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. Familiarity with it will give the practitioner tools to improve their inference pipeline from data collection to model selection.
Universidad Carlos III de Madrid（马德里卡洛斯三世大学）；Gregorio Marañón Health Research Institute（格雷戈里奥·马拉尼翁健康研究所）
The Bayesian approach to feature extraction, known as factor analysis (FA), has been widely studied in machine learning to obtain a latent representation of the data. An adequate selection of the probabilities and priors of these bayesian models allows the model to better adapt to the data nature (i.e. heterogeneity, sparsity), obtaining a more representative latent space. The objective of this article is to propose a general FA framework capable of modelling any problem. To do so, we start from the Bayesian Inter-Battery Factor Analysis (BIBFA) model, enhancing it with new functionalities to …
Beijing Institute of Technology（北京理工大学）；University of Technology Sydney（悉尼科技大学）
Bayesian optimization (BO) has been broadly applied to computational expensive problems, but it is still challenging to extend BO to high dimensions. Existing works are usually under strict assumption of an additive or a linear embedding structure for objective functions. This paper directly introduces a supervised dimension reduction method, Sliced Inverse Regression (SIR), to high dimensional Bayesian optimization, which could effectively learn the intrinsic sub-structure of objective function during the optimization. Furthermore, a kernel trick is developed to reduce computational complexit…
Given a set of possible models (e.g., Bayesian network structures) and a data sample, in the unsupervised model selection problem the task is to choose the most accurate model with respect to the domain joint probability distribution. In contrast to this, in supervised model selection it is a priori known that the chosen model will be used in the future for prediction tasks involving more ``focused' predictive distributions. Although focused predictive distributions can be produced from the joint probability distribution by marginalization, in practice the best model in the unsupervised sense …
Virtual screening aims to find desirable compounds from chemical library by using computational methods. For this purpose with machine learning, model outputs that can be interpreted as predictive probability will be beneficial, in that a high prediction score corresponds to high probability of correctness. In this work, we present a study on the prediction performance and reliability of graph neural networks trained with the recently proposed Bayesian learning algorithms. Our work shows that Bayesian learning algorithms allow well-calibrated predictions for various GNN architectures and class…
We consider Bayesian optimization in settings where observations can be adversarially biased, for example by an uncontrolled hidden confounder. Our first contribution is a reduction of the confounded setting to the dueling bandit model. Then we propose a novel approach for dueling bandits based on information-directed sampling (IDS). Thereby, we obtain the first efficient kernelized algorithm for dueling bandits that comes with cumulative regret guarantees. Our analysis further generalizes a previously proposed semi-parametric linear bandit model to non-linear reward functions, and uncovers in…
School of Engineering, University of Warwick, UK（华威大学工程学院，英国）；Warwick Center for Predictive Modelling, University of Warwick, UK（华威大学预测建模中心，英国）；Department of Statistics, University of Warwick, UK（华威大学统计系，英国）；Division of Translational Medicine, Warwick Medical School, UK（华威医学院转化医学部，英国）；Dept of Clinical Biochemistry, Division of Pathology, University Hospital Coventry and Warwickshire, Coventry, UK（考文垂和华威郡大学医院病理学部临床生物化学系，考文垂，英国）
We introduce a Bayesian framework for inference with a supervised version of the Gaussian process latent variable model. The framework overcomes the high correlations between latent variables and hyperparameters by using an unbiased pseudo estimate for the marginal likelihood that approximately integrates over the latent variables. This is used to construct a Markov Chain to explore the posterior of the hyperparameters. We demonstrate the procedure on simulated and real examples, showing its ability to capture uncertainty and multimodality of the hyperparameters and improved uncertainty quanti…
Although deep neural network (DNN) has achieved many state-of-the-art results, estimating the uncertainty presented in the DNN model and the data is a challenging task. Problems related to uncertainty such as classifying unknown classes (class which does not appear in the training data) data as known class with high confidence, is critically concerned in the safety domain area (e.g, autonomous driving, medical diagnosis). In this paper, we show that applying current Bayesian Neural Network (BNN) techniques alone does not effectively capture the uncertainty. To tackle this problem, we introduce…
Kyoto University（京都大学）；National Institute of Informatics（国立信息学研究所）
