We introduce a new, efficient, principled and backpropagation-compatible algorithm for learning a probability distribution on the weights of a neural network, called Bayes by Backprop. It regularises the weights by minimising a compression cost, known as the variational free energy or the expected lower bound on the marginal likelihood. We show that this principled kind of regularisation yields comparable performance to dropout on MNIST classification. We then demonstrate how the learnt uncertainty in the weights can be used to improve generalisation in non-linear regression problems, and how this weight uncertainty can be used to drive the exploration-exploitation trade-off in reinforcement learning.
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We introduce a new, efficient, principled and backpropagation-compatible algorithm for learning a probability distribution on the weights of a neural network, called Bayes by Backprop. It regularises the weights by minimising a compression cost, known as the variational free energy or the expected lower bound on the marginal likelihood. We show that this principled kind of regularisation yields comparable performance to dropout on MNIST classification. We then demonstrate how the learnt uncertainty in the weights can be used to improve generalisation in non-linear regression problems, and how this weight uncertainty can be used to drive the exploration-exploitation trade-off in reinforcement learning.
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在这项工作中,我们使用变分推论来量化无线电星系分类的深度学习模型预测的不确定性程度。我们表明,当标记无线电星系时,个体测试样本的模型后差水平与人类不确定性相关。我们探讨了各种不同重量前沿的模型性能和不确定性校准,并表明稀疏事先产生更良好的校准不确定性估计。使用单个重量的后部分布,我们表明我们可以通过从最低信噪比(SNR)中除去权重来修剪30%的完全连接的层权重,而无需显着损失性能。我们证明,可以使用基于Fisher信息的排名来实现更大程度的修剪,但我们注意到两种修剪方法都会影响Failaroff-Riley I型和II型无线电星系的不确定性校准。最后,我们表明,与此领域的其他工作相比,我们经历了冷的后效,因此后部必须缩小后加权以实现良好的预测性能。我们检查是否调整成本函数以适应模型拼盘可以弥补此效果,但发现它不会产生显着差异。我们还研究了原则数据增强的效果,并发现这改善了基线,而且还没有弥补观察到的效果。我们将其解释为寒冷的后效,因为我们的培训样本过于有效的策划导致可能性拼盘,并将其提高到未来无线电银行分类的潜在问题。
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我们在这里采用贝叶斯非参数混合模型,以将多臂匪徒扩展到尤其是汤普森采样,以扩展到存在奖励模型不确定性的场景。在随机的多臂强盗中,播放臂的奖励是由未知分布产生的。奖励不确定性,即缺乏有关奖励生成分布的知识,引起了探索 - 开发权的权衡:强盗代理需要同时了解奖励分布的属性,并顺序决定下一步要采取哪种操作。在这项工作中,我们通过采用贝叶斯非参数高斯混合模型来进行奖励模型不确定性,将汤普森的抽样扩展到场景中,以进行灵活的奖励密度估计。提出的贝叶斯非参数混合物模型汤普森采样依次学习了奖励模型,该模型最能近似于真实但未知的每臂奖励分布,从而实现了成功的遗憾表现。我们基于基于后验分析的新颖的分析得出的,这是一种针对该方法的渐近遗憾。此外,我们从经验上评估了其在多样化和以前难以捉摸的匪徒环境中的性能,例如,在指数级的家族中,奖励不受异常值和不同的每臂奖励分布。我们表明,拟议的贝叶斯非参数汤普森取样优于表现,无论是平均累积的遗憾和遗憾的波动,最先进的替代方案。在存在强盗奖励模型不确定性的情况下,提出的方法很有价值,因为它避免了严格的逐案模型设计选择,但提供了重要的遗憾。
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We investigate a local reparameterizaton technique for greatly reducing the variance of stochastic gradients for variational Bayesian inference (SGVB) of a posterior over model parameters, while retaining parallelizability. This local reparameterization translates uncertainty about global parameters into local noise that is independent across datapoints in the minibatch. Such parameterizations can be trivially parallelized and have variance that is inversely proportional to the minibatch size, generally leading to much faster convergence. Additionally, we explore a connection with dropout: Gaussian dropout objectives correspond to SGVB with local reparameterization, a scale-invariant prior and proportionally fixed posterior variance. Our method allows inference of more flexibly parameterized posteriors; specifically, we propose variational dropout, a generalization of Gaussian dropout where the dropout rates are learned, often leading to better models. The method is demonstrated through several experiments.
