独立训练的神经网络的集合是一种最新的方法，可以在深度学习中估算预测性不确定性，并且可以通过三角洲函数的混合物解释为后验分布的近似值。合奏的培训依赖于损失景观的非跨性别性和其单个成员的随机初始化，从而使后近似不受控制。本文提出了一种解决此限制的新颖和原则性的方法，最大程度地减少了函数空间中真实后验和内核密度估计器（KDE）之间的$ f $ divergence。我们从组合的角度分析了这一目标，并表明它在任何$ f $的混合组件方面都是supporular。随后，我们考虑了贪婪合奏结构的问题。从负$ f $ didivergence上的边际增益来量化后近似的改善，通过将新组件添加到KDE中得出，我们得出了集合方法的新型多样性项。我们的方法的性能在计算机视觉的分布外检测基准测试中得到了证明，该基准在多个数据集中训练的一系列架构中。我们方法的源代码可在https://github.com/oulu-imeds/greedy_ensembles_training上公开获得。

The problem of detecting the Out-of-Distribution (OoD) inputs is of paramount importance for Deep Neural Networks. It has been previously shown that even Deep Generative Models that allow estimating the density of the inputs may not be reliable and often tend to make over-confident predictions for OoDs, assigning to them a higher density than to the in-distribution data. This over-confidence in a single model can be potentially mitigated with Bayesian inference over the model parameters that take into account epistemic uncertainty. This paper investigates three approaches to Bayesian inference: stochastic gradient Markov chain Monte Carlo, Bayes by Backpropagation, and Stochastic Weight Averaging-Gaussian. The inference is implemented over the weights of the deep neural networks that parameterize the likelihood of the Variational Autoencoder. We empirically evaluate the approaches against several benchmarks that are often used for OoD detection: estimation of the marginal likelihood utilizing sampled model ensemble, typicality test, disagreement score, and Watanabe-Akaike Information Criterion. Finally, we introduce two simple scores that demonstrate the state-of-the-art performance.

Accurate uncertainty quantification is a major challenge in deep learning, as neural networks can make overconfident errors and assign high confidence predictions to out-of-distribution (OOD) inputs. The most popular approaches to estimate predictive uncertainty in deep learning are methods that combine predictions from multiple neural networks, such as Bayesian neural networks (BNNs) and deep ensembles. However their practicality in real-time, industrial-scale applications are limited due to the high memory and computational cost. Furthermore, ensembles and BNNs do not necessarily fix all the issues with the underlying member networks. In this work, we study principled approaches to improve uncertainty property of a single network, based on a single, deterministic representation. By formalizing the uncertainty quantification as a minimax learning problem, we first identify distance awareness, i.e., the model's ability to quantify the distance of a testing example from the training data, as a necessary condition for a DNN to achieve high-quality (i.e., minimax optimal) uncertainty estimation. We then propose Spectral-normalized Neural Gaussian Process (SNGP), a simple method that improves the distance-awareness ability of modern DNNs with two simple changes: (1) applying spectral normalization to hidden weights to enforce bi-Lipschitz smoothness in representations and (2) replacing the last output layer with a Gaussian process layer. On a suite of vision and language understanding benchmarks, SNGP outperforms other single-model approaches in prediction, calibration and out-of-domain detection. Furthermore, SNGP provides complementary benefits to popular techniques such as deep ensembles and data augmentation, making it a simple and scalable building block for probabilistic deep learning. Code is open-sourced at https://github.com/google/uncertainty-baselines

We introduce ensembles of stochastic neural networks to approximate the Bayesian posterior, combining stochastic methods such as dropout with deep ensembles. The stochastic ensembles are formulated as families of distributions and trained to approximate the Bayesian posterior with variational inference. We implement stochastic ensembles based on Monte Carlo dropout, DropConnect and a novel non-parametric version of dropout and evaluate them on a toy problem and CIFAR image classification. For CIFAR, the stochastic ensembles are quantitatively compared to published Hamiltonian Monte Carlo results for a ResNet-20 architecture. We also test the quality of the posteriors directly against Hamiltonian Monte Carlo simulations in a simplified toy model. Our results show that in a number of settings, stochastic ensembles provide more accurate posterior estimates than regular deep ensembles.

