In this paper we propose a Bayesian method for estimating architectural parameters of neural networks, namely layer size and network depth. We do this by learning concrete distributions over these parameters. Our results show that regular networks with a learnt structure can generalise better on small datasets, while fully stochastic networks can be more robust to parameter initialisation. The proposed method relies on standard neural variational learning and, unlike randomised architecture search, does not require a retraining of the model, thus keeping the computational overhead at minimum.
Jilin University（吉林大学）；Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education（教育部符号计算与知识工程重点实验室）
Bayesian optimization (BO) is an effective method of finding the global optima of black-box functions. Recently BO has been applied to neural architecture search and shows better performance than pure evolutionary strategies. All these methods adopt Gaussian processes (GPs) as surrogate function, with the handcraft similarity metrics as input. In this work, we propose a Bayesian graph neural network as a new surrogate, which can automatically extract features from deep neural architectures, and use such learned features to fit and characterize black-box objectives and their uncertainty. Based …
Deep neural networks (DNN) are versatile parametric models utilised successfully in a diverse number of tasks and domains. However, they have limitations---particularly from their lack of robustness and over-sensitivity to out of distribution samples. Bayesian Neural Networks, due to their formulation under the Bayesian framework, provide a principled approach to building neural networks that address these limitations. This paper describes a study that empirically evaluates and compares Bayesian Neural Networks to their equivalent point estimate Deep Neural Networks to quantify the predictive …
LTS2；EPFL（洛桑联邦理工学院）；IDCOM；University of Edinburgh（爱丁堡大学）
Recently the generalization error of deep neural networks has been analyzed through the PAC-Bayesian framework, for the case of fully connected layers. We adapt this approach to the convolutional setting.
Bayesian neural networks (BNNs) augment deep networks with uncertainty quantification by Bayesian treatment of the network weights. However, such models face the challenge of Bayesian inference in a high-dimensional and usually over-parameterized space. This paper investigates a new line of Bayesian deep learning by performing Bayesian inference on network structure. Instead of building structure from scratch inefficiently, we draw inspirations from neural architecture search to represent the network structure. We then develop an efficient stochastic variational inference approach which unifie…
In this work we perform outlier detection using ensembles of neural networks obtained by variational approximation of the posterior in a Bayesian neural network setting. The variational parameters are obtained by sampling from the true posterior by gradient descent. We show our outlier detection results are comparable to those obtained using other efficient ensembling methods.
Bayesian neural networks perform variational inference over the weights however calculation of the posterior distribution remains a challenge. Our work builds on variational inference techniques for bayesian neural networks using the original Evidence Lower Bound. In this paper, we present a stochastic bayesian neural network in which we maximize Evidence Lower Bound using a new objective function which we name as Stochastic Evidence Lower Bound. We evaluate our network on 5 publicly available UCI datasets using test RMSE and log likelihood as the evaluation metrics. We demonstrate that our wo…
University of Western Australia（西澳大学）；Murdoch University（莫道克大学）；Monash University（莫纳什大学）
Modern deep learning methods constitute incredibly powerful tools to tackle a myriad of challenging problems. However, since deep learning methods operate as black boxes, the uncertainty associated with their predictions is often challenging to quantify. Bayesian statistics offer a formalism to understand and quantify the uncertainty associated with deep neural network predictions. This tutorial provides an overview of the relevant literature and a complete toolset to design, implement, train, use and evaluate Bayesian Neural Networks, i.e. Stochastic Artificial Neural Networks trained using B…
Inference in deep Bayesian neural networks is only fully understood in the infinite-width limit, where the posterior flexibility afforded by increased depth washes out and the posterior predictive collapses to a shallow Gaussian process. Here, we interpret finite deep linear Bayesian neural networks as data-dependent scale mixtures of Gaussian process predictors across output channels. We leverage this observation to study representation learning in these networks, allowing us to connect limiting results obtained in previous studies within a unified framework. In total, these results advance o…
