Fully Bayesian Analysis of the Relevance Vector Machine Classification for Imbalanced Data
Wenyang Wang, Dongchu Sun, Zhuoqiong He
备注：
The extended and final version of this paper has been published with open access modality in the CAAI Transactions on Intelligence Technology and can be found at link https://ietresearch.onlinelibrary.wiley.com/doi/full/10.1049/cit2.12111. Please refer to the TRIT published version in your scientific papers
Relevance Vector Machine (RVM) is a supervised learning algorithm extended from Support Vector Machine (SVM) based on the Bayesian sparsity model. Compared with the regression problem, RVM classification is difficult to be conducted because there is no closed-form solution for the weight parameter posterior. Original RVM classification algorithm used Newton's method in optimization to obtain the mode of weight parameter posterior then approximated it by a Gaussian distribution in Laplace's method. It would work but just applied the frequency methods in a Bayesian framework. This paper proposes a Generic Bayesian approach for the RVM classification. We conjecture that our algorithm achieves convergent estimates of the quantities of interest compared with the nonconvergent estimates of the original RVM classification algorithm. Furthermore, a Fully Bayesian approach with the hierarchical hyperprior structure for RVM classification is proposed, which improves the classification performance, especially in the imbalanced data problem. By the numeric studies, our proposed algorithms obtain high classification accuracy rates. The Fully Bayesian hierarchical hyperprior method outperforms the Generic one for the imbalanced data classification.
While tasks could come with varying the number of instances and classes in realistic settings, the existing meta-learning approaches for few-shot classification assume that the number of instances per task and class is fixed. Due to such restriction, they learn to equally utilize the meta-knowledge across all the tasks, even when the number of instances per task and class largely varies. Moreover, they do not consider distributional difference in unseen tasks, on which the meta-knowledge may have less usefulness depending on the task relatedness. To overcome these limitations, we propose a nov…
UBMF: Uncertainty-Aware Bayesian Meta-Learning Framework for Fault Diagnosis with Imbalanced Industrial Data
Hangzhou International Innovation Institute, Beihang University（北京航空航天大学杭州国际创新研究院）；Institute of Reliability Engineering, Beihang University（北京航空航天大学可靠性工程研究所）；Science & Technology on Reliability & Environmental Engineering Laboratory（可靠性与环境工程技术重点实验室）；School of Reliability and Systems Engineering, Beihang University（北京航空航天大学可靠性与系统工程学院）
School of Management Engineering, Ulsan National Institute of Science and Technology (UNIST)（蔚山科学技术院管理工程学院）
In clinical research, the lack of events of interest often necessitates imbalanced learning. One approach to resolve this obstacle is data integration or sharing, but due to privacy concerns neither is practical. Therefore, there is an increasing demand for a platform on which an analysis can be performed in a federated environment while maintaining privacy. However, it is quite challenging to develop a federated learning algorithm that can address both privacy-preserving and class imbalanced issues. In this study, we introduce a federated generative model learning platform for generating samp…
Non-negative tensor factorization models enable predictive analysis on count data. Among them, Bayesian Poisson-Gamma models can derive full posterior distributions of latent factors and are less sensitive to sparse count data. However, current inference methods for these Bayesian models adopt restricted update rules for the posterior parameters. They also fail to share the update information to better cope with the data sparsity. Moreover, these models are not endowed with a component that handles the imbalance in count data values. In this paper, we propose a novel variational auto-encoder f…
Statistical modeling and inference problems with sample sizes substantially smaller than the number of available covariates are challenging. Chakraborty et al. (2012) did a full hierarchical Bayesian analysis of nonlinear regression in such situations using relevance vector machines based on reproducing kernel Hilbert space (RKHS). But they did not provide any theoretical properties associated with their procedure. The present paper revisits their problem, introduces a new class of global-local priors different from theirs, and provides results on posterior consistency as well as posterior con…
