We propose two generic methods for improving semi-supervised learning (SSL). The first integrates weight perturbation (WP) into existing "consistency regularization" (CR) based methods. We implement WP by leveraging variational Bayesian inference (VBI). The second method proposes a novel consistency loss called "maximum uncertainty regularization" (MUR). While most consistency losses act on perturbations in the vicinity of each data point, MUR actively searches for "virtual" points situated beyond this region that cause the most uncertain class predictions. This allows MUR to impose smoothness on a wider area in the input-output manifold. Our experiments show clear improvements in classification errors of various CR based methods when they are combined with VBI or MUR or both.
Exemplar-based methods rely on informative data points or prototypes to guide the optimization of learning algorithms. Such data facilitate interpretable model design and prediction. Of particular interest is the utility of exemplars in learning unsupervised deep representations. In this paper, we leverage hubs, which emerge as frequent neighbors in high-dimensional spaces, as exemplars to regularize a variational autoencoder and to learn a discriminative embedding for unsupervised down-stream tasks. We propose an unsupervised, data-driven regularization of the latent space with a mixture of h…
Federated Learning enables multiple data centers to train a central model collaboratively without exposing any confidential data. Even though deterministic models are capable of performing high prediction accuracy, their lack of calibration and capability to quantify uncertainty is problematic for safety-critical applications. Different from deterministic models, probabilistic models such as Bayesian neural networks are relatively well-calibrated and able to quantify uncertainty alongside their competitive prediction accuracy. Both of the approaches appear in the federated learning framework; …
Generalization is essential for deep learning. In contrast to previous works claiming that Deep Neural Networks (DNNs) have an implicit regularization implemented by the stochastic gradient descent, we demonstrate explicitly Bayesian regularizations in a specific category of DNNs, i.e., Convolutional Neural Networks (CNNs). First, we introduce a novel probabilistic representation for the hidden layers of CNNs and demonstrate that CNNs correspond to Bayesian networks with the serial connection. Furthermore, we show that the hidden layers close to the input formulate prior distributions, thus CN…
Université Pierre et Marie Curie（皮埃尔和玛丽·居里大学）；Sony CSL（索尼计算机科学研究所）；École Polytechnique（巴黎综合理工学院）
VAEs (Variational AutoEncoders) have proved to be powerful in the context of density modeling and have been used in a variety of contexts for creative purposes. In many settings, the data we model possesses continuous attributes that we would like to take into account at generation time. We propose in this paper GLSR-VAE, a Geodesic Latent Space Regularization for the Variational AutoEncoder architecture and its generalizations which allows a fine control on the embedding of the data into the latent space. When augmenting the VAE loss with this regularization, changes in the learned latent spa…
Variational autoencoders trained to minimize the reconstruction error are sensitive to the posterior collapse problem, that is the proposal posterior distribution is always equal to the prior. We propose a novel regularization method based on fraternal dropout to prevent posterior collapse. We evaluate our approach using several metrics and observe improvements in all the tested configurations.
Friedrich-Alexander Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡大学）
This paper discusses basic results and recent developments on variational regularization methods, as developed for inverse problems. In a typical setup we review basic properties needed to obtain a convergent regularization scheme and further discuss the derivation of quantitative estimates respectively needed ingredients such as Bregman distances for convex functionals. In addition to the approach developed for inverse problems we will also discuss variational regularization in machine learning and work out some connections to the classical regularization theory. In particular we will discuss…
We observe that the standard log likelihood training objective for a Recurrent Neural Network (RNN) model of time series data is equivalent to a variational Bayesian training objective, given the proper choice of generative and inference models. This perspective may motivate extensions to both RNNs and variational Bayesian models. We propose one such extension, where multiple particles are used for the hidden state of an RNN, allowing a natural representation of uncertainty or multimodality.