Bayesian interpretations of neural network have a long history, dating back to early work in the 1990's and have recently regained attention because of their desirable properties like uncertainty estimation, model robustness and regularisation. We want to discuss here the application of Bayesian models to knowledge sharing between neural networks. Knowledge sharing comes in different facets, such as transfer learning, model distillation and shared embeddings. All of these tasks have in common that learned "features" ought to be shared across different networks. Theoretically rooted in the conc…
Université Laval（拉瓦尔大学）；Inria（法国国家信息与自动化研究所）；University College London（伦敦大学学院）
We present a comprehensive study of multilayer neural networks with binary activation, relying on the PAC-Bayesian theory. Our contributions are twofold: (i) we develop an end-to-end framework to train a binary activated deep neural network, (ii) we provide nonvacuous PAC-Bayesian generalization bounds for binary activated deep neural networks. Our results are obtained by minimizing the expected loss of an architecture-dependent aggregation of binary activated deep neural networks. Our analysis inherently overcomes the fact that binary activation function is non-differentiable. The performance…
Kavli Institute for Cosmology（卡弗里宇宙学研究所）；University of Cambridge（剑桥大学）；University of Sussex（萨塞克斯大学）
The true posterior distribution of a Bayesian neural network is massively multimodal. Whilst most of these modes are functionally equivalent, we demonstrate that there remains a level of real multimodality that manifests in even the simplest neural network setups. It is only by fully marginalising over all posterior modes, using appropriate Bayesian sampling tools, that we can capture the split personalities of the network. The ability of a network trained in this manner to reason between multiple candidate solutions dramatically improves the generalisability of the model, a feature we contend…
University of Amsterdam（阿姆斯特丹大学）；TNO Intelligent Imaging（荷兰应用科学研究组织智能成像）；Canadian Institute For Advanced Research (CIFAR)（加拿大高级研究院）
We reinterpret multiplicative noise in neural networks as auxiliary random variables that augment the approximate posterior in a variational setting for Bayesian neural networks. We show that through this interpretation it is both efficient and straightforward to improve the approximation by employing normalizing flows while still allowing for local reparametrizations and a tractable lower bound. In experiments we show that with this new approximation we can significantly improve upon classical mean field for Bayesian neural networks on both predictive accuracy as well as predictive uncertaint…
Aalto University（阿尔托大学）；University of Manchester（曼彻斯特大学）
We introduce implicit Bayesian neural networks, a simple and scalable approach for uncertainty representation in deep learning. Standard Bayesian approach to deep learning requires the impractical inference of the posterior distribution over millions of parameters. Instead, we propose to induce a distribution that captures the uncertainty over neural networks by augmenting each layer's inputs with latent variables. We present appropriate input distributions and demonstrate state-of-the-art performance in terms of calibration, robustness and uncertainty characterisation over large-scale, multi-…
University of Toronto（多伦多大学）；Stanford Unviersity（斯坦福大学）
We perform scalable approximate inference in continuous-depth Bayesian neural networks. In this model class, uncertainty about separate weights in each layer gives hidden units that follow a stochastic differential equation. We demonstrate gradient-based stochastic variational inference in this infinite-parameter setting, producing arbitrarily-flexible approximate posteriors. We also derive a novel gradient estimator that approaches zero variance as the approximate posterior over weights approaches the true posterior. This approach brings continuous-depth Bayesian neural nets to a competitive …
University of California, Santa Barbara（加州大学圣巴巴拉分校）
Tensor decomposition is an effective approach to compress over-parameterized neural networks and to enable their deployment on resource-constrained hardware platforms. However, directly applying tensor compression in the training process is a challenging task due to the difficulty of choosing a proper tensor rank. In order to achieve this goal, this paper proposes a Bayesian tensorized neural network. Our Bayesian method performs automatic model compression via an adaptive tensor rank determination. We also present approaches for posterior density calculation and maximum a posteriori (MAP) est…
The connection between Bayesian neural networks and Gaussian processes gained a lot of attention in the last few years. Hidden units are proven to follow a Gaussian process limit when the layer width tends to infinity. Recent work has suggested that finite Bayesian neural networks may outperform their infinite counterparts because they adapt their internal representations flexibly. To establish solid ground for future research on finite-width neural networks, our goal is to study the prior induced on hidden units. Our main result is an accurate description of hidden units tails which shows tha…
University of Stuttgart（斯图加特大学）；Fraunhofer Institute for Manufacturing Engineering and Automation IPA（弗劳恩霍夫制造工程与自动化研究所）