A common strategy for sparse linear regression is to introduce regularization, which eliminates irrelevant features by letting the corresponding weights be zeros. However, regularization often shrinks the estimator for relevant features, which leads to incorrect feature selection. Motivated by the above-mentioned issue, we propose Bayesian masking (BM), a sparse estimation method which imposes no regularization on the weights. The key concept of BM is to introduce binary latent variables that randomly mask features. Estimating the masking rates determines the relevance of the features automati…
State Key Laboratory for Novel Software Technology（新型软件技术国家重点实验室）；Nanjing University（南京大学）
Bayesian optimization is a broadly applied methodology to optimize the expensive black-box function. Despite its success, it still faces the challenge from the high-dimensional search space. To alleviate this problem, we propose a novel Bayesian optimization framework (termed SILBO), which finds a low-dimensional space to perform Bayesian optimization iteratively through semi-supervised dimension reduction. SILBO incorporates both labeled points and unlabeled points acquired from the acquisition function to guide the embedding space learning. To accelerate the learning procedure, we present a …
Semi-supervised clustering is the task of clustering data points into clusters where only a fraction of the points are labelled. The true number of clusters in the data is often unknown and most models require this parameter as an input. Dirichlet process mixture models are appealing as they can infer the number of clusters from the data. However, these models do not deal with high dimensional data well and can encounter difficulties in inference. We present a novel nonparameteric Bayesian kernel based method to cluster data points without the need to prespecify the number of clusters or to mo…
Recently, techniques for applying convolutional neural networks to graph-structured data have emerged. Graph convolutional neural networks (GCNNs) have been used to address node and graph classification and matrix completion. Although the performance has been impressive, the current implementations have limited capability to incorporate uncertainty in the graph structure. Almost all GCNNs process a graph as though it is a ground-truth depiction of the relationship between nodes, but often the graphs employed in applications are themselves derived from noisy data or modelling assumptions. Spuri…
Predicting bioactivity and physical properties of small molecules is a central challenge in drug discovery. Deep learning is becoming the method of choice but studies to date focus on mean accuracy as the main metric. However, to replace costly and mission-critical experiments by models, a high mean accuracy is not enough: Outliers can derail a discovery campaign, thus models need reliably predict when it will fail, even when the training data is biased; experiments are expensive, thus models need to be data-efficient and suggest informative training sets using active learning. We show that un…
University of Tübingen（蒂宾根大学）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
Full Bayesian posteriors are rarely analytically tractable, which is why real-world Bayesian inference heavily relies on approximate techniques. Approximations generally differ from the true posterior and require diagnostic tools to assess whether the inference can still be trusted. We investigate a new approach to diagnosing approximate inference: the approximation mismatch is attributed to a change in the inductive bias by treating the approximations as exact and reverse-engineering the corresponding prior. We show that the problem is more complicated than it appears to be at first glance, b…
It is common practice in using regression type models for inferring causal effects, that inferring the correct causal relationship requires extra covariates are included or ``adjusted for''. Without performing this adjustment erroneous causal effects can be inferred. Given this phenomenon it is common practice to include as many covariates as possible, however such advice comes unstuck in the presence of M-bias. M-Bias is a problem in causal inference where the correct estimation of treatment effects requires that certain variables are not adjusted for i.e. are simply neglected from inclusion …
University College London（伦敦大学学院）；The Alan Turing Institute（艾伦·图灵研究所）
We propose a data-efficient Gaussian process-based Bayesian approach to the semi-supervised learning problem on graphs. The proposed model shows extremely competitive performance when compared to the state-of-the-art graph neural networks on semi-supervised learning benchmark experiments, and outperforms the neural networks in active learning experiments where labels are scarce. Furthermore, the model does not require a validation data set for early stopping to control over-fitting. Our model can be viewed as an instance of empirical distribution regression weighted locally by network connecti…
Nonnegative matrix factorization (NMF) with group sparsity constraints is formulated as a probabilistic graphical model and, assuming some observed data have been generated by the model, a feasible variational Bayesian algorithm is derived for learning model parameters. When used in a supervised learning scenario, NMF is most often utilized as an unsupervised feature extractor followed by classification in the obtained feature subspace. Having mapped the class labels to a more general concept of groups which underlie sparsity of the coefficients, what the proposed group sparse NMF model allows…
