We propose a unified framework for adaptive connection sampling in graph neural networks (GNNs) that generalizes existing stochastic regularization methods for training GNNs. The proposed framework not only alleviates over-smoothing and over-fitting tendencies of deep GNNs, but also enables learning with uncertainty in graph analytic tasks with GNNs. Instead of using fixed sampling rates or hand-tuning them as model hyperparameters in existing stochastic regularization methods, our adaptive connection sampling can be trained jointly with GNN model parameters in both global and local fashions. GNN training with adaptive connection sampling is shown to be mathematically equivalent to an efficient approximation of training Bayesian GNNs. Experimental results with ablation studies on benchmark datasets validate that adaptively learning the sampling rate given graph training data is the key to boost the performance of GNNs in semi-supervised node classification, less prone to over-smoothing and over-fitting with more robust prediction.
Recent advances in deep reinforcement learning have made significant strides in performance on applications such as Go and Atari games. However, developing practical methods to balance exploration and exploitation in complex domains remains largely unsolved. Thompson Sampling and its extension to reinforcement learning provide an elegant approach to exploration that only requires access to posterior samples of the model. At the same time, advances in approximate Bayesian methods have made posterior approximation for flexible neural network models practical. Thus, it is attractive to consider a…
In Bayesian Optimization (BO) we study black-box function optimization with noisy point evaluations and Bayesian priors. Convergence of BO can be greatly sped up by batching, where multiple evaluations of the black-box function are performed in a single round. The main difficulty in this setting is to propose at the same time diverse and informative batches of evaluation points. In this work, we introduce DPP-Batch Bayesian Optimization (DPP-BBO), a universal framework for inducing batch diversity in sampling based BO by leveraging the repulsive properties of Determinantal Point Processes (DPP…
Deployments of Bayesian Optimization (BO) for functions with stochastic evaluations, such as parameter tuning via cross validation and simulation optimization, typically optimize an average of a fixed set of noisy realizations of the objective function. However, disregarding the true objective function in this manner finds a high-precision optimum of the wrong function. To solve this problem, we propose Bayesian Optimization by Sampling Hierarchically (BOSH), a novel BO routine pairing a hierarchical Gaussian process with an information-theoretic framework to generate a growing pool of realiza…
Queensland University of Technology（昆士兰科技大学）；University of Alberta（阿尔伯塔大学）
We study Bayesian optimal control of a general class of smoothly parameterized Markov decision problems. Since computing the optimal control is computationally expensive, we design an algorithm that trades off performance for computational efficiency. The algorithm is a lazy posterior sampling method that maintains a distribution over the unknown parameter. The algorithm changes its policy only when the variance of the distribution is reduced sufficiently. Importantly, we analyze the algorithm and show the precise nature of the performance vs. computation tradeoff. Finally, we show the effecti…
Given a supervised machine learning problem where the training set has been subject to a known sampling bias, how can a model be trained to fit the original dataset? We achieve this through the Bayesian inference framework by altering the posterior distribution to account for the sampling function. We then apply this solution to binary logistic regression, and discuss scenarios where a dataset might be subject to intentional sample bias such as label imbalance. This technique is widely applicable for statistical inference on big data, from the medical sciences to image recognition to marketing…
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…
National Institute of Standards and Technology（美国国家标准与技术研究院）