Artificial neural networks (NNs) have become the de facto standard in machine learning. They allow learning highly nonlinear transformations in a plethora of applications. However, NNs usually only provide point estimates without systematically quantifying corresponding uncertainties. In this paper a novel approach towards fully Bayesian NNs is proposed, where training and predictions of a perceptron are performed within the Bayesian inference framework in closed-form. The weights and the predictions of the perceptron are considered Gaussian random variables. Analytical expressions for predict…
Georg-August University of Göttingen（哥廷根乔治-奥古斯特大学）；University of Tübingen（图宾根大学）
A recent paper by Liu et al. combines the topics of adversarial training and Bayesian Neural Networks (BNN) and suggests that adversarially trained BNNs are more robust against adversarial attacks than their non-Bayesian counterparts. Here, I analyze the proposed defense and suggest that one needs to adjust the adversarial attack to incorporate the stochastic nature of a Bayesian network to perform an accurate evaluation of its robustness. Using this new type of attack I show that there appears to be no strong evidence for higher robustness of the adversarially trained BNNs.
The last decade witnessed a growing interest in Bayesian learning. Yet, the technicality of the topic and the multitude of ingredients involved therein, besides the complexity of turning theory into practical implementations, limit the use of the Bayesian learning paradigm, preventing its widespread adoption across different fields and applications. This self-contained survey engages and introduces readers to the principles and algorithms of Bayesian Learning for Neural Networks. It provides an introduction to the topic from an accessible, practical-algorithmic perspective. Upon providing a ge…
Taiyuan University of Technology（太原理工大学）；Beihang University（北京航空航天大学）
We present a new method to approximate posterior probabilities of Bayesian Network using Deep Neural Network. Experiment results on several public Bayesian Network datasets shows that Deep Neural Network is capable of learning joint probability distri- bution of Bayesian Network by learning from a few observation and posterior probability distribution pairs with high accuracy. Compared with traditional approximate method likelihood weighting sampling algorithm, our method is much faster and gains higher accuracy in medium sized Bayesian Network. Another advantage of our method is that our meth…
We extend the empirical results from the structural equation model (SEM) published in the paper Assortment Planning for Retail Buying, Retail Store Operations, and Firm Performance [1] by implementing the directed acyclic graph as a causal Bayesian neural network. Neural network convergence is shown to improve with the removal of the node with the weakest SEM path when variational inference is provided by perturbing weights with Flipout layers, while results from perturbing weights at the output with the Vadam optimizer are inconclusive.
Probabilistic vehicle trajectory prediction is essential for robust safety of autonomous driving. Current methods for long-term trajectory prediction cannot guarantee the physical feasibility of predicted distribution. Moreover, their models cannot adapt to the driving policy of the predicted target human driver. In this work, we propose to overcome these two shortcomings by a Bayesian recurrent neural network model consisting of Bayesian-neural-network-based policy model and known physical model of the scenario. Bayesian neural network can ensemble complicated output distribution, enabling ri…
We introduce Graph Neural Processes (GNP), inspired by the recent work in conditional and latent neural processes. A Graph Neural Process is defined as a Conditional Neural Process that operates on arbitrary graph data. It takes features of sparsely observed context points as input, and outputs a distribution over target points. We demonstrate graph neural processes in edge imputation and discuss benefits and drawbacks of the method for other application areas. One major benefit of GNPs is the ability to quantify uncertainty in deep learning on graph structures. An additional benefit of this m…
Current neural architecture search (NAS) strategies focus only on finding a single, good, architecture. They offer little insight into why a specific network is performing well, or how we should modify the architecture if we want further improvements. We propose a Bayesian optimisation (BO) approach for NAS that combines the Weisfeiler-Lehman graph kernel with a Gaussian process surrogate. Our method optimises the architecture in a highly data-efficient manner: it is capable of capturing the topological structures of the architectures and is scalable to large graphs, thus making the high-dimen…
ETH Zürich（苏黎世联邦理工学院）；University of Amsterdam（阿姆斯特丹大学）；Imperial College London（帝国理工学院）
We propose a novel Bayesian neural network architecture that can learn invariances from data alone by inferring a posterior distribution over different weight-sharing schemes. We show that our model outperforms other non-invariant architectures, when trained on datasets that contain specific invariances. The same holds true when no data augmentation is performed.
