Uncertainty quantification is at the core of the reliability and robustness of machine learning. In this paper, we provide a theoretical framework to dissect the uncertainty, especially the epistemic component, in deep learning into procedural variability (from the training procedure) and data variability (from the training data), which is the first such attempt in the literature to our best knowledge. We then propose two approaches to estimate these uncertainties, one based on influence function and one on batching. We demonstrate how our approaches overcome the computational difficulties in applying classical statistical methods. Experimental evaluations on multiple problem settings corroborate our theory and illustrate how our framework and estimation can provide direct guidance on modeling and data collection effort to improve deep learning performance.
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Deep neural networks are highly susceptible to learning biases in visual data. While various methods have been proposed to mitigate such bias, the majority require explicit knowledge of the biases present in the training data in order to mitigate. We argue the relevance of exploring methods which are completely ignorant of the presence of any bias, but are capable of identifying and mitigating them. Furthermore, we propose using Bayesian neural networks with an epistemic uncertainty-weighted loss function to dynamically identify potential bias in individual training samples and to weight them during training. We find a positive correlation between samples subject to bias and higher epistemic uncertainties. Finally, we show the method has potential to mitigate visual bias on a bias benchmark dataset and on a real-world face detection problem, and we consider the merits and weaknesses of our approach.
Neural networks are ubiquitous in many tasks, but trusting their predictions is an open issue. Uncertainty quantification is required for many applications, and disentangled aleatoric and epistemic uncertainties are best. In this paper, we generalize methods to produce disentangled uncertainties to work with different uncertainty quantification methods, and evaluate their capability to produce disentangled uncertainties. Our results show that: there is an interaction between learning aleatoric and epistemic uncertainty, which is unexpected and violates assumptions on aleatoric uncertainty, some methods like Flipout produce zero epistemic uncertainty, aleatoric uncertainty is unreliable in the out-of-distribution setting, and Ensembles provide overall the best disentangling quality. We also explore the error produced by the number of samples hyper-parameter in the sampling softmax function, recommending N > 100 samples. We expect that our formulation and results help practitioners and researchers choose uncertainty methods and expand the use of disentangled uncertainties, as well as motivate additional research into this topic.
Epistemic uncertainty is the part of out-of-sample prediction error due to the lack of knowledge of the learner. Whereas previous work was focusing on model variance, we propose a principled approach for directly estimating epistemic uncertainty by learning to predict generalization error and subtracting an estimate of aleatoric uncertainty, i.e., intrinsic unpredictability. This estimator of epistemic uncertainty includes the effect of model bias (or misspecification) and is useful in interactive learning environments arising in active learning or reinforcement learning. In addition to discussing these properties of Direct Epistemic Uncertainty Prediction (DEUP), we illustrate its advantage against existing methods for uncertainty estimation on downstream tasks including sequential model optimization and reinforcement learning. We also evaluate the quality of uncertainty estimates from DEUP for probabilistic classification of images and for estimating uncertainty about synergistic drug combinations.
Computer models are widely used in decision support for energy systems operation, planning and policy. A system of models is often employed, where model inputs themselves arise from other computer models, with each model being developed by different teams of experts. Gaussian Process emulators can be used to approximate the behaviour of complex, computationally intensive models and used to generate predictions together with a measure of uncertainty about the predicted model output. This paper presents a computationally efficient framework for propagating uncertainty within a network of models with high-dimensional outputs used for energy planning. We present a case study from a UK county council considering low carbon technologies to transform its infrastructure to reach a net-zero carbon target. The system model considered for this case study is simple, however the framework can be applied to larger networks of more complex models.
A rising number of botnet families have been successfully detected using deep learning architectures. While the variety of attacks increases, these architectures should become more robust against attacks. They have been proven to be very sensitive to small but well constructed perturbations in the input. Botnet detection requires extremely low false-positive rates (FPR), which are not commonly attainable in contemporary deep learning. Attackers try to increase the FPRs by making poisoned samples. The majority of recent research has focused on the use of model loss functions to build adversarial examples and robust models. In this paper, two LSTM-based classification algorithms for botnet classification with an accuracy higher than 98\% are presented. Then, the adversarial attack is proposed, which reduces the accuracy to about30\%. Then, by examining the methods for computing the uncertainty, the defense method is proposed to increase the accuracy to about 70\%. By using the deep ensemble and stochastic weight averaging quantification methods it has been investigated the uncertainty of the accuracy in the proposed methods.