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Kullback-Leibler(KL)差异广泛用于贝叶斯神经网络(BNNS)的变异推理。然而,KL差异具有无限性和不对称性等局限性。我们检查了更通用,有限和对称的詹森 - 香农(JS)差异。我们根据几何JS差异为BNN制定新的损失函数,并表明基于KL差异的常规损失函数是其特殊情况。我们以封闭形式的高斯先验评估拟议损失函数的差异部分。对于任何其他一般的先验,都可以使用蒙特卡洛近似值。我们提供了实施这两种情况的算法。我们证明所提出的损失函数提供了一个可以调整的附加参数,以控制正则化程度。我们得出了所提出的损失函数在高斯先验和后代的基于KL差异的损失函数更好的条件。我们证明了基于嘈杂的CIFAR数据集和有偏见的组织病理学数据集的最新基于KL差异的BNN的性能提高。
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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。
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Deep learning tools have gained tremendous attention in applied machine learning. However such tools for regression and classification do not capture model uncertainty. In comparison, Bayesian models offer a mathematically grounded framework to reason about model uncertainty, but usually come with a prohibitive computational cost. In this paper we develop a new theoretical framework casting dropout training in deep neural networks (NNs) as approximate Bayesian inference in deep Gaussian processes. A direct result of this theory gives us tools to model uncertainty with dropout NNsextracting information from existing models that has been thrown away so far. This mitigates the problem of representing uncertainty in deep learning without sacrificing either computational complexity or test accuracy. We perform an extensive study of the properties of dropout's uncertainty. Various network architectures and nonlinearities are assessed on tasks of regression and classification, using MNIST as an example. We show a considerable improvement in predictive log-likelihood and RMSE compared to existing state-of-the-art methods, and finish by using dropout's uncertainty in deep reinforcement learning.
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Large multilayer neural networks trained with backpropagation have recently achieved state-ofthe-art results in a wide range of problems. However, using backprop for neural net learning still has some disadvantages, e.g., having to tune a large number of hyperparameters to the data, lack of calibrated probabilistic predictions, and a tendency to overfit the training data. In principle, the Bayesian approach to learning neural networks does not have these problems. However, existing Bayesian techniques lack scalability to large dataset and network sizes. In this work we present a novel scalable method for learning Bayesian neural networks, called probabilistic backpropagation (PBP). Similar to classical backpropagation, PBP works by computing a forward propagation of probabilities through the network and then doing a backward computation of gradients. A series of experiments on ten real-world datasets show that PBP is significantly faster than other techniques, while offering competitive predictive abilities. Our experiments also show that PBP provides accurate estimates of the posterior variance on the network weights.
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We propose a simultaneous learning and pruning algorithm capable of identifying and eliminating irrelevant structures in a neural network during the early stages of training. Thus, the computational cost of subsequent training iterations, besides that of inference, is considerably reduced. Our method, based on variational inference principles using Gaussian scale mixture priors on neural network weights, learns the variational posterior distribution of Bernoulli random variables multiplying the units/filters similarly to adaptive dropout. Our algorithm, ensures that the Bernoulli parameters practically converge to either 0 or 1, establishing a deterministic final network. We analytically derive a novel hyper-prior distribution over the prior parameters that is crucial for their optimal selection and leads to consistent pruning levels and prediction accuracy regardless of weight initialization or the size of the starting network. We prove the convergence properties of our algorithm establishing theoretical and practical pruning conditions. We evaluate the proposed algorithm on the MNIST and CIFAR-10 data sets and the commonly used fully connected and convolutional LeNet and VGG16 architectures. The simulations show that our method achieves pruning levels on par with state-of the-art methods for structured pruning, while maintaining better test-accuracy and more importantly in a manner robust with respect to network initialization and initial size.
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Variational methods have been previously explored as a tractable approximation to Bayesian inference for neural networks. However the approaches proposed so far have only been applicable to a few simple network architectures. This paper introduces an easy-to-implement stochastic variational method (or equivalently, minimum description length loss function) that can be applied to most neural networks. Along the way it revisits several common regularisers from a variational perspective. It also provides a simple pruning heuristic that can both drastically reduce the number of network weights and lead to improved generalisation. Experimental results are provided for a hierarchical multidimensional recurrent neural network applied to the TIMIT speech corpus.