Delft University of Technology（代尔夫特理工大学）；University College London（伦敦大学学院）
One-Shot Neural Architecture Search (NAS) is a promising method to significantly reduce search time without any separate training. It can be treated as a Network Compression problem on the architecture parameters from an over-parameterized network. However, there are two issues associated with most one-shot NAS methods. First, dependencies between a node and its predecessors and successors are often disregarded which result in improper treatment over zero operations. Second, architecture parameters pruning based on their magnitude is questionable. In this paper, we employ the classic Bayesian …
Bayesian Numerical Integration with Neural Networks
Bosch Center for Artificial Intelligence（博世人工智能中心）；University of Tübingen（蒂宾根大学）；MPI for Intelligent Systems（马克斯·普朗克智能系统研究所）；University College London（伦敦大学学院）；The Alan Turing Institute（艾伦·图灵研究所）
Bosch Center for Artificial Intelligence（博世人工智能中心）
Neural Ordinary Differential Equations (N-ODEs) are a powerful building block for learning systems, which extend residual networks to a continuous-time dynamical system. We propose a Bayesian version of N-ODEs that enables well-calibrated quantification of prediction uncertainty, while maintaining the expressive power of their deterministic counterpart. We assign Bayesian Neural Nets (BNNs) to both the drift and the diffusion terms of a Stochastic Differential Equation (SDE) that models the flow of the activation map in time. We infer the posterior on the BNN weights using a straightforward ad…
Two main obstacles preventing the widespread adoption of variational Bayesian neural networks are the high parameter overhead that makes them infeasible on large networks, and the difficulty of implementation, which can be thought of as "programming overhead." MC dropout [Gal and Ghahramani, 2016] is popular because it sidesteps these obstacles. Nevertheless, dropout is often harmful to model performance when used in networks with batch normalization layers [Li et al., 2018], which are an indispensable part of modern neural networks. We construct a general variational family for ensemble-based…
Bayesian neural networks provide a direct and natural way to extend standard deep neural networks to support probabilistic deep learning through the use of probabilistic layers that, traditionally, encode weight (and bias) uncertainty. In particular, hybrid Bayesian neural networks utilize standard deterministic layers together with few probabilistic layers judicially positioned in the networks for uncertainty estimation. A major aspect and benefit of Bayesian inference is that priors, in principle, provide the means to encode prior knowledge for use in inference and prediction. However, it is…
IBM research（IBM研究院）；MIT-IBM Watson AI Lab（麻省理工学院-IBM沃森人工智能实验室）；Harvard University（哈佛大学）
Bayesian Neural Networks (BNNs) have recently received increasing attention for their ability to provide well-calibrated posterior uncertainties. However, model selection---even choosing the number of nodes---remains an open question. Recent work has proposed the use of a horseshoe prior over node pre-activations of a Bayesian neural network, which effectively turns off nodes that do not help explain the data. In this work, we propose several modeling and inference advances that consistently improve the compactness of the model learned while maintaining predictive performance, especially in sm…
Univ. Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；Inria（法国国家信息与自动化研究所）；CNRS（法国国家科学研究中心）；Grenoble INP（格勒诺布尔国立高等物理、数学与信息学院）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Andalusian Research Institute in Data Science and Computational Intelligence (DaSCI)（安达卢西亚数据科学与计算智能研究所）；University of Granada（格拉纳达大学）
We investigate deep Bayesian neural networks with Gaussian weight priors and a class of ReLU-like nonlinearities. Bayesian neural networks with Gaussian priors are well known to induce an L2, "weight decay", regularization. Our results characterize a more intricate regularization effect at the level of the unit activations. Our main result establishes that the induced prior distribution on the units before and after activation becomes increasingly heavy-tailed with the depth of the layer. We show that first layer units are Gaussian, second layer units are sub-exponential, and units in deeper l…