In this study, we examine a clustering problem in which the covariates of each individual element in a dataset are associated with an uncertainty specific to that element. More specifically, we consider a clustering approach in which a pre-processing applying a non-linear transformation to the covariates is used to capture the hidden data structure. To this end, we approximate the sets representing the propagated uncertainty for the pre-processed features empirically. To exploit the empirical uncertainty sets, we propose a greedy and optimistic clustering (GOC) algorithm that finds better feature candidates over such sets, yielding more condensed clusters. As an important application, we apply the GOC algorithm to synthetic datasets of the orbital properties of stars generated through our numerical simulation mimicking the formation process of the Milky Way. The GOC algorithm demonstrates an improved performance in finding sibling stars originating from the same dwarf galaxy. These realistic datasets have also been made publicly available.
The adaptive processing of structured data is a long-standing research topic in machine learning that investigates how to automatically learn a mapping from a structured input to outputs of various nature. Recently, there has been an increasing interest in the adaptive processing of graphs, which led to the development of different neural network-based methodologies. In this thesis, we take a different route and develop a Bayesian Deep Learning framework for graph learning. The dissertation begins with a review of the principles over which most of the methods in the field are built, followed by a study on graph classification reproducibility issues. We then proceed to bridge the basic ideas of deep learning for graphs with the Bayesian world, by building our deep architectures in an incremental fashion. This framework allows us to consider graphs with discrete and continuous edge features, producing unsupervised embeddings rich enough to reach the state of the art on several classification tasks. Our approach is also amenable to a Bayesian nonparametric extension that automatizes the choice of almost all model's hyper-parameters. Two real-world applications demonstrate the efficacy of deep learning for graphs. The first concerns the prediction of information-theoretic quantities for molecular simulations with supervised neural models. After that, we exploit our Bayesian models to solve a malware-classification task while being robust to intra-procedural code obfuscation techniques. We conclude the dissertation with an attempt to blend the best of the neural and Bayesian worlds together. The resulting hybrid model is able to predict multimodal distributions conditioned on input graphs, with the consequent ability to model stochasticity and uncertainty better than most works. Overall, we aim to provide a Bayesian perspective into the articulated research field of deep learning for graphs.
Due to their increasing spread, confidence in neural network predictions became more and more important. However, basic neural networks do not deliver certainty estimates or suffer from over or under confidence. Many researchers have been working on understanding and quantifying uncertainty in a neural network's prediction. As a result, different types and sources of uncertainty have been identified and a variety of approaches to measure and quantify uncertainty in neural networks have been proposed. This work gives a comprehensive overview of uncertainty estimation in neural networks, reviews recent advances in the field, highlights current challenges, and identifies potential research opportunities. It is intended to give anyone interested in uncertainty estimation in neural networks a broad overview and introduction, without presupposing prior knowledge in this field. A comprehensive introduction to the most crucial sources of uncertainty is given and their separation into reducible model uncertainty and not reducible data uncertainty is presented. The modeling of these uncertainties based on deterministic neural networks, Bayesian neural networks, ensemble of neural networks, and test-time data augmentation approaches is introduced and different branches of these fields as well as the latest developments are discussed. For a practical application, we discuss different measures of uncertainty, approaches for the calibration of neural networks and give an overview of existing baselines and implementations. Different examples from the wide spectrum of challenges in different fields give an idea of the needs and challenges regarding uncertainties in practical applications. Additionally, the practical limitations of current methods for mission- and safety-critical real world applications are discussed and an outlook on the next steps towards a broader usage of such methods is given.
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 initializations. Its strong performance highlights the benefit of combining models with both weight and hyperparameter diversity. We further propose a parameter efficient version, hyper-batch ensembles, which builds on the layer structure of batch ensembles and self-tuning networks. The computational and memory costs of our method are notably lower than typical ensembles. On image classification tasks, with MLP, LeNet, and Wide ResNet 28-10 architectures, our methodology improves upon both deep and batch ensembles.
The notion of uncertainty is of major importance in machine learning and constitutes a key element of machine learning methodology. In line with the statistical tradition, uncertainty has long been perceived as almost synonymous with standard probability and probabilistic predictions. Yet, due to the steadily increasing relevance of machine learning for practical applications and related issues such as safety requirements, new problems and challenges have recently been identified by machine learning scholars, and these problems may call for new methodological developments. In particular, this includes the importance of distinguishing between (at least) two different types of uncertainty, often refereed to as aleatoric and epistemic. In this paper, we provide an introduction to the topic of uncertainty in machine learning as well as an overview of hitherto attempts at handling uncertainty in general and formalizing this distinction in particular.
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