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我们通过Pac-Bayes概括界的镜头研究冷后效应。我们认为,在非反应环境中,当训练样本的数量相对较小时,应考虑到冷后效应的讨论,即大概贝叶斯推理并不能容易地提供对样本外数据的性能的保证。取而代之的是,通过泛化结合更好地描述了样本外误差。在这种情况下,我们探讨了各种推理与PAC-Bayes目标的ELBO目标之间的联系。我们注意到,虽然Elbo和Pac-Bayes目标相似,但后一个目标自然包含温度参数$ \ lambda $,不限于$ \ lambda = 1 $。对于回归和分类任务,在各向同性拉普拉斯与后部的近似值的情况下,我们展示了这种对温度参数的PAC-bayesian解释如何捕获冷后效应。
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在使用多模式贝叶斯后部分布时,马尔可夫链蒙特卡罗(MCMC)算法难以在模式之间移动,并且默认变分或基于模式的近似推动将低估后不确定性。并且,即使找到最重要的模式,难以评估后部的相对重量。在这里,我们提出了一种使用MCMC,变分或基于模式的模式的并行运行的方法,以便尽可能多地击中多种模式或分离的区域,然后使用贝叶斯堆叠来组合这些用于构建分布的加权平均值的可扩展方法。通过堆叠从多模式后分布的堆叠,最小化交叉验证预测误差的结果,并且代表了比变分推断更好的不确定度,但它不一定是相当于渐近的,以完全贝叶斯推断。我们呈现理论一致性,其中堆叠推断逼近来自未衰退的模型和非混合采样器的真实数据生成过程,预测性能优于完全贝叶斯推断,因此可以被视为祝福而不是模型拼写下的诅咒。我们展示了几个模型家庭的实际实施:潜在的Dirichlet分配,高斯过程回归,分层回归,马蹄素变量选择和神经网络。
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情报依赖于代理商对其不知道的知识。可以根据多个输入的标签的联合预测质量来评估此能力。传统的神经网络缺乏这种能力,并且由于大多数研究都集中在边际预测上,因此这种缺点在很大程度上被忽略了。我们将认知神经网络(ENN)作为模型的界面,代表产生有用的关节预测所需的不确定性。虽然先前的不确定性建模方法(例如贝叶斯神经网络)可以表示为ENN,但这种新界面促进了联合预测和新型体系结构和算法的设计的比较。特别是,我们介绍了Epinet:一种可以补充任何常规神经网络(包括大型模型)的体系结构,并且可以通过适度的增量计算进行培训以估计不确定性。有了Epact,传统的神经网络的表现优于非常大的合奏,包括数百个或更多的颗粒,计算的数量级较低。我们在合成数据,成像网和一些强化学习任务中证明了这种功效。作为这项工作的一部分,我们开放源实验代码。
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Deep neural nets with a large number of parameters are very powerful machine learning systems. However, overfitting is a serious problem in such networks. Large networks are also slow to use, making it difficult to deal with overfitting by combining the predictions of many different large neural nets at test time. Dropout is a technique for addressing this problem. The key idea is to randomly drop units (along with their connections) from the neural network during training. This prevents units from co-adapting too much. During training, dropout samples from an exponential number of different "thinned" networks. At test time, it is easy to approximate the effect of averaging the predictions of all these thinned networks by simply using a single unthinned network that has smaller weights. This significantly reduces overfitting and gives major improvements over other regularization methods. We show that dropout improves the performance of neural networks on supervised learning tasks in vision, speech recognition, document classification and computational biology, obtaining state-of-the-art results on many benchmark data sets.
