Variational Bayes (VB) has been used to facilitate the calculation of the posterior distribution in the context of Bayesian inference of the parameters of nonlinear models from data. Previously an analytical formulation of VB has been derived for nonlinear model inference on data with additive gaussian noise as an alternative to nonlinear least squares. Here a stochastic solution is derived that avoids some of the approximations required of the analytical formulation, offering a solution that can be more flexibly deployed for nonlinear model inference problems. The stochastic VB solution was used for inference on a biexponential toy case and the algorithmic parameter space explored, before being deployed on real data from a magnetic resonance imaging study of perfusion. The new method was found to achieve comparable parameter recovery to the analytic solution and be competitive in terms of computational speed despite being reliant on sampling.
BayesPy is an open-source Python software package for performing variational Bayesian inference. It is based on the variational message passing framework and supports conjugate exponential family models. By removing the tedious task of implementing the variational Bayesian update equations, the user can construct models faster and in a less error-prone way. Simple syntax, flexible model construction and efficient inference make BayesPy suitable for both average and expert Bayesian users. It also supports some advanced methods such as stochastic and collapsed variational inference.
Collected data, which is used for analysis or prediction tasks, often have a hierarchical structure, for example, data from various people performing the same task. Modeling the data's structure can improve the reliability of the derived results and prediction performance of newly unobserved data. Bayesian modeling provides a tool-kit for designing hierarchical models. However, Markov Chain Monte Carlo methods which are commonly used for parameter estimation are computationally expensive. This often renders its use for many applications not applicable. However, variational Bayesian methods all…
We propose organisation conditions that yield a method for training SOM with adaptative neighborhood radius in a variational Bayesian framework. This method is validated on a non-stationary setting and compared in an high-dimensional setting with an other adaptative method.
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.
In this paper, a scale mixture of Normal distributions model is developed for classification and clustering of data having outliers and missing values. The classification method, based on a mixture model, focuses on the introduction of latent variables that gives us the possibility to handle sensitivity of model to outliers and to allow a less restrictive modelling of missing data. Inference is processed through a Variational Bayesian Approximation and a Bayesian treatment is adopted for model learning, supervised classification and clustering.
Given overlapping subsets of a set of taxa (e.g. species), and posterior distributions on phylogenetic tree topologies for each of these taxon sets, how can we infer a posterior distribution on phylogenetic tree topologies for the entire taxon set? Although the equivalent problem for in the non-Bayesian case has attracted substantial research, the Bayesian case has not attracted the attention it deserves. In this paper we develop a variational Bayes approach to this problem and demonstrate its effectiveness.
The motivations for using variational inference (VI) in neural networks differ significantly from those in latent variable models. This has a counter-intuitive consequence; more expressive variational approximations can provide significantly worse predictions as compared to those with less expressive families. In this work we make two contributions. First, we identify a cause of this performance gap, variational over-pruning. Second, we introduce a theoretically grounded explanation for this phenomenon. Our perspective sheds light on several related published results and provides intuition int…
In this paper, we study porous media flows in heterogeneous stochastic media. We propose an efficient forward simulation technique that is tailored for variational Bayesian inversion. As a starting point, the proposed forward simulation technique decomposes the solution into the sum of separable functions (with respect to randomness and the space), where each term is calculated based on a variational approach. This is similar to Proper Generalized Decomposition (PGD). Next, we apply a multiscale technique to solve for each term and, further, decompose the random function into 1D fields. As a r…
Variational approaches to approximate Bayesian inference provide very efficient means of performing parameter estimation and model selection. Among these, so-called variational-Laplace or VL schemes rely on Gaussian approximations to posterior densities on model parameters. In this note, we review the main variants of VL approaches, that follow from considering nonlinear models of continuous and/or categorical data. En passant, we also derive a few novel theoretical results that complete the portfolio of existing analyses of variational Bayesian approaches, including investigations of their as…
The classical approach to inverse problems is based on the optimization of a misfit function. Despite its computational appeal, such an approach suffers from many shortcomings, e.g., non-uniqueness of solutions, modeling prior knowledge, etc. The Bayesian formalism to inverse problems avoids most of the difficulties encountered by the optimization approach, albeit at an increased computational cost. In this work, we use information theoretic arguments to cast the Bayesian inference problem in terms of an optimization problem. The resulting scheme combines the theoretical soundness of fully Bay…