London School of Economics（伦敦政治经济学院）；Royal Holloway College（皇家霍洛威学院）；University of London（伦敦大学）
In this paper the problem of learning appropriate bias for an environment of related tasks is examined from a Bayesian perspective. The environment of related tasks is shown to be naturally modelled by the concept of an {\em objective} prior distribution. Sampling from the objective prior corresponds to sampling different learning tasks from the environment. It is argued that for many common machine learning problems, although we don't know the true (objective) prior for the problem, we do have some idea of a set of possible priors to which the true prior belongs. It is shown that under these …
University of Ljubljana（卢布尔雅那大学）；West University of Timisoara（蒂米什瓦拉西部大学）
Human annotations are an important source of information in the development of natural language understanding approaches. As under the pressure of productivity annotators can assign different labels to a given text, the quality of produced annotations frequently varies. This is especially the case if decisions are difficult, with high cognitive load, requires awareness of broader context, or careful consideration of background knowledge. To alleviate the problem, we propose two semi-supervised methods to guide the annotation process: a Bayesian deep learning model and a Bayesian ensemble metho…
Crowdsourcing has emerged as a powerful paradigm for efficiently labeling large datasets and performing various learning tasks, by leveraging crowds of human annotators. When additional information is available about the data, semi-supervised crowdsourcing approaches that enhance the aggregation of labels from human annotators are well motivated. This work deals with semi-supervised crowdsourced classification, under two regimes of semi-supervision: a) label constraints, that provide ground-truth labels for a subset of data; and b) potentially easier to obtain instance-level constraints, that …
Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；Shanghai Jiao Tong University（上海交通大学）
In emotion recognition, it is difficult to recognize human's emotional states using just a single modality. Besides, the annotation of physiological emotional data is particularly expensive. These two aspects make the building of effective emotion recognition model challenging. In this paper, we first build a multi-view deep generative model to simulate the generative process of multi-modality emotional data. By imposing a mixture of Gaussians assumption on the posterior approximation of the latent variables, our model can learn the shared deep representation from multiple modalities. To solve…
Self-Supervised Laplace Approximation for Bayesian Uncertainty Quantification
Rational Intelligence Lab, CISPA Helmholtz Center for Information Security Department of Statistics, LMU Munich（理性智能实验室，CISPA海德堡信息安全中心统计学系，慕尼黑大学）；Department of Statistics, LMU Munich（统计学系，慕尼黑大学）；Department of Computer Science, The University of Manchester（计算机科学系，曼彻斯特大学）
Technical University of Munich（慕尼黑工业大学）；University of Pennsylvania（宾夕法尼亚大学）；Munich Data Science Institute（慕尼黑数据科学研究所）
Neural Operators offer a powerful, data-driven tool for solving parametric PDEs as they can represent maps between infinite-dimensional function spaces. In this work, we employ physics-informed Neural Operators in the context of high-dimensional, Bayesian inverse problems. Traditional solution strategies necessitate an enormous, and frequently infeasible, number of forward model solves, as well as the computation of parametric derivatives. In order to enable efficient solutions, we extend Deep Operator Networks (DeepONets) by employing a RealNVP architecture which yields an invertible and diff…
Hierarchical probabilistic models, such as Gaussian mixture models, are widely used for unsupervised learning tasks. These models consist of observable and latent variables, which represent the observable data and the underlying data-generation process, respectively. Unsupervised learning tasks, such as cluster analysis, are regarded as estimations of latent variables based on the observable ones. The estimation of latent variables in semi-supervised learning, where some labels are observed, will be more precise than that in unsupervised, and one of the concerns is to clarify the effect of the…
University of Toulouse, IRIT/INP-ENSEEIHT（图卢兹大学 IRIT/INP-ENSEEIHT）
Within a supervised classification framework, labeled data are used to learn classifier parameters. Prior to that, it is generally required to perform dimensionality reduction via feature extraction. These preprocessing steps have motivated numerous research works aiming at recovering latent variables in an unsupervised context. This paper proposes a unified framework to perform classification and low-level modeling jointly. The main objective is to use the estimated latent variables as features for classification and to incorporate simultaneously supervised information to help latent variable…
The University of Adelaide（阿德莱德大学）；Queensland University of Technology（昆士兰科技大学）；CMU（卡内基梅隆大学）