In this paper, we propose a diversity-aware ensemble learning based algorithm, referred to as DAMVI, to deal with imbalanced binary classification tasks. Specifically, after learning base classifiers, the algorithm i) increases the weights of positive examples (minority class) which are "hard" to classify with uniformly weighted base classifiers; and ii) then learns weights over base classifiers by optimizing the PAC-Bayesian C-Bound that takes into account the accuracy and diversity between the classifiers. We show efficiency of the proposed approach with respect to state-of-art models on pre…
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…
One of the main challenges of deep learning tools is their inability to capture model uncertainty. While Bayesian deep learning can be used to tackle the problem, Bayesian neural networks often require more time and computational power to train than deterministic networks. Our work explores whether fully Bayesian networks are needed to successfully capture model uncertainty. We vary the number and position of Bayesian layers in a network and compare their performance on active learning with the MNIST dataset. We found that we can fully capture the model uncertainty by using only a few Bayesian…
Technical University of Denmark (DTU)（丹麦技术大学）；École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）
Specifying utility functions is a key step towards applying the discrete choice framework for understanding the behaviour processes that govern user choices. However, identifying the utility function specifications that best model and explain the observed choices can be a very challenging and time-consuming task. This paper seeks to help modellers by leveraging the Bayesian framework and the concept of automatic relevance determination (ARD), in order to automatically determine an optimal utility function specification from an exponentially large set of possible specifications in a purely data…
Credit risk modelling is an integral part of the global financial system. While there has been great attention paid to neural network models for credit default prediction, such models often lack the required interpretation mechanisms and measures of the uncertainty around their predictions. This work develops and compares Bayesian Neural Networks(BNNs) for credit card default modelling. This includes a BNNs trained by Gaussian approximation and the first implementation of BNNs trained by Hybrid Monte Carlo(HMC) in credit risk modelling. The results on the Taiwan Credit Dataset show that BNNs w…
Bayesian algorithmic perfumery: A Hierarchical Relevance Vector Machine for the Estimation of Personalized Fragrance Preferences based on Three Sensory Layers and Jungian Personality Archetypes
University of Hawaii Manoa（夏威夷大学马诺阿分校）；Coveo Solutions Inc.（Coveo解决方案公司）
We present a proof of a combinatorial conjecture from the second author's Ph.D. thesis. The proof relies on binomial and multinomial sums identities. We also discuss the relevance of the conjecture in the context of PAC-Bayesian machine learning.
Learning Relevant Contextual Variables Within Bayesian Optimization
Aalto University（阿尔托大学）；Inserm（法国国家健康与医学研究院）；Vaccine Research Institute（疫苗研究所）；Université de Bordeaux（波尔多大学）；Inria Bordeaux Sud-ouest（波尔多西南信息与自动化研究院）；Univ. Lille（里尔大学）；CNRS（法国国家科学研究中心）；Centrale Lille（里尔中央理工学院）；University of Manchester（曼彻斯特大学）
Bayesian neural networks (BNNs) can account for both aleatoric and epistemic uncertainty. However, in BNNs the priors are often specified over the weights which rarely reflects true prior knowledge in large and complex neural network architectures. We present a simple approach to incorporate prior knowledge in BNNs based on external summary information about the predicted classification probabilities for a given dataset. The available summary information is incorporated as augmented data and modeled with a Dirichlet process, and we derive the corresponding \emph{Summary Evidence Lower BOund}. …
This work considers methods for imposing sparsity in Bayesian regression with applications in nonlinear system identification. We first review automatic relevance determination (ARD) and analytically demonstrate the need to additional regularization or thresholding to achieve sparse models. We then discuss two classes of methods, regularization based and thresholding based, which build on ARD to learn parsimonious solutions to linear problems. In the case of orthogonal covariates, we analytically demonstrate favorable performance with regards to learning a small set of active terms in a linear…
RIKEN Center for Advanced Intelligence Project（理化学研究所先进智能项目中心）；Technische Universität Darmstadt（达姆施塔特工业大学）；The Hessian Center for Artificial Intelligence（黑森人工智能中心）
