While machine learning is rapidly being developed and deployed in health settings such as influenza prediction, there are critical challenges in using data from one environment in another due to variability in features; even within disease labels there can be differences (e.g. "fever" may mean something different reported in a doctor's office versus in an online app). Moreover, models are often built on passive, observational data which contain different distributions of population subgroups (e.g. men or women). Thus, there are two forms of instability between environments in this observational transport problem. We first harness knowledge from health to conceptualize the underlying causal structure of this problem in a health outcome prediction task. Based on sources of stability in the model, we posit that for human-sourced data and health prediction tasks we can combine environment and population information in a novel population-aware hierarchical Bayesian domain adaptation framework that harnesses multiple invariant components through population attributes when needed. We study the conditions under which invariant learning fails, leading to reliance on the environment-specific attributes. Experimental results for an influenza prediction task on four datasets gathered from different contexts show the model can improve prediction in the case of largely unlabelled target data from a new environment and different constituent population, by harnessing both environment and population invariant information. This work represents a novel, principled way to address a critical challenge by blending domain (health) knowledge and algorithmic innovation. The proposed approach will have a significant impact in many social settings wherein who and where the data comes from matters.
Université Laval（拉瓦尔大学）；Univ. of St-Etienne（圣艾蒂安大学）
This paper provides a theoretical analysis of domain adaptation based on the PAC-Bayesian theory. We propose an improvement of the previous domain adaptation bound obtained by Germain et al. in two ways. We first give another generalization bound tighter and easier to interpret. Moreover, we provide a new analysis of the constant term appearing in the bound that can be of high interest for developing new algorithmic solutions.
Population attributes are essential in health for understanding who the data represents and precision medicine efforts. Even within disease infection labels, patients can exhibit significant variability; "fever" may mean something different when reported in a doctor's office versus from an online app, precluding directly learning across different datasets for the same prediction task. This problem falls into the domain adaptation paradigm. However, research in this area has to-date not considered who generates the data; symptoms reported by a woman versus a man, for example, could also have di…
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…
Massachusetts Institute of Technology（麻省理工学院）；Harvard University（哈佛大学）
In this note we provide detailed derivations of two versions of small-variance asymptotics for hierarchical Dirichlet process (HDP) mixture models and the HDP hidden Markov model (HDP-HMM, a.k.a. the infinite HMM). We include derivations for the probabilities of certain CRP and CRF partitions, which are of more general interest.
Common statistical practice has shown that the full power of Bayesian methods is not realized until hierarchical priors are used, as these allow for greater "robustness" and the ability to "share statistical strength." Yet it is an ongoing challenge to provide a learning-theoretically sound formalism of such notions that: offers practical guidance concerning when and how best to utilize hierarchical models; provides insights into what makes for a good hierarchical prior; and, when the form of the prior has been chosen, can guide the choice of hyperparameter settings. We present a set of analyt…
In this paper, we provide two main contributions in PAC-Bayesian theory for domain adaptation where the objective is to learn, from a source distribution, a well-performing majority vote on a different target distribution. On the one hand, we propose an improvement of the previous approach proposed by Germain et al. (2013), that relies on a novel distribution pseudodistance based on a disagreement averaging, allowing us to derive a new tighter PAC-Bayesian domain adaptation bound for the stochastic Gibbs classifier. We specialize it to linear classifiers, and design a learning algorithm which …
INRIA, SIERRA Project-Team（法国国家信息与自动化研究所，SIERRA项目组）；D.I., Ecole Normale Superieure（巴黎高等师范学校计算机科学系）；Univ Lyon, UJM-Saint-Etienne, CNRS, IOGS, Laboratoire Hubert Curien UMR 5516（里昂大学，圣艾蒂安让·莫内大学，法国国家科学研究中心，IOGS，于贝尔·居里安实验室）；Université Laval（拉瓦尔大学）
We study the issue of PAC-Bayesian domain adaptation: We want to learn, from a source domain, a majority vote model dedicated to a target one. Our theoretical contribution brings a new perspective by deriving an upper-bound on the target risk where the distributions' divergence---expressed as a ratio---controls the trade-off between a source error measure and the target voters' disagreement. Our bound suggests that one has to focus on regions where the source data is informative.From this result, we derive a PAC-Bayesian generalization bound, and specialize it to linear classifiers. Then, we i…
This paper presents the Bayesian Hierarchical Words Representation (BHWR) learning algorithm. BHWR facilitates Variational Bayes word representation learning combined with semantic taxonomy modeling via hierarchical priors. By propagating relevant information between related words, BHWR utilizes the taxonomy to improve the quality of such representations. Evaluation of several linguistic datasets demonstrates the advantages of BHWR over suitable alternatives that facilitate Bayesian modeling with or without semantic priors. Finally, we further show that BHWR produces better representations for…
University of Torontoland（托伦托兰大学）；Googol ShallowMind；University of Edenborrow（伊登伯勒大学）