Traditional GANs use a deterministic generator function (typically a neural network) to transform a random noise input $z$ to a sample $\mathbf{x}$ that the discriminator seeks to distinguish. We propose a new GAN called Bayesian Conditional Generative Adversarial Networks (BC-GANs) that use a random generator function to transform a deterministic input $y'$ to a sample $\mathbf{x}$. Our BC-GANs extend traditional GANs to a Bayesian framework, and naturally handle unsupervised learning, supervised learning, and semi-supervised learning problems. Experiments show that the proposed BC-GANs outpe…
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…
Imperial College London（帝国理工学院）；King’s College London（伦敦国王学院）；The Royal Brompton & Harefield NHS Foundation Trust（皇家布朗普顿与哈菲尔德国民保健服务基金会信托）；University College London（伦敦大学学院）
Datasets are rarely a realistic approximation of the target population. Say, prevalence is misrepresented, image quality is above clinical standards, etc. This mismatch is known as sampling bias. Sampling biases are a major hindrance for machine learning models. They cause significant gaps between model performance in the lab and in the real world. Our work is a solution to prevalence bias. Prevalence bias is the discrepancy between the prevalence of a pathology and its sampling rate in the training dataset, introduced upon collecting data or due to the practioner rebalancing the training batc…
Land cover maps are a vital input variable to many types of environmental research and management. While they can be produced automatically by machine learning techniques, these techniques require substantial training data to achieve high levels of accuracy, which are not always available. One technique researchers use when labelled training data are scarce is domain adaptation (DA) -- where data from an alternate region, known as the source domain, are used to train a classifier and this model is adapted to map the study region, or target domain. The scenario we address in this paper is known…
We study the accuracy of Bayesian supervised method used to cluster individuals into genetically homogeneous groups on the basis of dominant or codominant molecular markers. We provide a formula relating an error criterion the number of loci used and the number of clusters. This formula is exact and holds for arbitrary number of clusters and markers. Our work suggests that dominant markers studies can achieve an accuracy similar to that of codominant markers studies if the number of markers used in the former is about 1.7 times larger than in the latter.
Neural network based generative models with discriminative components are a powerful approach for semi-supervised learning. However, these techniques a) cannot account for model uncertainty in the estimation of the model's discriminative component and b) lack flexibility to capture complex stochastic patterns in the label generation process. To avoid these problems, we first propose to use a discriminative component with stochastic inputs for increased noise flexibility. We show how an efficient Gibbs sampling procedure can marginalize the stochastic inputs when inferring missing labels in thi…
Overcoming Selection Bias in Statistical Studies With Amortized Bayesian Inference
University of Bonn（波恩大学）；Institut Pasteur（巴斯德研究所）；University of Freiburg（弗赖堡大学）；LMU University Hospital（慕尼黑大学附属医院）；German Center for Infection Research（德国感染研究中心）；Fraunhofer Institute ITMP（弗劳恩霍夫ITMP研究所）；Max von Pettenkofer Institute（马克斯·冯·佩滕科弗研究所）；LMU Munich（慕尼黑大学）；German Research Center for Environmental Health（德国环境健康研究中心）；Institut Necker-Enfants Malades（内克-儿童疾病研究所）
University of Maryland, Baltimore County（马里兰大学巴尔的摩县分校）
Intersectionality is a framework that analyzes how interlocking systems of power and oppression affect individuals along overlapping dimensions including race, gender, sexual orientation, class, and disability. Intersectionality theory therefore implies it is important that fairness in artificial intelligence systems be protected with regard to multi-dimensional protected attributes. However, the measurement of fairness becomes statistically challenging in the multi-dimensional setting due to data sparsity, which increases rapidly in the number of dimensions, and in the values per dimension. W…
A density estimation method in a Bayesian nonparametric framework is presented when recorded data are not coming directly from the distribution of interest, but from a length biased version. From a Bayesian perspective, efforts to computationally evaluate posterior quantities conditionally on length biased data were hindered by the inability to circumvent the problem of a normalizing constant. In this paper we present a novel Bayesian nonparametric approach to the length bias sampling problem which circumvents the issue of the normalizing constant. Numerical illustrations as well as a real dat…
A common concern with Bayesian methodology in scientific contexts is that inferences can be heavily influenced by subjective biases. As presented here, there are two types of bias for some quantity of interest: bias against and bias in favor. Based upon the principle of evidence, it is shown how to measure and control these biases for both hypothesis assessment and estimation problems. Optimality results are established for the principle of evidence as the basis of the approach to these problems. A close relationship is established between measuring bias in Bayesian inferences and frequentist …