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在机器学习中,代理需要估计不确定性,以有效地探索和适应并做出有效的决策。不确定性估计的一种常见方法维护了模型的合奏。近年来,已经提出了几种用于培训合奏的方法,并且在这些方法的各种成分的重要性方面占上风。在本文中,我们旨在解决已受到质疑的两种成分的好处 - 先前的功能和引导。我们表明,先前的功能可以显着改善整体代理在输入之间的关节预测,如果信噪比在输入之间有所不同,则引导程序为其他好处提供了额外的好处。我们的主张是通过理论和实验结果证明的。
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PAC-Bayes has recently re-emerged as an effective theory with which one can derive principled learning algorithms with tight performance guarantees. However, applications of PAC-Bayes to bandit problems are relatively rare, which is a great misfortune. Many decision-making problems in healthcare, finance and natural sciences can be modelled as bandit problems. In many of these applications, principled algorithms with strong performance guarantees would be very much appreciated. This survey provides an overview of PAC-Bayes performance bounds for bandit problems and an experimental comparison of these bounds. Our experimental comparison has revealed that available PAC-Bayes upper bounds on the cumulative regret are loose, whereas available PAC-Bayes lower bounds on the expected reward can be surprisingly tight. We found that an offline contextual bandit algorithm that learns a policy by optimising a PAC-Bayes bound was able to learn randomised neural network polices with competitive expected reward and non-vacuous performance guarantees.
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目前,难以获得贝叶斯方法深入学习的好处,这允许明确的知识规范,准确地捕获模型不确定性。我们呈现先前数据拟合网络(PFN)。 PFN利用大规模机器学习技术来近似一组一组后索。 PFN唯一要求工作的要求是能够从先前分配通过监督的学习任务(或函数)来采样。我们的方法将后近似的目标重新定为具有带有值的输入的监督分类问题:它反复从先前绘制任务(或功能),从中绘制一组数据点及其标签,掩盖其中一个标签并学习基于其余数据点的设定值输入对其进行概率预测。呈现来自新的监督学习任务的一组样本作为输入,PFNS在单个前向传播中对任意其他数据点进行概率预测,从而学习到近似贝叶斯推断。我们展示了PFN可以接近完全模仿高斯过程,并且还可以实现高效的贝叶斯推理对难以处理的问题,与当前方法相比,多个设置中有超过200倍的加速。我们在非常多样化的地区获得强烈的结果,如高斯过程回归,贝叶斯神经网络,小型表格数据集的分类,以及少量图像分类,展示了PFN的一般性。代码和培训的PFN在https://github.com/automl/transformerscandobayesianinference发布。
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我们提出了一种新的方法,可以在复杂模型(例如贝叶斯神经网络)中执行近似贝叶斯推断。该方法比马尔可夫链蒙特卡洛更可扩展到大数据,它具有比变异推断更具表现力的模型,并且不依赖于对抗训练(或密度比估计)。我们采用了构建两个模型的最新方法:(1)一个主要模型,负责执行回归或分类; (2)一个辅助,表达的(例如隐式)模型,该模型定义了主模型参数上的近似后验分布。但是,我们根据后验预测分布的蒙特卡洛估计值通过梯度下降来优化后验模型的参数 - 这是我们唯一的近似值(除后模型除外)。只需要指定一个可能性,可以采用各种形式,例如损失功能和合成可能性,从而提供无可能的方法的形式。此外,我们制定了该方法,使后样品可以独立于或有条件地取决于主要模型的输入。后一种方法被证明能够增加主要模型的明显复杂性。我们认为这在诸如替代和基于物理的模型之类的应用中很有用。为了促进贝叶斯范式如何提供不仅仅是不确定性量化的方式,我们证明了:不确定性量化,多模式以及具有最新预测的神经网络体系结构的应用。
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象征性的AI社区越来越多地试图在神经符号结构中接受机器学习,但由于文化障碍,仍在挣扎。为了打破障碍,这份相当有思想的个人备忘录试图解释和纠正统计,机器学习和深入学习的惯例,从局外人的角度进行深入学习。它提供了一个分步协议,用于设计一个机器学习系统,该系统满足符号AI社区认真对待所必需的最低理论保证,即,它讨论“在哪些条件下,我们可以停止担心和接受统计机器学习。 “一些亮点:大多数教科书都是为计划专门研究STAT/ML/DL的人编写的,应该接受术语。该备忘录适用于经验丰富的象征研究人员,他们听到了很多嗡嗡声,但仍然不确定和持怀疑态度。有关STAT/ML/DL的信息目前太分散或嘈杂而无法投资。此备忘录优先考虑紧凑性,并特别注意与象征性范式相互共鸣的概念。我希望这份备忘录能节省时间。它优先考虑一般数学建模,并且不讨论任何特定的函数近似器,例如神经网络(NNS),SVMS,决策树等。它可以对校正开放。将此备忘录视为与博客文章相似的内容,采用有关Arxiv的论文的形式。
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