Making inferences from data streams is a pervasive problem in many modern data analysis applications. But it requires to address the problem of continuous model updating and adapt to changes or drifts in the underlying data generating distribution. In this paper, we approach these problems from a Bayesian perspective covering general conjugate exponential models. Our proposal makes use of non-conjugate hierarchical priors to explicitly model temporal changes of the model parameters. We also derive a novel variational inference scheme which overcomes the use of non-conjugate priors while mainta…
University of Pittsburgh（匹兹堡大学）；Yonsei University（延世大学）
Multiclass neural networks are a common tool in modern unsupervised domain adaptation, yet an appropriate theoretical description for their non-uniform sample complexity is lacking in the adaptation literature. To fill this gap, we propose the first PAC-Bayesian adaptation bounds for multiclass learners. We facilitate practical use of our bounds by also proposing the first approximation techniques for the multiclass distribution divergences we consider. For divergences dependent on a Gibbs predictor, we propose additional PAC-Bayesian adaptation bounds which remove the need for inefficient Mon…
Tufts University（塔夫茨大学）；Tufts Medical Center（塔夫茨医学中心）
We consider the problem of forecasting the daily number of hospitalized COVID-19 patients at a single hospital site, in order to help administrators with logistics and planning. We develop several candidate hierarchical Bayesian models which directly capture the count nature of data via a generalized Poisson likelihood, model time-series dependencies via autoregressive and Gaussian process latent processes, and share statistical strength across related sites. We demonstrate our approach on public datasets for 8 hospitals in Massachusetts, U.S.A. and 10 hospitals in the United Kingdom. Further …
Istituto Dalle Molle di Studi sull’Intelligenza Artificiale (IDSIA)（达莱莫莱人工智能研究所（IDSIA））；USI（意大利语区大学）；SUPSI（瑞士南部应用科学与艺术大学）
Score functions for learning the structure of Bayesian networks in the literature assume that data are a homogeneous set of observations; whereas it is often the case that they comprise different related, but not homogeneous, data sets collected in different ways. In this paper we propose a new Bayesian Dirichlet score, which we call Bayesian Hierarchical Dirichlet (BHD). The proposed score is based on a hierarchical model that pools information across data sets to learn a single encompassing network structure, while taking into account the differences in their probabilistic structures. We der…
Columbia University（哥伦比亚大学）；University of Ljubljana（卢布尔雅那大学）；Aalto University（阿尔托大学）
Stacking is a widely used model averaging technique that asymptotically yields optimal predictions among linear averages. We show that stacking is most effective when model predictive performance is heterogeneous in inputs, and we can further improve the stacked mixture with a hierarchical model. We generalize stacking to Bayesian hierarchical stacking. The model weights are varying as a function of data, partially-pooled, and inferred using Bayesian inference. We further incorporate discrete and continuous inputs, other structured priors, and time series and longitudinal data. To verify the p…
Istituto Dalle Molle di studi sull’Intelligenza Artificiale (IDSIA)（达勒莫勒人工智能研究所 (IDSIA)）；University of Ljubljana（卢布尔雅那大学）
Usually one compares the accuracy of two competing classifiers via null hypothesis significance tests (nhst). Yet the nhst tests suffer from important shortcomings, which can be overcome by switching to Bayesian hypothesis testing. We propose a Bayesian hierarchical model which jointly analyzes the cross-validation results obtained by two classifiers on multiple data sets. It returns the posterior probability of the accuracies of the two classifiers being practically equivalent or significantly different. A further strength of the hierarchical model is that, by jointly analyzing the results ob…
Items in modern recommender systems are often organized in hierarchical structures. These hierarchical structures and the data within them provide valuable information for building personalized recommendation systems. In this paper, we propose a general hierarchical Bayesian learning framework, i.e., \emph{HBayes}, to learn both the structures and associated latent factors. Furthermore, we develop a variational inference algorithm that is able to learn model parameters with fast empirical convergence rate. The proposed HBayes is evaluated on two real-world datasets from different domains. The …
We present BOFFIN TTS (Bayesian Optimization For FIne-tuning Neural Text To Speech), a novel approach for few-shot speaker adaptation. Here, the task is to fine-tune a pre-trained TTS model to mimic a new speaker using a small corpus of target utterances. We demonstrate that there does not exist a one-size-fits-all adaptation strategy, with convincing synthesis requiring a corpus-specific configuration of the hyper-parameters that control fine-tuning. By using Bayesian optimization to efficiently optimize these hyper-parameter values for a target speaker, we are able to perform adaptation with…
Insight Centre for Data Analytics（洞察数据分析中心）；University College Dublin（都柏林大学）；Maynooth University（梅努斯大学）
This paper focuses on the problem of hierarchical non-overlapping clustering of a dataset. In such a clustering, each data item is associated with exactly one leaf node and each internal node is associated with all the data items stored in the sub-tree beneath it, so that each level of the hierarchy corresponds to a partition of the dataset. We develop a novel Bayesian nonparametric method combining the nested Chinese Restaurant Process (nCRP) and the Hierarchical Dirichlet Process (HDP). Compared with other existing Bayesian approaches, our solution tackles data with complex latent mixture fe…
Department of Technology, Management and Economics, Danish Technical University（丹麦技术大学技术、管理与经济系）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
Analyzing and understanding the structure of complex relational data is important in many applications including analysis of the connectivity in the human brain. Such networks can have prominent patterns on different scales, calling for a hierarchically structured model. We propose two non-parametric Bayesian hierarchical network models based on Gibbs fragmentation tree priors, and demonstrate their ability to capture nested patterns in simulated networks. On real networks we demonstrate detection of hierarchical structure and show predictive performance on par with the state of the art. We en…