We formulate the problem of neural network optimization as Bayesian filtering, where the observations are the backpropagated gradients. While neural network optimization has previously been studied using natural gradient methods which are closely related to Bayesian inference, they were unable to recover standard optimizers such as Adam and RMSprop with a root-mean-square gradient normalizer, instead getting a mean-square normalizer. To recover the root-mean-square normalizer, we find it necessary to account for the temporal dynamics of all the other parameters as they are geing optimized. The…
University of Tübingen（图宾根大学）；MPI for Intelligent Systems, Tübingen（图宾根智能系统研究所）
Despite their compelling theoretical properties, Bayesian neural networks (BNNs) tend to perform worse than frequentist methods in classification-based uncertainty quantification (UQ) tasks such as out-of-distribution (OOD) detection. In this paper, based on empirical findings in prior works, we hypothesize that this issue is because even recent Bayesian methods have never considered OOD data in their training processes, even though this "OOD training" technique is an integral part of state-of-the-art frequentist UQ methods. To validate this, we treat OOD data as a first-class citizen in BNN t…
Harvard University（哈佛大学）；IBM T.J. Watson Research Center（IBM托马斯·J·沃森研究中心）
Bayesian Neural Networks (BNNs) place priors over the parameters in a neural network. Inference in BNNs, however, is difficult; all inference methods for BNNs are approximate. In this work, we empirically compare the quality of predictive uncertainty estimates for 10 common inference methods on both regression and classification tasks. Our experiments demonstrate that commonly used metrics (e.g. test log-likelihood) can be misleading. Our experiments also indicate that inference innovations designed to capture structure in the posterior do not necessarily produce high quality posterior approxi…
Deep Bayesian neural network has aroused a great attention in recent years since it combines the benefits of deep neural network and probability theory. Because of this, the network can make predictions and quantify the uncertainty of the predictions at the same time, which is important in many life-threatening areas. However, most of the recent researches are mainly focusing on making the Bayesian neural network easier to train, and proposing methods to estimate the uncertainty. I notice there are very few works that properly discuss the ways to measure the performance of the Bayesian neural …
Ensembling can improve the performance of Neural Networks, but existing approaches struggle when the architecture likelihood surface has dispersed, narrow peaks. Furthermore, existing methods construct equally weighted ensembles, and this is likely to be vulnerable to the failure modes of the weaker architectures. By viewing ensembling as approximately marginalising over architectures we construct ensembles using the tools of Bayesian Quadrature -- tools which are well suited to the exploration of likelihood surfaces with dispersed, narrow peaks. Additionally, the resulting ensembles consist o…
Ensembles of neural networks (NNs) have long been used to estimate predictive uncertainty; a small number of NNs are trained from different initialisations and sometimes on differing versions of the dataset. The variance of the ensemble's predictions is interpreted as its epistemic uncertainty. The appeal of ensembling stems from being a collection of regular NNs - this makes them both scalable and easily implementable. They have achieved strong empirical results in recent years, often presented as a practical alternative to more costly Bayesian NNs (BNNs). The departure from Bayesian methodol…
Harvard T.H. Chan School of Public Health（哈佛大学陈曾熙公共卫生学院）；Harvard University（哈佛大学）