A Variational Approach to Bayesian Phylogenetic Inference
Peking University（北京大学）；Howard Hughes Medical Institute（霍华德·休斯医学研究所）；Fred Hutchinson Cancer Research Center（弗雷德·哈钦森癌症研究中心）；University of Washington（华盛顿大学）
University of Sussex（萨塞克斯大学）；University of Bristol（布里斯托尔大学）
We develop variational Laplace for Bayesian neural networks (BNNs) which exploits a local approximation of the curvature of the likelihood to estimate the ELBO without the need for stochastic sampling of the neural-network weights. The Variational Laplace objective is simple to evaluate, as it is (in essence) the log-likelihood, plus weight-decay, plus a squared-gradient regularizer. Variational Laplace gave better test performance and expected calibration errors than maximum a-posteriori inference and standard sampling-based variational inference, despite using the same variational approximat…
We develop variational Laplace for Bayesian neural networks (BNNs) which exploits a local approximation of the curvature of the likelihood to estimate the ELBO without the need for stochastic sampling of the neural-network weights. The Variational Laplace objective is simple to evaluate, as it is (in essence) the log-likelihood, plus weight-decay, plus a squared-gradient regularizer. Variational Laplace gave better test performance and expected calibration errors than maximum a-posteriori inference and standard sampling-based variational inference, despite using the same variational approximat…
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…
In this note we consider setups in which variational objectives for Bayesian neural networks can be computed in closed form. In particular we focus on single-layer networks in which the activation function is piecewise polynomial (e.g. ReLU). In this case we show that for a Normal likelihood and structured Normal variational distributions one can compute a variational lower bound in closed form. In addition we compute the predictive mean and variance in closed form. Finally, we also show how to compute approximate lower bounds for other likelihoods (e.g. softmax classification). In experiments…
VinAI Research（VinAI研究院）；University of Texas, Austin（德克萨斯大学奥斯汀分校）；Hanoi University of Science and Technology（河内科技大学）
Approximate inference in Bayesian deep networks exhibits a dilemma of how to yield high fidelity posterior approximations while maintaining computational efficiency and scalability. We tackle this challenge by introducing a novel variational structured approximation inspired by the Bayesian interpretation of Dropout regularization. Concretely, we focus on the inflexibility of the factorized structure in Dropout posterior and then propose an improved method called Variational Structured Dropout (VSD). VSD employs an orthogonal transformation to learn a structured representation on the variation…
Rice University（莱斯大学）；Northwestern University（西北大学）；University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）；OpenStax
We propose VarFA, a variational inference factor analysis framework that extends existing factor analysis models for educational data mining to efficiently output uncertainty estimation in the model's estimated factors. Such uncertainty information is useful, for example, for an adaptive testing scenario, where additional tests can be administered if the model is not quite certain about a students' skill level estimation. Traditional Bayesian inference methods that produce such uncertainty information are computationally expensive and do not scale to large data sets. VarFA utilizes variational…
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…
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…
Complex network reconstruction is a hot topic in many fields. Currently, the most popular data-driven reconstruction framework is based on lasso. However, it is found that, in the presence of noise, lasso loses efficiency for weighted networks. This paper builds a new framework to cope with this problem. The key idea is to employ a series of linear regression problems to model the relationship between network nodes, and then to use an efficient variational Bayesian algorithm to infer the unknown coefficients. The numerical experiments conducted on both synthetic and real data demonstrate that …
University of Electronic Science and Technology of China（电子科技大学）；China Academy of Engineering Physics（中国工程物理研究院）
In this paper, we consider the problem of low-rank phase retrieval whose objective is to estimate a complex low-rank matrix from magnitude-only measurements. We propose a hierarchical prior model for low-rank phase retrieval, in which a Gaussian-Wishart hierarchical prior is placed on the underlying low-rank matrix to promote the low-rankness of the matrix. Based on the proposed hierarchical model, a variational expectation-maximization (EM) algorithm is developed. The proposed method is less sensitive to the choice of the initialization point and works well with random initialization. Simulat…
We study the properties of variational Bayes approximations for exponential family models with missing values. It is shown that the iterative algorithm for obtaining the variational Bayesian estimator converges locally to the true value with probability 1 as the sample size becomes inde nitely large. Moreover, the variational posterior distribution is proved to be asymptotically normal.
