The 3D modelling of indoor environments and the generation of process simulations play an important role in factory and assembly planning. In brownfield planning cases existing data are often outdated and incomplete especially for older plants, which were mostly planned in 2D. Thus, current environment models cannot be generated directly on the basis of existing data and a holistic approach on how to build such a factory model in a highly automated fashion is mostly non-existent. Major steps in generating an environment model in a production plant include data collection and pre-processing, object identification as well as pose estimation. In this work, we elaborate a methodical workflow, which starts with the digitalization of large-scale indoor environments and ends with the generation of a static environment or simulation model. The object identification step is realized using a Bayesian neural network capable of point cloud segmentation. We elaborate how the information on network uncertainty generated by a Bayesian segmentation framework can be used in order to build up a more accurate environment model. The steps of data collection and point cloud segmentation as well as the resulting model accuracy are evaluated on a real-world data set collected at the assembly line of a large-scale automotive production plant. The segmentation network is further evaluated on the publicly available Stanford Large-Scale 3D Indoor Spaces data set. The Bayesian segmentation network clearly surpasses the performance of the frequentist baseline and allows us to increase the accuracy of the model placement in a simulation scene considerably.
Brain and Spine Institute（脑与脊柱研究所）；ETH（苏黎世联邦理工学院）；INSERM（法国国家健康与医学研究院）
This note is concerned with an accurate and computationally efficient variational bayesian treatment of mixed-effects modelling. We focus on group studies, i.e. empirical studies that report multiple measurements acquired in multiple subjects. When approached from a bayesian perspective, such mixed-effects models typically rely upon a hierarchical generative model of the data, whereby both within- and between-subject effects contribute to the overall observed variance. The ensuing VB scheme can be used to assess statistical significance at the group level and/or to capture inter-individual dif…
KTH Royal Institute of Technology（瑞典皇家理工学院）；University of Bath（巴斯大学）；University of Bristol（布里斯托大学）
In this paper, we introduce a method for segmenting time series data using tools from Bayesian nonparametrics. We consider the task of temporal segmentation of a set of time series data into representative stationary segments. We use Gaussian process (GP) priors to impose our knowledge about the characteristics of the underlying stationary segments, and use a nonparametric distribution to partition the sequences into such segments, formulated in terms of a prior distribution on segment length. Given the segmentation, the model can be viewed as a variant of a Gaussian mixture model where the mi…
University of Tartu（塔尔图大学）；Royal Holloway, University of London（伦敦大学皇家霍洛威学院）
We consider the problem of estimating the maximum posterior probability (MAP) state sequence for a finite state and finite emission alphabet hidden Markov model (HMM) in the Bayesian setup, where both emission and transition matrices have Dirichlet priors. We study a training set consisting of thousands of protein alignment pairs. The training data is used to set the prior hyperparameters for Bayesian MAP segmentation. Since the Viterbi algorithm is not applicable any more, there is no simple procedure to find the MAP path, and several iterative algorithms are considered and compared. The main…
Sharif University of Technology（谢里夫理工大学）；City University of Hong Kong（香港城市大学）
Generative dynamic texture models (GDTMs) are widely used for dynamic texture (DT) segmentation in the video sequences. GDTMs represent DTs as a set of linear dynamical systems (LDSs). A major limitation of these models concerns the automatic selection of a proper number of DTs. Dirichlet process mixture (DPM) models which have appeared recently as the cornerstone of the non-parametric Bayesian statistics, is an optimistic candidate toward resolving this issue. Under this motivation to resolve the aforementioned drawback, we propose a novel non-parametric fully Bayesian approach for DT segment…
We present a novel, scalable and Bayesian approach to modelling the occurrence of pairs of symbols (i,j) drawn from a large vocabulary. Observed pairs are assumed to be generated by a simple popularity based selection process followed by censoring using a preference function. By basing inference on the well-founded principle of variational bounding, and using new site-independent bounds, we show how a scalable inference procedure can be obtained for large data sets. State of the art results are presented on real-world movie viewing data.