Variational inference enables approximate posterior inference of the highly over-parameterized neural networks that are popular in modern machine learning. Unfortunately, such posteriors are known to exhibit various pathological behaviors. We prove that as the number of hidden units in a single-layer Bayesian neural network tends to infinity, the function-space posterior mean under mean-field variational inference actually converges to zero, completely ignoring the data. This is in contrast to the true posterior, which converges to a Gaussian process. Our work provides insight into the over-re…
While Bayesian neural networks have many appealing characteristics, current priors do not easily allow users to specify basic properties such as expected lengthscale or amplitude variance. In this work, we introduce Poisson Process Radial Basis Function Networks, a novel prior that is able to encode amplitude stationarity and input-dependent lengthscale. We prove that our novel formulation allows for a decoupled specification of these properties, and that the estimated regression function is consistent as the number of observations tends to infinity. We demonstrate its behavior on synthetic an…
We introduce TyXe, a Bayesian neural network library built on top of Pytorch and Pyro. Our leading design principle is to cleanly separate architecture, prior, inference and likelihood specification, allowing for a flexible workflow where users can quickly iterate over combinations of these components. In contrast to existing packages TyXe does not implement any layer classes, and instead relies on architectures defined in generic Pytorch code. TyXe then provides modular choices for canonical priors, variational guides, inference techniques, and layer selections for a Bayesian treatment of the…
In this paper, we propose an analytical method for performing tractable approximate Gaussian inference (TAGI) in Bayesian neural networks. The method enables the analytical Gaussian inference of the posterior mean vector and diagonal covariance matrix for weights and biases. The method proposed has a computational complexity of $\mathcal{O}(n)$ with respect to the number of parameters $n$, and the tests performed on regression and classification benchmarks confirm that, for a same network architecture, it matches the performance of existing methods relying on gradient backpropagation.
ETH Zürich（苏黎世联邦理工学院）；University of Cambridge（剑桥大学）；Imperial College London（帝国理工学院）；University of Bristol（布里斯托大学）
Bayesian neural networks have shown great promise in many applications where calibrated uncertainty estimates are crucial and can often also lead to a higher predictive performance. However, it remains challenging to choose a good prior distribution over their weights. While isotropic Gaussian priors are often chosen in practice due to their simplicity, they do not reflect our true prior beliefs well and can lead to suboptimal performance. Our new library, BNNpriors, enables state-of-the-art Markov Chain Monte Carlo inference on Bayesian neural networks with a wide range of predefined priors, …
University of Maryland, College Park（马里兰大学帕克分校）；Amazon Web Services（亚马逊云科技）；Amazon.com, Inc.（亚马逊公司）
Bayesian learning of model parameters in neural networks is important in scenarios where estimates with well-calibrated uncertainty are important. In this paper, we propose Bayesian quantized networks (BQNs), quantized neural networks (QNNs) for which we learn a posterior distribution over their discrete parameters. We provide a set of efficient algorithms for learning and prediction in BQNs without the need to sample from their parameters or activations, which not only allows for differentiable learning in QNNs, but also reduces the variance in gradients. We evaluate BQNs on MNIST, Fashion-MN…
Cambridge University（剑桥大学）；University of Potsdam（波茨坦大学）；University Of Bath（巴斯大学）
In this work we explore a new framework for approximate Bayesian inference in large datasets based on stochastic control (i.e. Schrödinger bridges). We advocate stochastic control as a finite time and low variance alternative to popular steady-state methods such as stochastic gradient Langevin dynamics (SGLD). Furthermore, we discuss and adapt the existing theoretical guarantees of this framework and establish connections to already existing VI routines in SDE-based models.