The Australian National University（澳大利亚国立大学）；Data61/NICTA；Monash University（莫纳什大学）；Duke University（杜克大学）
The Dirichlet process and its extension, the Pitman-Yor process, are stochastic processes that take probability distributions as a parameter. These processes can be stacked up to form a hierarchical nonparametric Bayesian model. In this article, we present efficient methods for the use of these processes in this hierarchical context, and apply them to latent variable models for text analytics. In particular, we propose a general framework for designing these Bayesian models, which are called topic models in the computer science community. We then propose a specific nonparametric Bayesian topic…
Qiushi Academy for Advanced Studies, Zhejiang University（浙江大学求是高等研究院）；College of Computer Science and Technology, Zhejiang University（浙江大学计算机科学与技术学院）；State University of New York at Buffalo（纽约州立大学布法罗分校）；Zhejiang University School of Medicine（浙江大学医学院）
Domain adaptation is an important technique to alleviate performance degradation caused by domain shift, e.g., when training and test data come from different domains. Most existing deep adaptation methods focus on reducing domain shift by matching marginal feature distributions through deep transformations on the input features, due to the unavailability of target domain labels. We show that domain shift may still exist via label distribution shift at the classifier, thus deteriorating model performances. To alleviate this issue, we propose an approximate joint distribution matching scheme by…
In this paper, we introduce a probabilistic model for learning nonnegative matrix factorization (NMF) that is commonly used for predicting missing values and finding hidden patterns in the data, in which the matrix factors are latent variables associated with each data dimension. The nonnegativity constraint for the latent factors is handled by choosing priors with support on the nonnegative subspace. Bayesian inference procedure based on Gibbs sampling is employed. We evaluate the model on several real-world datasets including MovieLens 100K and MovieLens 1M with different sizes and dimension…
Conditional Hierarchical Bayesian Tucker Decomposition for Genetic Data Analysis
Engineering Sciences and Applied Mathematics（应用数学与工程科学）；Industrial Engineering and Management Sciences（工业工程与管理科学）；Preventive Medicine (Health and Biomedical Informatics)（预防医学（健康与生物医学信息学））
Existing methods for sparse channel estimation typically provide an estimate computed as the solution maximizing an objective function defined as the sum of the log-likelihood function and a penalization term proportional to the l1-norm of the parameter of interest. However, other penalization terms have proven to have strong sparsity-inducing properties. In this work, we design pilot-assisted channel estimators for OFDM wireless receivers within the framework of sparse Bayesian learning by defining hierarchical Bayesian prior models that lead to sparsity-inducing penalization terms. The estim…
The Alan Turing Institute（艾伦·图灵研究所）；Imperial College London（帝国理工学院）；University of Warwick（华威大学）
Potential violent criminals will often need to go through a sequence of preparatory steps before they can execute their plans. During this escalation process police have the opportunity to evaluate the threat posed by such people through what they know, observe and learn from intelligence reports about their activities. In this paper we customise a three-level Bayesian hierarchical model to describe this process. This is able to propagate both routine and unexpected evidence in real time. We discuss how to set up such a model so that it calibrates to domain expert judgments. The model illustra…
We present a novel hierarchical distance-dependent Bayesian model for event coreference resolution. While existing generative models for event coreference resolution are completely unsupervised, our model allows for the incorporation of pairwise distances between event mentions -- information that is widely used in supervised coreference models to guide the generative clustering processing for better event clustering both within and across documents. We model the distances between event mentions using a feature-rich learnable distance function and encode them as Bayesian priors for nonparametr…
We study a two-level multiview learning with more than two views under the PAC-Bayesian framework. This approach, sometimes referred as late fusion, consists in learning sequentially multiple view-specific classifiers at the first level, and then combining these view-specific classifiers at the second level. Our main theoretical result is a generalization bound on the risk of the majority vote which exhibits a term of diversity in the predictions of the view-specific classifiers. From this result it comes out that controlling the trade-off between diversity and accuracy is a key element for mu…
Computer Vision Center（计算机视觉中心）；Universitat Autónoma de Barcelona（巴塞罗那自治大学）
A key topic in classification is the accuracy loss produced when the data distribution in the training (source) domain differs from that in the testing (target) domain. This is being recognized as a very relevant problem for many computer vision tasks such as image classification, object detection, and object category recognition. In this paper, we present a novel domain adaptation method that leverages multiple target domains (or sub-domains) in a hierarchical adaptation tree. The core idea is to exploit the commonalities and differences of the jointly considered target domains. Given the rel…
In the need for low assumption inferential methods in infinite-dimensional settings, Bayesian adaptive estimation via a prior distribution that does not depend on the regularity of the function to be estimated nor on the sample size is valuable. We elucidate relationships among the main approaches followed to design priors for minimax-optimal rate-adaptive estimation meanwhile shedding light on the underlying ideas.