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…
Technion – Israel Institute of Technology（以色列理工学院）
In the Bayesian reinforcement learning (RL) setting, a prior distribution over the unknown problem parameters -- the rewards and transitions -- is assumed, and a policy that optimizes the (posterior) expected return is sought. A common approximation, which has been recently popularized as meta-RL, is to train the agent on a sample of $N$ problem instances from the prior, with the hope that for large enough $N$, good generalization behavior to an unseen test instance will be obtained. In this work, we study generalization in Bayesian RL under the probably approximately correct (PAC) framework, …
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…
Univ Lyon, Ens de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique（里昂大学，里昂高等师范学院，克洛德·贝尔纳大学，法国国家科学研究中心，物理实验室）；IRIT/INP-ENSEEIHT, University of Toulouse（图卢兹大学 IRIT/INP-ENSEEIHT）
Piecewise constant denoising can be solved either by deterministic optimization approaches, based on the Potts model, or by stochastic Bayesian procedures. The former lead to low computational time but require the selection of a regularization parameter, whose value significantly impacts the achieved solution, and whose automated selection remains an involved and challenging problem. Conversely, fully Bayesian formalisms encapsulate the regularization parameter selection into hierarchical models, at the price of high computational costs. This contribution proposes an operational strategy that …
Existing Bayesian models, especially nonparametric Bayesian methods, rely on specially conceived priors to incorporate domain knowledge for discovering improved latent representations. While priors can affect posterior distributions through Bayes' rule, imposing posterior regularization is arguably more direct and in some cases more natural and general. In this paper, we present regularized Bayesian inference (RegBayes), a novel computational framework that performs posterior inference with a regularization term on the desired post-data posterior distribution under an information theoretical f…
Asymmetric regularization mechanism for GAN training with Variational Inequalities
Department of Advanced Computing Sciences, Maastricht University（先进计算科学系，马斯特里赫特大学）；Department of Mathematical Sciences, Politecnico di Torino（数学科学系，托斯卡纳理工学院）
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.
Univ. Bordeaux（波尔多大学）；Bordeaux INP（波尔多国立理工学院）；CNRS（法国国家科学研究中心）；Université de Paris（巴黎大学）
In this work, we propose a framework to learn a local regularization model for solving general image restoration problems. This regularizer is defined with a fully convolutional neural network that sees the image through a receptive field corresponding to small image patches. The regularizer is then learned as a critic between unpaired distributions of clean and degraded patches using a Wasserstein generative adversarial networks based energy. This yields a regularization function that can be incorporated in any image restoration problem. The efficiency of the framework is finally shown on den…
In this paper, we introduce Deep Probabilistic Ensembles (DPEs), a scalable technique that uses a regularized ensemble to approximate a deep Bayesian Neural Network (BNN). We do so by incorporating a KL divergence penalty term into the training objective of an ensemble, derived from the evidence lower bound used in variational inference. We evaluate the uncertainty estimates obtained from our models for active learning on visual classification. Our approach steadily improves upon active learning baselines as the annotation budget is increased.
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 paper, the traditional model based variational method and learning based algorithms are naturally integrated to address mixed noise removal problem. To be different from single type noise (e.g. Gaussian) removal, it is a challenge problem to accurately discriminate noise types and levels for each pixel. We propose a variational method to iteratively estimate the noise parameters, and then the algorithm can automatically classify the noise according to the different statistical parameters. The proposed variational problem can be separated into regularization, synthesis, parameter estima…
Vector Institute（向量研究所）；University of Toronto（多伦多大学）；Google Brain（谷歌大脑）；Princeton University（普林斯顿大学）
Variational auto-encoders (VAEs) are a powerful approach to unsupervised learning. They enable scalable approximate posterior inference in latent-variable models using variational inference (VI). A VAE posits a variational family parameterized by a deep neural network called an encoder that takes data as input. This encoder is shared across all the observations, which amortizes the cost of inference. However the encoder of a VAE has the undesirable property that it maps a given observation and a semantics-preserving transformation of it to different latent representations. This "inconsistency"…
London School of Economics（伦敦政治经济学院）；JP Morgan Chase & Co.（摩根大通公司）