University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）；IBM Research（IBM研究院）
Bayesian decision theory provides an elegant framework for acting optimally under uncertainty when tractable posterior distributions are available. Modern Bayesian models, however, typically involve intractable posteriors that are approximated with, potentially crude, surrogates. This difficulty has engendered loss-calibrated techniques that aim to learn posterior approximations that favor high-utility decisions. In this paper, focusing on Bayesian neural networks, we develop methods for correcting approximate posterior predictive distributions encouraging them to prefer high-utility decisions…
University of Warsaw（华沙大学）；Polish National Institute for Machine Learning（波兰国家机器学习研究所）；Adam Mickiewicz University（亚当·密茨凯维奇大学）；Nomagic
One of the most popular estimation methods in Bayesian neural networks (BNN) is mean-field variational inference (MFVI). In this work, we show that neural networks with ReLU activation function induce posteriors, that are hard to fit with MFVI. We provide a theoretical justification for this phenomenon, study it empirically, and report the results of a series of experiments to investigate the effect of activation function on the calibration of BNNs. We find that using Leaky ReLU activations leads to more Gaussian-like weight posteriors and achieves a lower expected calibration error (ECE) than…
University of Amsterdam（阿姆斯特丹大学）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
We propose a new variational family for Bayesian neural networks. We decompose the variational posterior into two components, where the radial component captures the strength of each neuron in terms of its magnitude; while the directional component captures the statistical dependencies among the weight parameters. The dependencies learned via the directional density provide better modeling performance compared to the widely-used Gaussian mean-field-type variational family. In addition, the strength of input and output neurons learned via the radial density provides a structured way to compress…
University of Toronto（多伦多大学）；Vector Institute（向量研究所）；Tsinghua University（清华大学）
Variational Bayesian neural networks (BNNs) perform variational inference over weights, but it is difficult to specify meaningful priors and approximate posteriors in a high-dimensional weight space. We introduce functional variational Bayesian neural networks (fBNNs), which maximize an Evidence Lower BOund (ELBO) defined directly on stochastic processes, i.e. distributions over functions. We prove that the KL divergence between stochastic processes equals the supremum of marginal KL divergences over all finite sets of inputs. Based on this, we introduce a practical training objective which ap…
IBM Research（IBM研究院）；MIT-IBM Watson AI Lab（麻省理工学院-IBM沃森人工智能实验室）；Center for Computational Health（计算健康中心）
In federated learning problems, data is scattered across different servers and exchanging or pooling it is often impractical or prohibited. We develop a Bayesian nonparametric framework for federated learning with neural networks. Each data server is assumed to provide local neural network weights, which are modeled through our framework. We then develop an inference approach that allows us to synthesize a more expressive global network without additional supervision, data pooling and with as few as a single communication round. We then demonstrate the efficacy of our approach on federated lea…
We propose Radial Bayesian Neural Networks (BNNs): a variational approximate posterior for BNNs which scales well to large models while maintaining a distribution over weight-space with full support. Other scalable Bayesian deep learning methods, like MC dropout or deep ensembles, have discrete support-they assign zero probability to almost all of the weight-space. Unlike these discrete support methods, Radial BNNs' full support makes them suitable for use as a prior for sequential inference. In addition, they solve the conceptual challenges with the a priori implausibility of weight distribut…
Imperial College London（帝国理工学院）；University of Bristol（布里斯托大学）；University of Cambridge（剑桥大学）；ETH Zürich（苏黎世联邦理工学院）
Bayesian neural networks that incorporate data augmentation implicitly use a ``randomly perturbed log-likelihood [which] does not have a clean interpretation as a valid likelihood function'' (Izmailov et al. 2021). Here, we provide several approaches to developing principled Bayesian neural networks incorporating data augmentation. We introduce a ``finite orbit'' setting which allows likelihoods to be computed exactly, and give tight multi-sample bounds in the more usual ``full orbit'' setting. These models cast light on the origin of the cold posterior effect. In particular, we find that the …
Direct Loss Minimization (DLM) has been proposed as a pseudo-Bayesian method motivated as regularized loss minimization. Compared to variational inference, it replaces the loss term in the evidence lower bound (ELBO) with the predictive log loss, which is the same loss function used in evaluation. A number of theoretical and empirical results in prior work suggest that DLM can significantly improve over ELBO optimization for some models. However, as we point out in this paper, this is not the case for Bayesian neural networks (BNNs). The paper explores the practical performance of DLM for BNN,…
Comparing Bayesian neural networks (BNNs) with different widths is challenging because, as the width increases, multiple model properties change simultaneously, and, inference in the finite-width case is intractable. In this work, we empirically compare finite- and infinite-width BNNs, and provide quantitative and qualitative explanations for their performance difference. We find that when the model is mis-specified, increasing width can hurt BNN performance. In these cases, we provide evidence that finite-width BNNs generalize better partially due to the properties of their frequency spectrum…