Optimization is becoming increasingly common in scientific and engineering domains. Oftentimes, these problems involve various levels of stochasticity or uncertainty in generating proposed solutions. Therefore, optimization in these scenarios must consider this stochasticity to properly guide the design of future experiments. Here, we adapt Bayesian optimization to handle uncertain outcomes, proposing a new framework called stochastic sampling Bayesian optimization (SSBO). We show that the bounds on expected regret for an upper confidence bound search in SSBO resemble those of earlier Bayesian…
University of Oxford（牛津大学）；UC Berkeley（加州大学伯克利分校）；IBM Research, Zurich（IBM研究院苏黎世分部）
We present Acquisition Thompson Sampling (ATS), a novel technique for batch Bayesian Optimization (BO) based on the idea of sampling multiple acquisition functions from a stochastic process. We define this process through the dependency of the acquisition functions on a set of model hyper-parameters. ATS is conceptually simple, straightforward to implement and, unlike other batch BO methods, it can be employed to parallelize any sequential acquisition function or to make existing parallel methods scale further. We present experiments on a variety of benchmark functions and on the hyper-paramet…
In Bayesian optimization, accounting for the importance of the output relative to the input is a crucial yet challenging exercise, as it can considerably improve the final result but often involves inaccurate and cumbersome entropy estimations. We approach the problem from the perspective of importance-sampling theory, and advocate the use of the likelihood ratio to guide the search algorithm towards regions of the input space where the objective function to be minimized assumes abnormally small values. The likelihood ratio acts as a sampling weight and can be computed at each iteration withou…
Target encoding is an effective encoding technique of categorical variables and is often used in machine learning systems for processing tabular data sets with mixed numeric and categorical variables. Recently en enhanced version of this encoding technique was proposed by using conjugate Bayesian modeling. This paper presents a further development of Bayesian encoding method by using sampling techniques, which helps in extracting information from intra-category distribution of the target variable, improves generalization and reduces target leakage.
Bayesian low-rank matrix factorization techniques have become an essential tool for relational data analysis and matrix completion. A standard approach is to assign zero-mean Gaussian priors on the columns or rows of factor matrices to create a conjugate system. This choice of prior leads to simple implementations; however it also causes symmetries in the posterior distribution that can severely reduce the efficiency of Markov-chain Monte-Carlo (MCMC) sampling approaches. In this paper, we propose a simple modification to the prior choice that provably breaks these symmetries and maintains/imp…
State University of New York at Buffalo（纽约州立大学布法罗分校）；Fudan University（复旦大学）
Scalable Bayesian sampling is playing an important role in modern machine learning, especially in the fast-developed unsupervised-(deep)-learning models. While tremendous progresses have been achieved via scalable Bayesian sampling such as stochastic gradient MCMC (SG-MCMC) and Stein variational gradient descent (SVGD), the generated samples are typically highly correlated. Moreover, their sample-generation processes are often criticized to be inefficient. In this paper, we propose a novel self-adversarial learning framework that automatically learns a conditional generator to mimic the behavi…
Monte Carlo sampling for Bayesian posterior inference is a common approach used in machine learning. The Markov Chain Monte Carlo procedures that are used are often discrete-time analogues of associated stochastic differential equations (SDEs). These SDEs are guaranteed to leave invariant the required posterior distribution. An area of current research addresses the computational benefits of stochastic gradient methods in this setting. Existing techniques rely on estimating the variance or covariance of the subsampling error, and typically assume constant variance. In this article, we propose …
University of Cambridge（剑桥大学）；Google Research（谷歌研究院）
We introduce repriorisation, a data-dependent reparameterisation which transforms a Bayesian neural network (BNN) posterior to a distribution whose KL divergence to the BNN prior vanishes as layer widths grow. The repriorisation map acts directly on parameters, and its analytic simplicity complements the known neural network Gaussian process (NNGP) behaviour of wide BNNs in function space. Exploiting the repriorisation, we develop a Markov chain Monte Carlo (MCMC) posterior sampling algorithm which mixes faster the wider the BNN. This contrasts with the typically poor performance of MCMC in hi…