Variational Bayesian phylogenetic inference (VBPI) provides a promising general variational framework for efficient estimation of phylogenetic posteriors. However, the current diagonal Lognormal branch length approximation would significantly restrict the quality of the approximating distributions. In this paper, we propose a new type of VBPI, VBPI-NF, as a first step to empower phylogenetic posterior estimation with deep learning techniques. By handling the non-Euclidean branch length space of phylogenetic models with carefully designed permutation equivariant transformations, VBPI-NF uses no…
Bayesian Non-negative Matrix Factorization (NMF) is a promising approach for understanding uncertainty and structure in matrix data. However, a large volume of applied work optimizes traditional non-Bayesian NMF objectives that fail to provide a principled understanding of the non-identifiability inherent in NMF-- an issue ideally addressed by a Bayesian approach. Despite their suitability, current Bayesian NMF approaches have failed to gain popularity in an applied setting; they sacrifice flexibility in modeling for tractable computation, tend to get stuck in local modes, and require many tho…
This paper introduces Distributed Stein Variational Gradient Descent (DSVGD), a non-parametric generalized Bayesian inference framework for federated learning. DSVGD maintains a number of non-random and interacting particles at a central server to represent the current iterate of the model global posterior. The particles are iteratively downloaded and updated by one of the agents with the end goal of minimizing the global free energy. By varying the number of particles, DSVGD enables a flexible trade-off between per-iteration communication load and number of communication rounds. DSVGD is show…
A brief comment on A variational Bayesian approach for inverse problems with skew-t error distributions (Guha et al., Journal of Computational Physics 301 (2015) 377-393) is given in this letter.
National University of Singapore（新加坡国立大学）；MIT-IBM Watson AI Lab（麻省理工学院-IBM沃森人工智能实验室）；MIT（麻省理工学院）
This paper presents a novel variational inference framework for deriving a family of Bayesian sparse Gaussian process regression (SGPR) models whose approximations are variationally optimal with respect to the full-rank GPR model enriched with various corresponding correlation structures of the observation noises. Our variational Bayesian SGPR (VBSGPR) models jointly treat both the distributions of the inducing variables and hyperparameters as variational parameters, which enables the decomposability of the variational lower bound that in turn can be exploited for stochastic optimization. Such…
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…
A mean field variational Bayes approach to support vector machines (SVMs) using the latent variable representation on Polson & Scott (2012) is presented. This representation allows circumvention of many of the shortcomings associated with classical SVMs including automatic penalty parameter selection, the ability to handle dependent samples, missing data and variable selection. We demonstrate on simulated and real datasets that our approach is easily extendable to non-standard situations and outperforms the classical SVM approach whilst remaining computationally efficient.