深度神经网络易于对异常值过度自信的预测。贝叶斯神经网络和深度融合都已显示在某种程度上减轻了这个问题。在这项工作中，我们的目标是通过提议预测由高斯混合模型的后续的高斯混合模型来结合这两种方法的益处，该高斯混合模型包括独立培训的深神经网络的LAPPALL近似的加权和。该方法可以与任何一组预先训练的网络一起使用，并且与常规合并相比，只需要小的计算和内存开销。理论上我们验证了我们的方法从训练数据中的培训数据和虚拟化的基本线上的标准不确定量级基准测试中的“远离”的过度控制。

我们研究了回归中神经网络（NNS）的模型不确定性的方法。为了隔离模型不确定性的效果，我们专注于稀缺训练数据的无噪声环境。我们介绍了关于任何方法都应满足的模型不确定性的五个重要的逃亡者。但是，我们发现，建立的基准通常无法可靠地捕获其中一些逃避者，即使是贝叶斯理论要求的基准。为了解决这个问题，我们介绍了一种新方法来捕获NNS的模型不确定性，我们称之为基于神经优化的模型不确定性（NOMU）。 NOMU的主要思想是设计一个由两个连接的子NN组成的网络体系结构，一个用于模型预测，一个用于模型不确定性，并使用精心设计的损耗函数进行训练。重要的是，我们的设计执行NOMU满足我们的五个Desiderata。由于其模块化体系结构，NOMU可以为任何给定（先前训练）NN提供模型不确定性，如果访问其培训数据。我们在各种回归任务和无嘈杂的贝叶斯优化（BO）中评估NOMU，并具有昂贵的评估。在回归中，NOMU至少和最先进的方法。在BO中，Nomu甚至胜过所有考虑的基准。

我们表明，著名的混音的有效性[Zhang等，2018]，如果而不是将其用作唯一的学习目标，就可以进一步改善它，而是将其用作标准跨侧面损失的附加规则器。这种简单的变化不仅提供了太大的准确性，而且在大多数情况下，在各种形式的协变量转移和分布外检测实验下，在大多数情况下，混合量的预测不确定性估计质量都显着提高了。实际上，我们观察到混合物在检测出分布样本时可能会产生大量退化的性能，因为我们在经验上表现出来，因为它倾向于学习在整个过程中表现出高渗透率的模型。很难区分分布样本与近分离样本。为了显示我们的方法的功效（RegMixup），我们在视觉数据集（Imagenet＆Cifar-10/100）上提供了详尽的分析和实验，并将其与最新方法进行比较，以进行可靠的不确定性估计。

随着我们远离数据，预测不确定性应该增加，因为各种各样的解释与鲜为人知的信息一致。我们引入了远距离感知的先验（DAP）校准，这是一种纠正训练域之外贝叶斯深度学习模型过度自信的方法。我们将DAPS定义为模型参数的先验分布，该模型参数取决于输入，通过其与训练集的距离度量。DAP校准对后推理方法不可知，可以作为后处理步骤进行。我们证明了其在各种分类和回归问题中对几个基线的有效性，包括旨在测试远离数据的预测分布质量的基准。

不确定性的量化对于采用机器学习至关重要，尤其是拒绝分布（OOD）数据回到人类专家进行审查。然而，进步一直很慢，因为计算效率和不确定性估计质量之间必须达到平衡。因此，许多人使用神经网络或蒙特卡洛辍学的深层集合来进行相对最小的计算和记忆时合理的不确定性估计。出乎意料的是，当我们专注于$ \ leq 1 \％$ frese-falds正率（FPR）的现实世界中的约束时，先前的方法无法可靠地检测到OOD样本。值得注意的是，即使高斯随机噪声也无法触发这些流行的OOD技术。我们通过设计一种简单的对抗训练计划来帮助缓解这个问题，该计划结合了辍学合奏所预测的认知不确定性的攻击。我们证明了这种方法可以改善标准数据（即未经对抗制作）上的OOD检测性能，并将标准化的部分AUC从近乎随机的猜测性能提高到$ \ geq 0.75 $。