Carnegie Mellon University（卡内基梅隆大学）；University of Massachusetts, Amherst（马萨诸塞大学阿默斯特分校）
We design and analyse variations of the classical Thompson sampling (TS) procedure for Bayesian optimisation (BO) in settings where function evaluations are expensive, but can be performed in parallel. Our theoretical analysis shows that a direct application of the sequential Thompson sampling algorithm in either synchronous or asynchronous parallel settings yields a surprisingly powerful result: making $n$ evaluations distributed among $M$ workers is essentially equivalent to performing $n$ evaluations in sequence. Further, by modeling the time taken to complete a function evaluation, we show…
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…
A fundamental task in machine learning and related fields is to perform inference on Bayesian networks. Since exact inference takes exponential time in general, a variety of approximate methods are used. Gibbs sampling is one of the most accurate approaches and provides unbiased samples from the posterior but it has historically been too expensive for large models. In this paper, we present an optimized, parallel Gibbs sampler augmented with state replication (SAME or State Augmented Marginal Estimation) to decrease convergence time. We find that SAME can improve the quality of parameter estim…
University at Buffalo（布法罗大学）；Duke University（杜克大学）
There has been recent interest in developing scalable Bayesian sampling methods such as stochastic gradient MCMC (SG-MCMC) and Stein variational gradient descent (SVGD) for big-data analysis. A standard SG-MCMC algorithm simulates samples from a discrete-time Markov chain to approximate a target distribution, thus samples could be highly correlated, an undesired property for SG-MCMC. In contrary, SVGD directly optimizes a set of particles to approximate a target distribution, and thus is able to obtain good approximations with relatively much fewer samples. In this paper, we propose a principl…
In this work, we empirically explore the question: how can we assess the quality of samples from some target distribution? We assume that the samples are provided by some valid Monte Carlo procedure, so we are guaranteed that the collection of samples will asymptotically approximate the true distribution. Most current evaluation approaches focus on two questions: (1) Has the chain mixed, that is, is it sampling from the distribution? and (2) How independent are the samples (as MCMC procedures produce correlated samples)? Focusing on the case of Bayesian nonnegative matrix factorization, we emp…
Gatsby Computational Neuroscience Unit（盖比计算神经科学单元）；University College London（伦敦大学学院）
Markov jump processes and continuous time Bayesian networks are important classes of continuous time dynamical systems. In this paper, we tackle the problem of inferring unobserved paths in these models by introducing a fast auxiliary variable Gibbs sampler. Our approach is based on the idea of uniformization, and sets up a Markov chain over paths by sampling a finite set of virtual jump times and then running a standard hidden Markov model forward filtering-backward sampling algorithm over states at the set of extant and virtual jump times. We demonstrate significant computational benefits ov…
In this work we define a unified mathematical framework to deepen our understanding of the role of stochastic gradient (SG) noise on the behavior of Markov chain Monte Carlo sampling (SGMCMC) algorithms. Our formulation unlocks the design of a novel, practical approach to posterior sampling, which makes the SG noise isotropic using a fixed learning rate that we determine analytically, and that requires weaker assumptions than existing algorithms. In contrast, the common traits of existing \sgmcmc algorithms is to approximate the isotropy condition either by drowning the gradients in additive n…
We study the Bayesian model averaging approach to learning Bayesian network structures (DAGs) from data. We develop new algorithms including the first algorithm that is able to efficiently sample DAGs according to the exact structure posterior. The DAG samples can then be used to construct estimators for the posterior of any feature. We theoretically prove good properties of our estimators and empirically show that our estimators considerably outperform the estimators from the previous state-of-the-art methods.