School of Mathematics and Statistics（数学与统计学院）；University of Melbourne（墨尔本大学）
In this work, we advocate for the importance of singular learning theory (SLT) as it pertains to the theory and practice of variational inference in Bayesian neural networks (BNNs). To begin, using SLT, we lay to rest some of the confusion surrounding discrepancies between downstream predictive performance measured via e.g., the test log predictive density, and the variational objective. Next, we use the SLT-corrected asymptotic form for singular posterior distributions to inform the design of the variational family itself. Specifically, we build upon the idealized variational family introduce…
NTT DATA Mathematical Systems Inc.（NTT数据数学系统公司）；Tokyo Institute of Technology（东京工业大学）
Non-negative matrix factorization (NMF) is a knowledge discovery method that is used in many fields. Variational inference and Gibbs sampling methods for it are also wellknown. However, the variational approximation error has not been clarified yet, because NMF is not statistically regular and the prior distribution used in variational Bayesian NMF (VBNMF) has zero or divergence points. In this paper, using algebraic geometrical methods, we theoretically analyze the difference in negative log evidence (a.k.a. free energy) between VBNMF and Bayesian NMF, i.e., the Kullback-Leibler divergence be…
We develop an optimization algorithm suitable for Bayesian learning in complex models. Our approach relies on natural gradient updates within a general black-box framework for efficient training with limited model-specific derivations. It applies within the class of exponential-family variational posterior distributions, for which we extensively discuss the Gaussian case for which the updates have a rather simple form. Our Quasi Black-box Variational Inference (QBVI) framework is readily applicable to a wide class of Bayesian inference problems and is of simple implementation as the updates of…
We show how to use a variational approximation to the logistic function to perform approximate inference in Bayesian networks containing discrete nodes with continuous parents. Essentially, we convert the logistic function to a Gaussian, which facilitates exact inference, and then iteratively adjust the variational parameters to improve the quality of the approximation. We demonstrate experimentally that this approximation is faster and potentially more accurate than sampling. We also introduce a simple new technique for handling evidence, which allows us to handle arbitrary distributions on o…
Radboud University（拉德堡德大学）；University of Utrecht（乌得勒支大学）；University of Amsterdam（阿姆斯特丹大学）
In this paper, we introduce a new form of amortized variational inference by using the forward KL divergence in a joint-contrastive variational loss. The resulting forward amortized variational inference is a likelihood-free method as its gradient can be sampled without bias and without requiring any evaluation of either the model joint distribution or its derivatives. We prove that our new variational loss is optimized by the exact posterior marginals in the fully factorized mean-field approximation, a property that is not shared with the more conventional reverse KL inference. Furthermore, w…
Federated Bayesian learning offers a principled framework for the definition of collaborative training algorithms that are able to quantify epistemic uncertainty and to produce trustworthy decisions. Upon the completion of collaborative training, an agent may decide to exercise her legal "right to be forgotten", which calls for her contribution to the jointly trained model to be deleted and discarded. This paper studies federated learning and unlearning in a decentralized network within a Bayesian framework. It specifically develops federated variational inference (VI) solutions based on the d…
Continuous-time Bayesian networks (CTBNs) constitute a general and powerful framework for modeling continuous-time stochastic processes on networks. This makes them particularly attractive for learning the directed structures among interacting entities. However, if the available data is incomplete, one needs to simulate the prohibitively complex CTBN dynamics. Existing approximation techniques, such as sampling and low-order variational methods, either scale unfavorably in system size, or are unsatisfactory in terms of accuracy. Inspired by recent advances in statistical physics, we present a …
In this paper, we employ variational arguments to establish a connection between ensemble methods for Neural Networks and Bayesian inference. We consider an ensemble-based scheme where each model/particle corresponds to a perturbation of the data by means of parametric bootstrap and a perturbation of the prior. We derive conditions under which any optimization steps of the particles makes the associated distribution reduce its divergence to the posterior over model parameters. Such conditions do not require any particular form for the approximation and they are purely geometrical, giving insig…