贝叶斯范式有可能解决深度神经网络的核心问题，如校准和数据效率低差。唉，缩放贝叶斯推理到大量的空间通常需要限制近似。在这项工作中，我们表明它足以通过模型权重的小子集进行推动，以便获得准确的预测后断。另一个权重被保存为点估计。该子网推断框架使我们能够在这些子集上使用表现力，否则难以相容的后近近似。特别是，我们将子网线性化LAPLACE作为一种简单，可扩展的贝叶斯深度学习方法：我们首先使用线性化的拉普拉斯近似来获得所有重量的地图估计，然后在子网上推断出全协方差高斯后面。我们提出了一个子网选择策略，旨在最大限度地保护模型的预测性不确定性。经验上，我们的方法对整个网络的集合和较少的表达后近似进行了比较。

随机梯度马尔可夫链蒙特卡洛（SGMCMC）被认为是大型模型（例如贝叶斯神经网络）中贝叶斯推断的金标准。由于从业人员在这些模型中面临速度与准确性权衡，因此变异推理（VI）通常是可取的选择。不幸的是，VI对后部的分解和功能形式做出了有力的假设。在这项工作中，我们提出了一个新的非参数变分近似，该近似没有对后验功能形式进行假设，并允许从业者指定算法应尊重或断裂的确切依赖性。该方法依赖于在修改的能量函数上运行的新的langevin型算法，其中潜在变量的一部分是在马尔可夫链的早期迭代中平均的。这样，统计依赖性可以以受控的方式破裂，从而使链条混合更快。可以以“辍学”方式进一步修改该方案，从而导致更大的可扩展性。我们在CIFAR-10，SVHN和FMNIST上测试RESNET-20的计划。在所有情况下，与SG-MCMC和VI相比，我们都会发现收敛速度和/或最终精度的提高。

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 separately with out-of-class examples generated by a conditional GAN and complement this with a one-vs-all image classifier. In our experiments, in particular on CIFAR10, CIFAR100 and Tiny ImageNet, we improve over the OoD detection and FP detection performance of state-of-the-art GAN-training based classifiers. Furthermore, we also find that the generated GAN examples do not significantly affect the calibration error of our classifier and result in a significant gain in model accuracy.

We propose SWA-Gaussian (SWAG), a simple, scalable, and general purpose approach for uncertainty representation and calibration in deep learning. Stochastic Weight Averaging (SWA), which computes the first moment of stochastic gradient descent (SGD) iterates with a modified learning rate schedule, has recently been shown to improve generalization in deep learning. With SWAG, we fit a Gaussian using the SWA solution as the first moment and a low rank plus diagonal covariance also derived from the SGD iterates, forming an approximate posterior distribution over neural network weights; we then sample from this Gaussian distribution to perform Bayesian model averaging. We empirically find that SWAG approximates the shape of the true posterior, in accordance with results describing the stationary distribution of SGD iterates. Moreover, we demonstrate that SWAG performs well on a wide variety of tasks, including out of sample detection, calibration, and transfer learning, in comparison to many popular alternatives including MC dropout, KFAC Laplace, SGLD, and temperature scaling.

我们有兴趣估计深神经网络的不确定性，这些神经网络在许多科学和工程问题中起着重要作用。在本文中，我们提出了一个引人注目的新发现，即具有相同权重初始化的神经网络的合奏，在数据集中受到持续偏差的转移而训练会产生稍微不一致的训练模型，其中预测的差异是强大的指标。认知不确定性。使用神经切线核（NTK），我们证明了这种现象是由于NTK不变的部分而发生的。由于这是通过微不足道的输入转换来实现的，因此我们表明可以使用单个神经网络（使用我们称为$ \ delta- $ uq的技术）来近似它，从而通过边缘化效果来估计预测周围的不确定性偏见。我们表明，$ \ delta- $ uq的不确定性估计值优于各种基准测试的当前方法 - 异常拒绝，分配变化下的校准以及黑匣子功能的顺序设计优化。

It is known that neural networks have the problem of being over-confident when directly using the output label distribution to generate uncertainty measures. Existing methods mainly resolve this issue by retraining the entire model to impose the uncertainty quantification capability so that the learned model can achieve desired performance in accuracy and uncertainty prediction simultaneously. However, training the model from scratch is computationally expensive and may not be feasible in many situations. In this work, we consider a more practical post-hoc uncertainty learning setting, where a well-trained base model is given, and we focus on the uncertainty quantification task at the second stage of training. We propose a novel Bayesian meta-model to augment pre-trained models with better uncertainty quantification abilities, which is effective and computationally efficient. Our proposed method requires no additional training data and is flexible enough to quantify different uncertainties and easily adapt to different application settings, including out-of-domain data detection, misclassification detection, and trustworthy transfer learning. We demonstrate our proposed meta-model approach's flexibility and superior empirical performance on these applications over multiple representative image classification benchmarks.