Current variational inference methods for hierarchical Bayesian nonparametric models can neither characterize the correlation structure among latent variables due to the mean-field setting, nor infer the true posterior dimension because of the universal truncation. To overcome these limitations, we propose the conditional and adaptively truncated variational inference method (CATVI) by maximizing the nonparametric evidence lower bound and integrating Monte Carlo into the variational inference framework. CATVI enjoys several advantages over traditional methods, including a smaller divergence be…
In recent years Variation Autoencoders have become one of the most popular unsupervised learning of complicated distributions.Variational Autoencoder (VAE) provides more efficient reconstructive performance over a traditional autoencoder. Variational auto enocders make better approximaiton than MCMC. The VAE defines a generative process in terms of ancestral sampling through a cascade of hidden stochastic layers. They are a directed graphic models. Variational autoencoder is trained to maximise the variational lower bound. Here we are trying maximise the likelihood and also at the same time we…
Variational Autoencoder (VAE), a simple and effective deep generative model, has led to a number of impressive empirical successes and spawned many advanced variants and theoretical investigations. However, recent studies demonstrate that, when equipped with expressive generative distributions (aka. decoders), VAE suffers from learning uninformative latent representations with the observation called KL Varnishing, in which case VAE collapses into an unconditional generative model. In this work, we introduce mutual posterior-divergence regularization, a novel regularization that is able to cont…
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…
Center for Music Technology, Georgia Institute of Technology（佐治亚理工学院音乐技术中心）
Selective manipulation of data attributes using deep generative models is an active area of research. In this paper, we present a novel method to structure the latent space of a Variational Auto-Encoder (VAE) to encode different continuous-valued attributes explicitly. This is accomplished by using an attribute regularization loss which enforces a monotonic relationship between the attribute values and the latent code of the dimension along which the attribute is to be encoded. Consequently, post-training, the model can be used to manipulate the attribute by simply changing the latent code of …
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…
University College of London（伦敦大学学院）；Athens University of Economics and Business（雅典经济与商业大学）；The Alan Turing Institute（艾伦·图灵研究所）
We present a scalable approach to performing approximate fully Bayesian inference in generic state space models. The proposed method is an alternative to particle MCMC that provides fully Bayesian inference of both the dynamic latent states and the static parameters of the model. We build up on recent advances in computational statistics that combine variational methods with sequential Monte Carlo sampling and we demonstrate the advantages of performing full Bayesian inference over the static parameters rather than just performing variational EM approximations. We illustrate how our approach e…
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…
Regularization by denoising: Bayesian model and Langevin-within-split Gibbs sampling
Institut Denis Poisson, University of Orléans（德尼·泊松研究所，奥尔良大学）；University of Toulouse, IRIT/INP-ENSEEIHT, CNRS（图卢兹大学，法国国家信息与自动化研究所/国立高等电子、电子技术、计算机与机械学院，法国国家科学研究中心）
本文提出一种基于去噪正则化（RED）的图像反演贝叶斯框架，并设计了内含Langevin Monte Carlo步骤的分裂Gibbs采样算法，通过去模糊等任务验证了其有效性。
Deep neural networks (DNNs) often require good regularizers to generalize well. Currently, state-of-the-art DNN regularization techniques consist in randomly dropping units and/or connections on each iteration of the training algorithm. Dropout and DropConnect are characteristic examples of such regularizers, that are widely popular among practitioners. However, a drawback of such approaches consists in the fact that their postulated probability of random unit/connection omission is a constant that must be heuristically selected based on the obtained performance in some validation set. To alle…
University of Wisconsin Madison（威斯康星大学麦迪逊分校）；Brown University（布朗大学）；University of Chicago（芝加哥大学）
The aim of this paper is to provide new theoretical and computational understanding on two loss regularizations employed in deep learning, known as local entropy and heat regularization. For both regularized losses we introduce variational characterizations that naturally suggest a two-step scheme for their optimization, based on the iterative shift of a probability density and the calculation of a best Gaussian approximation in Kullback-Leibler divergence. Under this unified light, the optimization schemes for local entropy and heat regularized loss differ only over which argument of the Kull…
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…
Carnegie Mellon University（卡内基梅隆大学）；Amazon.com, Inc.（亚马逊公司）；Stanford Unviersity（斯坦福大学）；University of Texas, Austin（德克萨斯大学奥斯汀分校）；Google（谷歌）