Automatic segmentation methods based on deep learning have recently demonstrated state-of-the-art performance, outperforming the ordinary methods. Nevertheless, these methods are inapplicable for small datasets, which are very common in medical problems. To this end, we propose a knowledge transfer method between diseases via the Generative Bayesian Prior network. Our approach is compared to a pre-train approach and random initialization and obtains the best results in terms of Dice Similarity Coefficient metric for the small subsets of the Brain Tumor Segmentation 2018 database (BRATS2018).
University of Copenhagen（哥本哈根大学）；Erasmus Medical Center（伊拉斯谟医学中心）
Suppose one is faced with the challenge of tissue segmentation in MR images, without annotators at their center to provide labeled training data. One option is to go to another medical center for a trained classifier. Sadly, tissue classifiers do not generalize well across centers due to voxel intensity shifts caused by center-specific acquisition protocols. However, certain aspects of segmentations, such as spatial smoothness, remain relatively consistent and can be learned separately. Here we present a smoothness prior that is fit to segmentations produced at another medical center. This inf…
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…
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…
Brain tumor segmentation from Magnetic Resonance Images (MRIs) is an important task to measure tumor responses to treatments. However, automatic segmentation is very challenging. This paper presents an automatic brain tumor segmentation method based on a Normalized Gaussian Bayesian classification and a new 3D Fluid Vector Flow (FVF) algorithm. In our method, a Normalized Gaussian Mixture Model (NGMM) is proposed and used to model the healthy brain tissues. Gaussian Bayesian Classifier is exploited to acquire a Gaussian Bayesian Brain Map (GBBM) from the test brain MR images. GBBM is further p…
National Institute of Mental Health（国家精神卫生研究所）；McGovern Institute for Brain Research, Massachusetts Institute of Technology（麻省理工学院麦戈文脑研究所）
In this paper, we describe a Bayesian deep neural network (DNN) for predicting FreeSurfer segmentations of structural MRI volumes, in minutes rather than hours. The network was trained and evaluated on a large dataset (n = 11,480), obtained by combining data from more than a hundred different sites, and also evaluated on another completely held-out dataset (n = 418). The network was trained using a novel spike-and-slab dropout-based variational inference approach. We show that, on these datasets, the proposed Bayesian DNN outperforms previously proposed methods, in terms of the similarity betw…
Unsupervised image segmentation aims at clustering the set of pixels of an image into spatially homogeneous regions. We introduce here a class of Bayesian nonparametric models to address this problem. These models are based on a combination of a Potts-like spatial smoothness component and a prior on partitions which is used to control both the number and size of clusters. This class of models is flexible enough to include the standard Potts model and the more recent Potts-Dirichlet Process model \cite{Orbanz2008}. More importantly, any prior on partitions can be introduced to control the globa…
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 Optimization is a useful tool for experiment design. Unfortunately, the classical, sequential setting of Bayesian Optimization does not translate well into laboratory experiments, for instance battery design, where measurements may come from different sources and their evaluations may require significant waiting times. Multi-fidelity Bayesian Optimization addresses the setting with measurements from different sources. Asynchronous batch Bayesian Optimization provides a framework to select new experiments before the results of the prior experiments are revealed. This paper proposes an …
A new Bayesian image segmentation algorithm is proposed by combining a loopy belief propagation with an inverse real space renormalization group transformation to reduce the computational time. In results of our experiment, we observe that the proposed method can reduce the computational time to less than one-tenth of that taken by conventional Bayesian approaches.
Automatic segmentation methods based on deep learning have recently demonstrated state-of-the-art performance, outperforming the ordinary methods. Nevertheless, these methods are inapplicable for small datasets, which are very common in medical problems. To this end, we propose a knowledge transfer method between diseases via the Generative Bayesian Prior network. Our approach is compared to a pre-train approach and random initialization and obtains the best results in terms of Dice Similarity Coefficient metric for the small subsets of the Brain Tumor Segmentation 2018 database (BRATS2018).