贝叶斯神经网络（BNNS）通过提供认知不确定性的原则概率表示，有望在协变量转移下改善概括。但是，基于重量的BNN通常会在大规模体系结构和数据集的高计算复杂性上挣扎。基于节点的BNN最近被引入了可扩展的替代方案，该替代方案通过将每个隐藏节点乘以潜在的随机变量来诱导认知不确定性，同时学习权重的点刻度。在本文中，我们将这些潜在的噪声变量解释为训练过程中简单和域 - 不合时宜数据扰动的隐式表示，从而产生了由于输入损坏而导致协变量转移的BNN。我们观察到，隐性腐败的多样性取决于潜在变量的熵，并提出了一种直接的方法来增加训练期间这些变量的熵。我们评估了分布外图像分类基准测试的方法，并显示出由于输入扰动而导致的协变量转移下基于节点的BNN的不确定性估计。作为副作用，该方法还提供了针对嘈杂训练标签的鲁棒性。

最近出现了一系列用于估计具有单个正向通行证的深神经网络中的认知不确定性的新方法，最近已成为贝叶斯神经网络的有效替代方法。在信息性表示的前提下，这些确定性不确定性方法（DUM）在检测到分布（OOD）数据的同时在推理时添加可忽略的计算成本时实现了强大的性能。但是，目前尚不清楚dums是否经过校准，可以无缝地扩展到现实世界的应用 - 这都是其实际部署的先决条件。为此，我们首先提供了DUMS的分类法，并在连续分配转移下评估其校准。然后，我们将它们扩展到语义分割。我们发现，尽管DUMS尺度到现实的视觉任务并在OOD检测方面表现良好，但当前方法的实用性受到分配变化下的校准不良而破坏的。

收购用于监督学习的标签可能很昂贵。为了提高神经网络回归的样本效率，我们研究了活跃的学习方法，这些方法可以适应地选择未标记的数据进行标记。我们提出了一个框架，用于从（与网络相关的）基础内核，内核转换和选择方法中构造此类方法。我们的框架涵盖了许多基于神经网络的高斯过程近似以及非乘式方法的现有贝叶斯方法。此外，我们建议用草图的有限宽度神经切线核代替常用的最后层特征，并将它们与一种新型的聚类方法结合在一起。为了评估不同的方法，我们引入了一个由15个大型表格回归数据集组成的开源基准。我们所提出的方法的表现优于我们的基准测试上的最新方法，缩放到大数据集，并在不调整网络体系结构或培训代码的情况下开箱即用。我们提供开源代码，包括所有内核，内核转换和选择方法的有效实现，并可用于复制我们的结果。

现代深度学习方法构成了令人难以置信的强大工具，以解决无数的挑战问题。然而，由于深度学习方法作为黑匣子运作，因此与其预测相关的不确定性往往是挑战量化。贝叶斯统计数据提供了一种形式主义来理解和量化与深度神经网络预测相关的不确定性。本教程概述了相关文献和完整的工具集，用于设计，实施，列车，使用和评估贝叶斯神经网络，即使用贝叶斯方法培训的随机人工神经网络。

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 to model uncertainty due to distributional mismatch either implicitly through model uncertainty or as data uncertainty. This work proposes a new framework for modeling predictive uncertainty called Prior Networks (PNs) which explicitly models distributional uncertainty. PNs do this by parameterizing a prior distribution over predictive distributions. This work focuses on uncertainty for classification and evaluates PNs on the tasks of identifying out-of-distribution (OOD) samples and detecting misclassification on the MNIST and CIFAR-10 datasets, where they are found to outperform previous methods. Experiments on synthetic and MNIST data show that unlike previous non-Bayesian methods PNs are able to distinguish between data and distributional uncertainty.