Meta-analysis is a statistical method used in evidence synthesis for combining, analyzing and summarizing studies that have the same target endpoint and aims to derive a pooled quantitative estimate using fixed and random effects models or network models. Differences among included studies depend on variations in target populations (i.e. heterogeneity) and variations in study quality due to study design and execution (i.e. bias). The risk of bias is usually assessed qualitatively using critical appraisal, and quantitative bias analysis can be used to evaluate the influence of bias on the quant…
Bayesian generative models can flag performance loss, bias, and out-of-distribution image content
Instituto Universitario de Investigación en Tecnología Centrada en el Ser Humano, Universitat Politècnica de València（瓦伦西亚理工大学人类中心技术研究大学学院）；Technical University of Denmark（丹麦技术大学）
We design a double-or-quits game to compare the speed of learning one's specific ability with the speed of rising confidence as the task gets increasingly difficult. We find that people on average learn to be overconfident faster than they learn their true ability and we present an intuitive-Bayesian model of confidence which integrates confidence biases and learning. Uncertainty about one's true ability to perform a task in isolation can be responsible for large and stable confidence biases, namely limited discrimination, the hard--easy effect, the Dunning--Kruger effect, conservative learnin…
Uber AI Labs（Uber人工智能实验室）；Cornell University（康奈尔大学）
Generative adversarial networks (GANs) can implicitly learn rich distributions over images, audio, and data which are hard to model with an explicit likelihood. We present a practical Bayesian formulation for unsupervised and semi-supervised learning with GANs. Within this framework, we use stochastic gradient Hamiltonian Monte Carlo to marginalize the weights of the generator and discriminator networks. The resulting approach is straightforward and obtains good performance without any standard interventions such as feature matching, or mini-batch discrimination. By exploring an expressive pos…
The Eurovision Song Contest is an annual musical competition held among active members of the European Broadcasting Union since 1956. The event is televised live across Europe. Each participating country presents a song and receive a vote based on a combination of tele-voting and jury. Over the years, this has led to speculations of tactical voting, discriminating against some participants and thus inducing bias in the final results. In this paper we investigate the presence of positive or negative bias (which may roughly indicate favouritisms or discrimination) in the votes based on geographi…
Supervised Bayesian joint graphical model for simultaneous network estimation and subgroup identification
School of Statistics and Data Science, Shanghai University of International Business and Economics（上海对外经贸大学统计与数据科学学院）；School of Statistics and Data Science, Shanghai University of Finance and Economics（上海财经大学统计与数据科学学院）；Department of Biostatistics, Yale School of Public Health（耶鲁公共卫生学院生物统计学系）
University of Amsterdam（阿姆斯特丹大学）；Leiden University（莱顿大学）；Statistics Netherlands（荷兰统计局）；Tinbergen Institute（丁伯根研究所）
In this paper, we study the accuracy of values aggregated over classes predicted by a classification algorithm. The problem is that the resulting aggregates (e.g., sums of a variable) are known to be biased. The bias can be large even for highly accurate classification algorithms, in particular when dealing with class-imbalanced data. To correct this bias, the algorithm's classification error rates have to be estimated. In this estimation, two issues arise when applying existing bias correction methods. First, inaccuracies in estimating classification error rates have to be taken into account.…
We present a robust Bayesian method to analyze forestry data when samples are selected with probability proportional to length from a finite population of unknown size. Specifically, we use Bayesian predictive inference to estimate the finite population mean of shrub widths in a limestone quarry dominated by re-growth of mountain mahogany. The data on shrub widths are collected using transect sampling and it is assumed that the probability that a shrub is selected is proportional to its width; this is length-biased sampling. In this type of sampling, the population size is also unknown and thi…
Bayesian hybrid models fuse physics-based insights with machine learning constructs to correct for systematic bias. In this paper, we compare Bayesian hybrid models against physics-based glass-box and Gaussian process black-box surrogate models. We consider ballistic firing as an illustrative case study for a Bayesian decision-making workflow. First, Bayesian calibration is performed to estimate model parameters. We then use the posterior distribution from Bayesian analysis to compute optimal firing conditions to hit a target via a single-stage stochastic program. The case study demonstrates t…