University of Cambridge（剑桥大学）；The Alan Turing Institute（艾伦·图灵研究所）；University of California Los Angeles（加州大学洛杉矶分校）
Analyzing electronic health records (EHR) poses significant challenges because often few samples are available describing a patient's health and, when available, their information content is highly diverse. The problem we consider is how to integrate sparsely sampled longitudinal data, missing measurements informative of the underlying health status and fixed demographic information to produce estimated survival distributions updated through a patient's follow up. We propose a nonparametric probabilistic model that generates survival trajectories from an ensemble of Bayesian trees that learns …
This paper presents a Bayesian generative model for dependent Cox point processes, alongside an efficient inference scheme which scales as if the point processes were modelled independently. We can handle missing data naturally, infer latent structure, and cope with large numbers of observed processes. A further novel contribution enables the model to work effectively in higher dimensional spaces. Using this method, we achieve vastly improved predictive performance on both 2D and 1D real data, validating our structured approach.
Tampere University（坦佩雷大学）；University of Bath（巴斯大学）
The electroencephalography (EEG) source imaging problem is very sensitive to the electrical modelling of the skull of the patient under examination. Unfortunately, the currently available EEG devices and their embedded software do not take this into account; instead, it is common to use a literature-based skull conductivity parameter. In this paper, we propose a statistical method based on the Bayesian approximation error approach to compensate for source imaging errors due to the unknown skull conductivity and, simultaneously, to compute a low-order estimate for the actual skull conductivity …
Due to freely available, tailored software, Bayesian statistics is fast becoming the dominant paradigm in archaeological chronology construction. Such software provides users with powerful tools for Bayesian inference for chronological models with little need to undertake formal study of statistical modelling or computer programming. This runs the risk that it is reduced to the status of a black-box which is not sensible given the power and complexity of the modelling tools it implements. In this paper we seek to offer intuitive insight to ensure that readers from the archaeological research c…
This paper presents a Bayesian image segmentation model based on Potts prior and loopy belief propagation. The proposed Bayesian model involves several terms, including the pairwise interactions of Potts models, and the average vectors and covariant matrices of Gauss distributions in color image modeling. These terms are often referred to as hyperparameters in statistical machine learning theory. In order to determine these hyperparameters, we propose a new scheme for hyperparameter estimation based on conditional maximization of entropy in the Potts prior. The algorithm is given based on loop…
Dropout has recently emerged as a powerful and simple method for training neural networks preventing co-adaptation by stochastically omitting neurons. Dropout is currently not grounded in explicit modelling assumptions which so far has precluded its adoption in Bayesian modelling. Using Bayesian entropic reasoning we show that dropout can be interpreted as optimal inference under constraints. We demonstrate this on an analytically tractable regression model providing a Bayesian interpretation of its mechanism for regularizing and preventing co-adaptation as well as its connection to other Baye…
We propose a Bayesian semiparametric approach for registration of multiple point processes. Our approach entails modelling the mean measures of the phase-varying point processes with a Bernstein-Dirichlet prior, which induces a prior on the space of all warp functions. Theoretical results on the support of the induced priors are derived, and posterior consistency is obtained under mild conditions. Numerical experiments suggest a good performance of the proposed methods, and a climatology real-data example is used to showcase how the method can be employed in practice.
Changepoint analysis (also known as segmentation analysis) aims at analyzing an ordered, one-dimensional vector, in order to find locations where some characteristic of the data changes. Many models and algorithms have been studied under this theme, including models for changes in mean and / or variance, changes in linear regression parameters, etc. In this work, we are interested in an algorithm for the segmentation of long duration acoustic signals; the segmentation is based on the change of the RMS power of the signal. We investigate a Bayesian model with two possible parameterizations, and…
Shape information is of great importance in many applications. For example, the oil-bearing capacity of sand bodies, the subterranean remnants of ancient rivers, is related to their cross-sectional shapes. The analysis of these shapes is therefore of some interest, but current classifications are simplistic and ad hoc. In this paper, we describe the first steps towards a coherent statistical analysis of these shapes by deriving the integrated likelihood for data shapes given class parameters. The result is of interest beyond this particular application.