Collected data, which is used for analysis or prediction tasks, often have a hierarchical structure, for example, data from various people performing the same task. Modeling the data's structure can improve the reliability of the derived results and prediction performance of newly unobserved data. Bayesian modeling provides a tool-kit for designing hierarchical models. However, Markov Chain Monte Carlo methods which are commonly used for parameter estimation are computationally expensive. This often renders its use for many applications not applicable. However, variational Bayesian methods all…
Bayesian algorithmic perfumery: A Hierarchical Relevance Vector Machine for the Estimation of Personalized Fragrance Preferences based on Three Sensory Layers and Jungian Personality Archetypes
Hierarchical models are versatile tools for joint modeling of data sets arising from different, but related, sources. Fully Bayesian inference may, however, become computationally prohibitive if the source-specific data models are complex, or if the number of sources is very large. To facilitate computation, we propose an approach, where inference is first made independently for the parameters of each data set, whereupon the obtained posterior samples are used as observed data in a substitute hierarchical model, based on a scaled likelihood function. Compared to direct inference in a full hier…
The level set approach has proven widely successful in the study of inverse problems for interfaces, since its systematic development in the 1990s. Recently it has been employed in the context of Bayesian inversion, allowing for the quantification of uncertainty within the reconstruction of interfaces. However the Bayesian approach is very sensitive to the length and amplitude scales in the prior probabilistic model. This paper demonstrates how the scale-sensitivity can be circumvented by means of a hierarchical approach, using a single scalar parameter. Together with careful consideration of …
Bayesian Low-Rank Factorization for Robust Model Adaptation
Interactive Systems Lab, Karlsruhe Institut of Technology (KIT), Germany（交互系统实验室，卡尔斯鲁厄理工学院（KIT），德国）；InterACT, Carnegie Mellon University (CMU), USA（InterACT，卡内基梅隆大学（CMU），美国）
This paper introduces a new sparse Bayesian learning (SBL) algorithm that jointly recovers a temporal sequence of edge maps from noisy and under-sampled Fourier data. The new method is cast in a Bayesian framework and uses a prior that simultaneously incorporates intra-image information to promote sparsity in each individual edge map with inter-image information to promote similarities in any unchanged regions. By treating both the edges as well as the similarity between adjacent images as random variables, there is no need to separately form regions of change. Thus we avoid both additional co…
We classify two types of Hierarchical Bayesian Model found in the literature as Hierarchical Prior Model (HPM) and Hierarchical Stochastic Model (HSM). Then, we focus on studying the theoretical implications of the HSM. Using examples of polynomial functions, we show that the HSM is capable of separating different types of uncertainties in a system and quantifying uncertainty of reduced order models under the Bayesian model class selection framework. To tackle the huge computational cost for analyzing HSM, we propose an efficient approximation scheme based on Importance Sampling and Empirical …
Demographic studies of cosmic populations must contend with measurement errors and selection effects. We survey some of the key ideas astronomers have developed to deal with these complications, in the context of galaxy surveys and the literature on corrections for Malmquist and Eddington bias. From the perspective of modern statistics, such corrections arise naturally in the context of multilevel models, particularly in Bayesian treatments of such models: hierarchical Bayesian models. We survey some key lessons from hierarchical Bayesian modeling, including shrinkage estimation, which is clos…