Chalmers University of Technology（查尔姆斯理工大学）；AstraZeneca AB（阿斯利康公司）
We study the problem of performing automated experiment design for drug screening through Bayesian inference and optimisation. In particular, we compare and contrast the behaviour of linear-Gaussian models and Gaussian processes, when used in conjunction with upper confidence bound algorithms, Thompson sampling, or bounded horizon tree search. We show that non-myopic sophisticated exploration techniques using sparse tree search have a distinct advantage over methods such as Thompson sampling or upper confidence bounds in this setting. We demonstrate the significant superiority of the approach …
University of Turku（图尔库大学）；Natural Resources Institute Finland (LUKE)（芬兰自然资源研究所）
In large-area forest inventories a trade-off between the amount of data to be sampled and the costs of collecting the data is necessary. It is not always possible to have a very large data sample when dealing with sampling-based inventories. It is therefore necessary to optimize the sampling design in order to achieve optimal population parameter estimation. On the contrary, the availability of remote sensing (RS) data correlated with the forest inventory variables is usually much higher. The combination of RS and the sampled field measurement data is often used for improving the forest invent…
Microsoft Research（微软研究院）；University of Sydney（悉尼大学）
We provide a method for approximating Bayesian inference using rejection sampling. We not only make the process efficient, but also dramatically reduce the memory required relative to conventional methods by combining rejection sampling with particle filtering. We also provide an approximate form of rejection sampling that makes rejection filtering tractable in cases where exact rejection sampling is not efficient. Finally, we present several numerical examples of rejection filtering that show its ability to track time dependent parameters in online settings and also benchmark its performance …
The R package BiDAG implements Markov chain Monte Carlo (MCMC) methods for structure learning and sampling of Bayesian networks. The package includes tools to search for a maximum a posteriori (MAP) graph and to sample graphs from the posterior distribution given the data. A new hybrid approach to structure learning enables inference in large graphs. In the first step, we define a reduced search space by means of the PC algorithm or based on prior knowledge. In the second step, an iterative order MCMC scheme proceeds to optimize within the restricted search space and estimate the MAP graph. Sa…
We design a new myopic strategy for a wide class of sequential design of experiment (DOE) problems, where the goal is to collect data in order to to fulfil a certain problem specific goal. Our approach, Myopic Posterior Sampling (MPS), is inspired by the classical posterior (Thompson) sampling algorithm for multi-armed bandits and leverages the flexibility of probabilistic programming and approximate Bayesian inference to address a broad set of problems. Empirically, this general-purpose strategy is competitive with more specialised methods in a wide array of DOE tasks, and more importantly, e…
Reinforcement learning studies how to balance exploration and exploitation in real-world systems, optimizing interactions with the world while simultaneously learning how the world operates. One general class of algorithms for such learning is the multi-armed bandit setting. Randomized probability matching, based upon the Thompson sampling approach introduced in the 1930s, has recently been shown to perform well and to enjoy provable optimality properties. It permits generative, interpretable modeling in a Bayesian setting, where prior knowledge is incorporated, and the computed posteriors nat…
Chalmers University of Technology（查尔姆斯理工大学）；University of Oslo（奥斯陆大学）
We address the problem of Bayesian reinforcement learning using efficient model-based online planning. We propose an optimism-free Bayes-adaptive algorithm to induce deeper and sparser exploration with a theoretical bound on its performance relative to the Bayes optimal policy, with a lower computational complexity. The main novelty is the use of a candidate policy generator, to generate long-term options in the planning tree (over beliefs), which allows us to create much sparser and deeper trees. Experimental results on different environments show that in comparison to the state-of-the-art, o…
University of Southern California（南加州大学）；University of California, San Diego（加州大学圣地亚哥分校）
The problem of adaptive sampling for estimating probability mass functions (pmf) uniformly well is considered. Performance of the sampling strategy is measured in terms of the worst-case mean squared error. A Bayesian variant of the existing upper confidence bound (UCB) based approaches is proposed. It is shown analytically that the performance of this Bayesian variant is no worse than the existing approaches. The posterior distribution on the pmfs in the Bayesian setting allows for a tighter computation of upper confidence bounds which leads to significant performance gains in practice. Using…
In this paper we address the following question: Can we approximately sample from a Bayesian posterior distribution if we are only allowed to touch a small mini-batch of data-items for every sample we generate?. An algorithm based on the Langevin equation with stochastic gradients (SGLD) was previously proposed to solve this, but its mixing rate was slow. By leveraging the Bayesian Central Limit Theorem, we extend the SGLD algorithm so that at high mixing rates it will sample from a normal approximation of the posterior, while for slow mixing rates it will mimic the behavior of SGLD with a pre…