Aalto University（阿尔托大学）；University of Tübingen（蒂宾根大学）
Recent machine learning advances have proposed black-box estimation of unknown continuous-time system dynamics directly from data. However, earlier works are based on approximative ODE solutions or point estimates. We propose a novel Bayesian nonparametric model that uses Gaussian processes to infer posteriors of unknown ODE systems directly from data. We derive sparse variational inference with decoupled functional sampling to represent vector field posteriors. We also introduce a probabilistic shooting augmentation to enable efficient inference from arbitrarily long trajectories. The method …
In theory, Bayesian nonparametric (BNP) models are well suited to streaming data scenarios due to their ability to adapt model complexity with the observed data. Unfortunately, such benefits have not been fully realized in practice; existing inference algorithms are either not applicable to streaming applications or not extensible to BNP models. For the special case of Dirichlet processes, streaming inference has been considered. However, there is growing interest in more flexible BNP models building on the class of normalized random measures (NRMs). We work within this general framework and p…
Helsinki Institute for Information Technology HIIT（赫尔辛基信息技术研究所 HIIT）；University of Helsinki（赫尔辛基大学）
Bayesian decision theory outlines a rigorous framework for making optimal decisions based on maximizing expected utility over a model posterior. However, practitioners often do not have access to the full posterior and resort to approximate inference strategies. In such cases, taking the eventual decision-making task into account while performing the inference allows for calibrating the posterior approximation to maximize the utility. We present an automatic pipeline that co-opts continuous utilities into variational inference algorithms to account for decision-making. We provide practical str…
We develop a framework for generalized variational inference in infinite-dimensional function spaces and use it to construct a method termed Gaussian Wasserstein inference (GWI). GWI leverages the Wasserstein distance between Gaussian measures on the Hilbert space of square-integrable functions in order to determine a variational posterior using a tractable optimisation criterion and avoids pathologies arising in standard variational function space inference. An exciting application of GWI is the ability to use deep neural networks in the variational parametrisation of GWI, combining their sup…
Gaussian multiplicative noise is commonly used as a stochastic regularisation technique in training of deterministic neural networks. A recent paper reinterpreted the technique as a specific algorithm for approximate inference in Bayesian neural networks; several extensions ensued. We show that the log-uniform prior used in all the above publications does not generally induce a proper posterior, and thus Bayesian inference in such models is ill-posed. Independent of the log-uniform prior, the correlated weight noise approximation has further issues leading to either infinite objective or high …
Online Passive-Aggressive (PA) learning is a class of online margin-based algorithms suitable for a wide range of real-time prediction tasks, including classification and regression. PA algorithms are formulated in terms of deterministic point-estimation problems governed by a set of user-defined hyperparameters: the approach fails to capture model/prediction uncertainty and makes their performance highly sensitive to hyperparameter configurations. In this paper, we introduce a novel PA learning framework for regression that overcomes the above limitations. We contribute a Bayesian state-space…
University of Toronto（多伦多大学）；Vector Institute（向量研究所）
This paper focuses on Bayesian Optimization in combinatorial spaces. In many applications in the natural science. Broad applications include the study of molecules, proteins, DNA, device structures and quantum circuit designs, a on optimization over combinatorial categorical spaces is needed to find optimal or pareto-optimal solutions. However, only a limited amount of methods have been proposed to tackle this problem. Many of them depend on employing Gaussian Process for combinatorial Bayesian Optimizations. Gaussian Processes suffer from scalability issues for large data sizes as their scali…
Natural image statistics exhibit hierarchical dependencies across multiple scales. Representing such prior knowledge in non-factorial latent tree models can boost performance of image denoising, inpainting, deconvolution or reconstruction substantially, beyond standard factorial "sparse" methodology. We derive a large scale approximate Bayesian inference algorithm for linear models with non-factorial (latent tree-structured) scale mixture priors. Experimental results on a range of denoising and inpainting problems demonstrate substantially improved performance compared to MAP estimation or to …