Bayesian methods for modelling and inference are being increasingly used in the cryospheric sciences, and glaciology in particular. Here, we present a review of recent works in glaciology that adopt a Bayesian approach when conducting an analysis. We organise the chapter into three categories: i) Gaussian-Gaussian models, ii) Bayesian hierarchical models, and iii) Bayesian calibration approaches. In addition, we present two detailed case studies that involve the application of Bayesian hierarchical models in glaciology. The first case study is on the spatial prediction of surface mass balance …
Insurance risks data typically exhibit skewed behaviour. In this paper, we propose a Bayesian approach to capture the main features of these datasets. This work extends the methodology introduced in Villa and Walker (2014a) by considering an extra parameter which captures the skewness of the data. In particular, a skewed Student-t distribution is considered. Two datasets are analysed: the Danish fire losses and the US indemnity loss. The analysis is carried with an objective Bayesian approach. For the discrete parameter representing the number of the degrees of freedom, we adopt a novel prior …
In a recent paper, we have proposed an unsupervised algorithm for audio signal segmentation entirely based on Bayesian methods. In its first implementation, however, the method showed poor computational performance. In this paper we address this question by describing a fast parallel implementation using the Cython library for Python; we use open GSL methods for standard mathematical functions, and the OpenMP framework for parallelization. We also offer a detailed analysis on the sensibility of the algorithm to its different parameters, and show its application to real-life subacquatic signals…
The network flow optimization approach is offered for Bayesian segmentation of gray-scale and color images. It is supposed image pixels are characterized by a feature function taking finite number of arbitrary rational values (it can be either intensity values or other characteristics of images). The clusters of homogeneous pixels are described by labels with values in another set of rational numbers. They are assumed to be dependent and distributed according to either the exponential or the Gaussian Gibbs law. Instead traditionally used local neighborhoods of nearest pixels the completely con…
How to estimate heterogeneity, e.g. the effect of some variable differing across observations, is a key question in political science. Methods for doing so make simplifying assumptions about the underlying nature of the heterogeneity to draw reliable inferences. This paper allows a common way of simplifying complex phenomenon (placing observations with similar effects into discrete groups) to be integrated into regression analysis. The framework allows researchers to (i) use their prior knowledge to guide which groups are permissible and (ii) appropriately quantify uncertainty. The paper does …
University of Potsdam（波茨坦大学）；École Nationale de la Statistique et de l’administration économique（国家统计与经济管理学院）；CNRS（法国国家科学研究中心）；Université Paris-Dauphine（巴黎九大）；PSL Research University（巴黎文理研究大学）
We present a case-study demonstrating the usefulness of Bayesian hierarchical mixture modelling for investigating cognitive processes. In sentence comprehension, it is widely assumed that the distance between linguistic co-dependents affects the latency of dependency resolution: the longer the distance, the longer the retrieval time (the distance-based account). An alternative theory, direct-access, assumes that retrieval times are a mixture of two distributions: one distribution represents successful retrievals (these are independent of dependency distance) and the other represents an initial…
Consider a set of categorical variables where at least one of them is binary. The log-linear model that describes the counts in the resulting contingency table implies a specific logistic regression model, with the binary variable as the outcome. Within the Bayesian framework, the $g$-prior and mixtures of $g$-priors are commonly assigned to the parameters of a generalized linear model. We prove that assigning a $g$-prior (or a mixture of $g$-priors) to the parameters of a certain log-linear model designates a $g$-prior (or a mixture of $g$-priors) on the parameters of the corresponding logist…
We consider latent Gaussian fields for modelling spatial dependence in the context of both spatial point patterns and areal data, providing two different applications. The inhomogeneous Log-Gaussian Cox Process model is specified to describe a seismic sequence occurred in Greece, resorting to the Stochastic Partial Differential Equations. The Besag-York-Mollie model is fitted for disease mapping of the Covid-19 infection in the North of Italy. These models both belong to the class of Bayesian hierarchical models with latent Gaussian fields whose posterior is not available in closed form. There…