Imperial College London（帝国理工学院）；King’s College London（伦敦国王学院）；University College London（伦敦大学学院）
We derive a family of loss functions to train models in the presence of sampling bias. Examples are when the prevalence of a pathology differs from its sampling rate in the training dataset, or when a machine learning practioner rebalances their training dataset. Sampling bias causes large discrepancies between model performance in the lab and in more realistic settings. It is omnipresent in medical imaging applications, yet is often overlooked at training time or addressed on an ad-hoc basis. Our approach is based on Bayesian risk minimization. For arbitrary likelihood models we derive the as…
Deep neural networks(NNs) have achieved impressive performance, often exceed human performance on many computer vision tasks. However, one of the most challenging issues that still remains is that NNs are overconfident in their predictions, which can be very harmful when this arises in safety critical applications. In this paper, we show that predictive uncertainty can be efficiently estimated when we incorporate the concept of gradients uncertainty into posterior sampling. The proposed method is tested on two different datasets, MNIST for in-distribution confusing examples and notMNIST for ou…
School of Electrical Information and Communication Engineering, Huazhong University of Science & Technology（华中科技大学电子信息与通信学院）；Microsoft AI & Research（微软人工智能与研究）；Machine Learning Department, Carnegie Mellon University（卡内基梅隆大学机器学习系）
Recent techniques built on Generative Adversarial Networks (GANs), such as Cycle-Consistent GANs, are able to learn mappings among different domains built from unpaired datasets, through min-max optimization games between generators and discriminators. However, it remains challenging to stabilize the training process and thus cyclic models fall into mode collapse accompanied by the success of discriminator. To address this problem, we propose an novel Bayesian cyclic model and an integrated cyclic framework for inter-domain mappings. The proposed method motivated by Bayesian GAN explores the f…
The University of Sydney（悉尼大学）；JD Explore Academy（京东探索研究院）
The right to be forgotten has been legislated in many countries, but its enforcement in the AI industry would cause unbearable costs. When single data deletion requests come, companies may need to delete the whole models learned with massive resources. Existing works propose methods to remove knowledge learned from data for explicitly parameterized models, which however are not appliable to the sampling-based Bayesian inference, i.e., Markov chain Monte Carlo (MCMC), as MCMC can only infer implicit distributions. In this paper, we propose the first machine unlearning algorithm for MCMC. We fir…
Variants of Triplet networks are robust entities for learning a discriminative embedding subspace. There exist different triplet mining approaches for selecting the most suitable training triplets. Some of these mining methods rely on the extreme distances between instances, and some others make use of sampling. However, sampling from stochastic distributions of data rather than sampling merely from the existing embedding instances can provide more discriminative information. In this work, we sample triplets from distributions of data rather than from existing instances. We consider a multivar…
We study Bayesian estimation of mixture models and argue in favor of fitting the marginal posterior distribution over component assignments directly, rather than Gibbs sampling from the joint posterior on components and parameters as is commonly done. Some previous authors have found the former approach to have slow mixing, but we show that, implemented correctly, it can achieve excellent performance. In particular, we describe a new Monte Carlo algorithm for sampling from the marginal posterior of a general integrable mixture that makes use of rejection-free sampling from the prior over compo…
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）
A popular approach to semi-supervised learning proceeds by endowing the input data with a graph structure in order to extract geometric information and incorporate it into a Bayesian framework. We introduce new theory that gives appropriate scalings of graph parameters that provably lead to a well-defined limiting posterior as the size of the unlabeled data set grows. Furthermore, we show that these consistency results have profound algorithmic implications. When consistency holds, carefully designed graph-based Markov chain Monte Carlo algorithms are proved to have a uniform spectral gap, ind…
We study the problem of sampling from the power posterior distribution in Bayesian Gaussian mixture models, a robust version of the classical posterior. This power posterior is known to be non-log-concave and multi-modal, which leads to exponential mixing times for some standard MCMC algorithms. We introduce and study the Reflected Metropolis-Hastings Random Walk (RMRW) algorithm for sampling. For symmetric two-component Gaussian mixtures, we prove that its mixing time is bounded as $d^{1.5}(d + \Vert θ_{0} \Vert^2)^{4.5}$ as long as the sample size $n$ is of the order $d (d + \Vert θ_{0} \Ver…
We derive explicit Bayesian nonparametric analysis for a species sampling model with finitely many types of Gibbs form of type $α= -1$ recently introduced in Gnedin (2009). Our results complement existing analysis under Gibbs priors of type $α\in [0, 1)$ proposed in Lijoi et al. (2008). Calculations rely on a groups sequential construction of Gibbs partitions introduced in Cerquetti (2008).