Relevance vector machine (RVM) is a popular sparse Bayesian learning model typically used for prediction. Recently it has been shown that improper priors assumed on multiple penalty parameters in RVM may lead to an improper posterior. Currently in the literature, the sufficient conditions for posterior propriety of RVM do not allow improper priors over the multiple penalty parameters. In this article, we propose a single penalty relevance vector machine (SPRVM) model in which multiple penalty parameters are replaced by a single penalty and we consider a semi Bayesian approach for fitting the S…
Mechanistic simulation models are inverted against observations in order to gain inference on modeled processes. However, with the increasing ability to collect high resolution observations, these observations represent more patterns of detailed processes that are not part of a modeling purpose. This mismatch results in model discrepancies, i.e. systematic differences between observations and model predictions. When discrepancies are not accounted for properly, posterior uncertainty is underestimated. Furthermore parameters are inferred so that model discrepancies appear with observation data …
To incorporate prior knowledge as well as measurement uncertainties in the traditional long short term memory (LSTM) neural networks, an efficient sparse Bayesian training algorithm is introduced to the network architecture. The proposed scheme automatically determines relevant neural connections and adapts accordingly, in contrast to the classical LSTM solution. Due to its flexibility, the new LSTM scheme is less prone to overfitting, and hence can approximate time dependent solutions by use of a smaller data set. On a structural nonlinear finite element application we show that the self-regu…
High resolution geospatial data are challenging because standard geostatistical models based on Gaussian processes are known to not scale to large data sizes. While progress has been made towards methods that can be computed more efficiently, considerably less attention has been devoted to big data methods that allow the description of complex relationships between several outcomes recorded at high resolutions by different sensors. Our Bayesian multivariate regression models based on spatial multivariate trees (SpamTrees) achieve scalability via conditional independence assumptions on latent r…
The Bayesian Lasso is constructed in the linear regression framework and applies the Gibbs sampling to estimate the regression parameters. This paper develops a new sparse learning model, named the Bayesian Lasso Sparse (BLS) model, that takes the hierarchical model formulation of the Bayesian Lasso. The main difference from the original Bayesian Lasso lies in the estimation procedure; the BLS method uses a learning algorithm based on the type-II maximum likelihood procedure. Opposed to the Bayesian Lasso, the BLS provides sparse estimates of the regression parameters. The BLS method is also d…
This paper proposes Bayesian mosaic, a parallelizable composite posterior, for scalable Bayesian inference on a broad class of multivariate discrete data models. Sampling is embarrassingly parallel since Bayesian mosaic is a multiplication of component posteriors that can be independently sampled from. Analogous to composite likelihood methods, these component posteriors are based on univariate or bivariate marginal densities. Utilizing the fact that the score functions of these densities are unbiased, we show that Bayesian mosaic is consistent and asymptotically normal under mild conditions. …
University of Cambridge（剑桥大学）；IT University of Copenhagen（哥本哈根信息技术大学）
In this paper, we study the trade-offs of different inference approaches for Bayesian matrix factorisation methods, which are commonly used for predicting missing values, and for finding patterns in the data. In particular, we consider Bayesian nonnegative variants of matrix factorisation and tri-factorisation, and compare non-probabilistic inference, Gibbs sampling, variational Bayesian inference, and a maximum-a-posteriori approach. The variational approach is new for the Bayesian nonnegative models. We compare their convergence, and robustness to noise and sparsity of the data, on both synt…
University of Oxford（牛津大学）；Technische Universität Darmstadt（达姆施塔特工业大学）
Unstructured data from diverse sources, such as social media and aerial imagery, can provide valuable up-to-date information for intelligent situation assessment. Mining these different information sources could bring major benefits to applications such as situation awareness in disaster zones and mapping the spread of diseases. Such applications depend on classifying the situation across a region of interest, which can be depicted as a spatial "heatmap". Annotating unstructured data using crowdsourcing or automated classifiers produces individual classifications at sparse locations that typic…