Distributed inference/estimation in Bayesian framework in the context of sensor networks has recently received much attention due to its broad applicability. The variational Bayesian (VB) algorithm is a technique for approximating intractable integrals arising in Bayesian inference. In this paper, we propose two novel distributed VB algorithms for general Bayesian inference problem, which can be applied to a very general class of conjugate-exponential models. In the first approach, the global natural parameters at each node are optimized using a stochastic natural gradient that utilizes the Ri…
University of Toronto Institute for Aerospace Studies（多伦多大学航空航天研究所）
Variational Bayesian inference is an important machine-learning tool that finds application from statistics to robotics. The goal is to find an approximate probability density function (PDF) from a chosen family that is in some sense 'closest' to the full Bayesian posterior. Closeness is typically defined through the selection of an appropriate loss functional such as the Kullback-Leibler (KL) divergence. In this paper, we explore a new formulation of variational inference by exploiting the fact that (most) PDFs are members of a Bayesian Hilbert space under careful definitions of vector additi…
We consider online sequential decision problems where an agent must balance exploration and exploitation. We derive a set of Bayesian `optimistic' policies which, in the stochastic multi-armed bandit case, includes the Thompson sampling policy. We provide a new analysis showing that any algorithm producing policies in the optimistic set enjoys $\tilde O(\sqrt{AT})$ Bayesian regret for a problem with $A$ actions after $T$ rounds. We extend the regret analysis for optimistic policies to bilinear saddle-point problems which include zero-sum matrix games and constrained bandits as special cases. I…
Brain and Spine Institute（脑与脊柱研究所）；ETH（苏黎世联邦理工学院）；INSERM（法国国家健康与医学研究院）
This note is concerned with an accurate and computationally efficient variational bayesian treatment of mixed-effects modelling. We focus on group studies, i.e. empirical studies that report multiple measurements acquired in multiple subjects. When approached from a bayesian perspective, such mixed-effects models typically rely upon a hierarchical generative model of the data, whereby both within- and between-subject effects contribute to the overall observed variance. The ensuing VB scheme can be used to assess statistical significance at the group level and/or to capture inter-individual dif…
University of Oxford（牛津大学）；Oxford Man Institute（牛津曼学院）
Evaluating the log determinant of a positive definite matrix is ubiquitous in machine learning. Applications thereof range from Gaussian processes, minimum-volume ellipsoids, metric learning, kernel learning, Bayesian neural networks, Determinental Point Processes, Markov random fields to partition functions of discrete graphical models. In order to avoid the canonical, yet prohibitive, Cholesky $\mathcal{O}(n^{3})$ computational cost, we propose a novel approach, with complexity $\mathcal{O}(n^{2})$, based on a constrained variational Bayes algorithm. We compare our method to Taylor, Chebyshe…
University of Warsaw（华沙大学）；ETH Zurich（苏黎世联邦理工学院）；University of Amsterdam（阿姆斯特丹大学）；Google Research（谷歌研究院）；Imperial College London（帝国理工学院）；University of California, Irvine（加利福尼亚大学尔湾分校）；Microsoft Research（微软研究院）
Variational Bayesian Inference is a popular methodology for approximating posterior distributions over Bayesian neural network weights. Recent work developing this class of methods has explored ever richer parameterizations of the approximate posterior in the hope of improving performance. In contrast, here we share a curious experimental finding that suggests instead restricting the variational distribution to a more compact parameterization. For a variety of deep Bayesian neural networks trained using Gaussian mean-field variational inference, we find that the posterior standard deviations c…
TU Kaiserslautern（凯泽斯劳滕工业大学）；MindGarage；Imperial College London（帝国理工学院）；NeuralSpace；Luleå University of Technology（吕勒奥理工大学）
We introduce a novel uncertainty estimation for classification tasks for Bayesian convolutional neural networks with variational inference. By normalizing the output of a Softplus function in the final layer, we estimate aleatoric and epistemic uncertainty in a coherent manner. The intractable posterior probability distributions over weights are inferred by Bayes by Backprop. Firstly, we demonstrate how this reliable variational inference method can serve as a fundamental construct for various network architectures. On multiple datasets in supervised learning settings (MNIST, CIFAR-10, CIFAR-1…
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…