In most applications of model-based Markov decision processes, the parameters for the unknown underlying model are often estimated from the empirical data. Due to noise, the policy learnedfrom the estimated model is often far from the optimal policy of the underlying model. When applied to the environment of the underlying model, the learned policy results in suboptimal performance, thus calling for solutions with better generalization performance. In this work we take a Bayesian perspective and regularize the objective function of the Markov decision process with prior information in order to…
Nanjing University of Posts and Telecommunications（南京邮电大学）
Bayesian optimization (BO) is a powerful paradigm for derivative-free global optimization of a black-box objective function (BOF) that is expensive to evaluate. However, the overhead of BO can still be prohibitive for problems with highly expensive function evaluations. In this paper, we investigate how to reduce the required number of function evaluations for BO without compromise in solution quality. We explore the idea of posterior regularization to harness low fidelity (LF) data within the Gaussian process upper confidence bound (GP-UCB) framework. The LF data can arise from previous evalu…
Over-parameterized models, such as DeepNets and ConvNets, form a class of models that are routinely adopted in a wide variety of applications, and for which Bayesian inference is desirable but extremely challenging. Variational inference offers the tools to tackle this challenge in a scalable way and with some degree of flexibility on the approximation, but for over-parameterized models this is challenging due to the over-regularization property of the variational objective. Inspired by the literature on kernel methods, and in particular on structured approximations of distributions of random …
UiT The Arctic University of Norway（挪威北极大学UiT）；NORCE Norwegian Research Centre（NORCE挪威研究中心）
Full characterization of the spectral behavior of generative models based on neural networks remains an open issue. Recent research has focused heavily on generative adversarial networks and the high-frequency discrepancies between real and generated images. The current solution to avoid this is to either replace transposed convolutions with bilinear up-sampling or add a spectral regularization term in the generator. It is well known that Variational Autoencoders (VAEs) also suffer from these issues. In this work, we propose a simple 2D Fourier transform-based spectral regularization loss for …
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…
We present a Bayesian view of counterfactual risk minimization (CRM) for offline learning from logged bandit feedback. Using PAC-Bayesian analysis, we derive a new generalization bound for the truncated inverse propensity score estimator. We apply the bound to a class of Bayesian policies, which motivates a novel, potentially data-dependent, regularization technique for CRM. Experimental results indicate that this technique outperforms standard $L_2$ regularization, and that it is competitive with variance regularization while being both simpler to implement and more computationally efficient.
Extending Mean-Field Variational Inference via Entropic Regularization: Theory and Computation
Department of Statistics Columbia University（统计系 哥伦比亚大学）；Department of Computer Science and Department of Statistics Columbia University（计算机科学系和统计系 哥伦比亚大学）
Grocery recommendation is an important recommendation use-case, which aims to predict which items a user might choose to buy in the future, based on their shopping history. However, existing methods only represent each user and item by single deterministic points in a low-dimensional continuous space. In addition, most of these methods are trained by maximizing the co-occurrence likelihood with a simple Skip-gram-based formulation, which limits the expressive ability of their embeddings and the resulting recommendation performance. In this paper, we propose the Variational Bayesian Context-Awa…
While the impact of variational inference (VI) on posterior inference in a fixed generative model is well-characterized, its role in regularizing a learned generative model when used in variational autoencoders (VAEs) is poorly understood. We study the regularizing effects of variational distributions on learning in generative models from two perspectives. First, we analyze the role that the choice of variational family plays in imparting uniqueness to the learned model by restricting the set of optimal generative models. Second, we study the regularization effect of the variational family on …
University of Nottingham（诺丁汉大学）；University of Oxford（牛津大学）
Bayesian methods have proved powerful in many applications for the inference of model parameters from data. These methods are based on Bayes' theorem, which itself is deceptively simple. However, in practice the computations required are intractable even for simple cases. Hence methods for Bayesian inference have historically either been significantly approximate, e.g., the Laplace approximation, or achieve samples from the exact solution at significant computational expense, e.g., Markov Chain Monte Carlo methods. Since around the year 2000 so-called Variational approaches to Bayesian inferen…
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…