MIT LIDS（麻省理工学院信息与决策系统实验室）；MRC-BSU, University of Cambridge（剑桥大学MRC生物统计组）；Universidad Rey Juan Carlos（胡安·卡洛斯国王大学）
Modeling the probability distribution of rows in tabular data and generating realistic synthetic data is a non-trivial task. Tabular data usually contains a mix of discrete and continuous columns. Continuous columns may have multiple modes whereas discrete columns are sometimes imbalanced making the modeling difficult. Existing statistical and deep neural network models fail to properly model this type of data. We design TGAN, which uses a conditional generative adversarial network to address these challenges. To aid in a fair and thorough comparison, we design a benchmark with 7 simulated and…
One major impediment to the wider use of deep learning for clinical decision making is the difficulty of assigning a level of confidence to model predictions. Currently, deep Bayesian neural networks and sparse Gaussian processes are the main two scalable uncertainty estimation methods. However, deep Bayesian neural network suffers from lack of expressiveness, and more expressive models such as deep kernel learning, which is an extension of sparse Gaussian process, captures only the uncertainty from the higher level latent space. Therefore, the deep learning model under it lacks interpretabili…
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）
Multi-view problems can be faced with latent variable models since they are able to find low-dimensional projections that fairly capture the correlations among the multiple views that characterise each datum. On the other hand, high-dimensionality and non-linear issues are traditionally handled by kernel methods, inducing a (non)-linear function between the latent projection and the data itself. However, they usually come with scalability issues and exposition to overfitting. Here, we propose merging both approaches into single model so that we can exploit the best features of multi-view laten…
Universidad Rey Juan Carlos（胡安卡洛斯国王大学）；Ecole Polytechnique（巴黎综合理工学院）；Institut Polytechnique de Paris（巴黎理工学院）
The expressive power of Bayesian kernel-based methods has led them to become an important tool across many different facets of artificial intelligence, and useful to a plethora of modern application domains, providing both power and interpretability via uncertainty analysis. This article introduces and discusses two methods which straddle the areas of probabilistic Bayesian schemes and kernel methods for regression: Gaussian Processes and Relevance Vector Machines. Our focus is on developing a common framework with which to view these methods, via intermediate methods a probabilistic version o…
We propose a new approach to explain Bayesian Networks. The approach revolves around a new definition of a probabilistic argument and the evidence it provides. We define a notion of independent arguments, and propose an algorithm to extract a list of relevant, independent arguments given a Bayesian Network, a target node and a set of observations. To demonstrate the relevance of the arguments, we show how we can use the extracted arguments to approximate message passing. Finally, we show a simple scheme to explain the arguments in natural language.
Comment: Bayesian Checking of the Second Levels of Hierarchical Models
我们讨论了Evans和Moshonov [Bayesian Analysis 1（2006）893- 914，Bayesian Statistics and Its Applications（2007）145- 159]关于检查先验数据冲突的方法及其与本文提出的方法的相关性。[arXiv：0802.0743]
Sparse Bayesian Learning (SBL) is a powerful framework for attaining sparsity in probabilistic models. Herein, we propose a coordinate ascent algorithm for SBL termed Relevance Matching Pursuit (RMP) and show that, as its noise variance parameter goes to zero, RMP exhibits a surprising connection to Stepwise Regression. Further, we derive novel guarantees for Stepwise Regression algorithms, which also shed light on RMP. Our guarantees for Forward Regression improve on deterministic and probabilistic results for Orthogonal Matching Pursuit with noise. Our analysis of Backward Regression on dete…
Flexible Empirical Bayesian Approaches to Pharmacovigilance for Simultaneous Signal Detection and Signal Strength Estimation in Spontaneous Reporting Systems Data
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 an Automatic Relevance Determination prior Bayesian Neural Network(BNN-ARD) weight l2-norm measure as a feature importance statistic for the model-x knockoff filter. We show on both simulated data and the Norwegian wind farm dataset that the proposed feature importance statistic yields statistically significant improvements relative to similar feature importance measures in both variable selection power and predictive performance on a real world dataset.