The focus in this paper is Bayesian system identification based on noisy incomplete modal data where we can impose spatially-sparse stiffness changes when updating a structural model. To this end, based on a similar hierarchical sparse Bayesian learning model from our previous work, we propose two Gibbs sampling algorithms. The algorithms differ in their strategies to deal with the posterior uncertainty of the equation-error precision parameter, but both sample from the conditional posterior probability density functions (PDFs) for the structural stiffness parameters and system modal parameter…
Optimality results for two outstanding Bayesian estimation problems are given in this paper: the estimation of the sampling distribution for the squared total variation function and the estimation of the density for the $L^1$-squared loss function. The posterior predictive distribution provides the solution to these problems. Some examples are presented to illustrate it. The Bayesian estimation problem of a distribution function is also addressed. Consistency of the estimator of the density is proved.
Cluster sampling is common in survey practice, and the corresponding inference has been predominantly design-based. We develop a Bayesian framework for cluster sampling and account for the design effect in the outcome modeling. We consider a two-stage cluster sampling design where the clusters are first selected with probability proportional to cluster size, and then units are randomly sampled inside selected clusters. Challenges arise when the sizes of nonsampled cluster are unknown. We propose nonparametric and parametric Bayesian approaches for predicting the unknown cluster sizes, with thi…
The design of sampling set (DoS) for bandlimited graph signals (GS) has been extensively studied in recent years, but few of them exploit the benefits of the stochastic prior of GS. In this work, we introduce the optimization framework for Bayesian DoS of bandlimited GS. We also illustrate how the choice of different sampling sets affects the estimation error and how the prior knowledge influences the result of DoS compared with the non-Bayesian DoS by the aid of analyzing Gershgorin discs of error metric matrix. Finally, based on our analysis, we propose a heuristic algorithm for DoS to avoid…
In the case of informative sampling the sampling scheme explicitly or implicitly depends on the response variable. As a result, the sample distribution of response variable can- not be used for making inference about the population. In this research I investigate the problem of informative sampling from the Bayesian perspective. Application of the Bayesian approach permits solving the problems, which arise due to complexity of the models, being used for handling informative sampling. The main objective of the re- search is to combine the elements of the classical sampling theory and Bayesian a…
Radial basis functions are a common mathematical tool used to construct a smooth interpolating function from a set of data points. A spatial prior based on thin-plate spline radial basis functions can be easily implemented resulting in a posterior that can be sampled directly using Monte Carlo integration, avoiding the computational burden and potential inefficiency of an Monte Carlo Markov Chain (MCMC) sampling scheme. The derivation of the prior and sampling scheme are demonstrated.
We present dynesty, a public, open-source, Python package to estimate Bayesian posteriors and evidences (marginal likelihoods) using Dynamic Nested Sampling. By adaptively allocating samples based on posterior structure, Dynamic Nested Sampling has the benefits of Markov Chain Monte Carlo algorithms that focus exclusively on posterior estimation while retaining Nested Sampling's ability to estimate evidences and sample from complex, multi-modal distributions. We provide an overview of Nested Sampling, its extension to Dynamic Nested Sampling, the algorithmic challenges involved, and the variou…
