementation of semi-structured deep distributional regression, a flexible framework to learn conditional distributions based on the combination of additive regression models and deep networks. Our implementation encompasses (1) a modular neural network building system based on the deep learning library \pkg{TensorFlow} for the fusion of various statistical and deep learning approaches, (2) an orthogonalization cell to allow for an interpretable combination of different subnetworks, as well as (3) pre-processing steps necessary to set up such models. The softwar…