The aim of this paper is to model the length of registration at university and its associated academic outcome for undergraduate students at the Pontificia Universidad Católica de Chile. Survival time is defined as the time until the end of the enrollment period, which can relate to different reasons - graduation or two types of dropout - that are driven by different processes. Hence, a competing risks model is employed for the analysis. The issue of separation of the outcomes (which precludes maximum likelihood estimation) is handled through the use of Bayesian inference with an appropriately…
The celebrated Abakaliki smallpox data have appeared numerous times in the epidemic modelling literature, but in almost all cases only a specific subset of the data is considered. There is one previous analysis of the full data set, but this relies on approximation methods to derive a likelihood. The data themselves continue to be of interest due to concerns about the possible re-emergence of smallpox as a bioterrorism weapon. We present the first full Bayesian analysis using data-augmentation Markov chain Monte Carlo methods which avoid the need for likelihood approximations. Results include …
University of Bristol（布里斯托大学）；Heriot Watt University（赫瑞瓦特大学）
This paper presents a new Bayesian estimation technique for hidden Potts-Markov random fields with unknown regularisation parameters, with application to fast unsupervised K-class image segmentation. The technique is derived by first removing the regularisation parameter from the Bayesian model by marginalisation, followed by a small-variance-asymptotic (SVA) analysis in which the spatial regularisation and the integer-constrained terms of the Potts model are decoupled. The evaluation of this SVA Bayesian estimator is then relaxed into a problem that can be computed efficiently by iteratively …
Chain Event Graphs (CEGs) are a widely applicable class of probabilistic graphical model that can represent context-specific independence statements and asymmetric unfoldings of events in an easily interpretable way. Existing model selection literature on CEGs has largely focused on obtaining the maximum a posteriori (MAP) CEG. However, MAP selection is well-known to ignore model uncertainty. Here, we explore the use of Bayesian model averaging over this class. We demonstrate how this approach can quantify model uncertainty and leads to more robust inference by identifying shared features acro…
We aim at modelling the appearance of distinct tags in a sequence of labelled objects. Common examples of this type of data include words in a corpus or distinct species in a sample. These sequential discoveries are often summarised via accumulation curves, which count the number of distinct entities observed in an increasingly large set of objects. We propose a novel Bayesian nonparametric method for species sampling modelling by directly specifying the probability of a new discovery, therefore allowing for flexible specifications. The asymptotic behavior and finite sample properties of such …
Copula models have become one of the most widely used tools in the applied modelling of multivariate data. Similarly, Bayesian methods are increasingly used to obtain efficient likelihood-based inference. However, to date, there has been only limited use of Bayesian approaches in the formulation and estimation of copula models. This article aims to address this shortcoming in two ways. First, to introduce copula models and aspects of copula theory that are especially relevant for a Bayesian analysis. Second, to outline Bayesian approaches to formulating and estimating copula models, and their …
As a Bayesian approach to fitting motorway traffic flow models remains rare in the literature, we explore empirically the sampling challenges this approach offers which have to do with the strong correlations and multi-modality of the posterior distribution. In particular, we provide a unified statistical model to estimate using motorway data both boundary conditions and fundamental diagram parameters in LWR, a well known motorway traffic flow model. This allows us to provide a traffic flow density estimation method that is shown to be superior to two methods found in the traffic flow literatu…
Quantitative Fitness Analysis (QFA) is a high-throughput experimental and computational methodology for measuring the growth of microbial populations. QFA screens can be used to compare the health of cell populations with and without a mutation in a query gene in order to infer genetic interaction strengths genome-wide, examining thousands of separate genotypes. We introduce Bayesian, hierarchical models of population growth rates and genetic interactions that better reflect QFA experimental design than current approaches. Our new approach models population dynamics and genetic interaction sim…
This paper introduces Bayesian supervised and unsupervised segmentation algorithms aimed at oceanic segmentation of SAR images. The data term, \emph{i.e}., the density of the observed backscattered signal given the region, is modeled by a finite mixture of Gamma densities with a given predefined number of components. To estimate the parameters of the class conditional densities, a new expectation maximization algorithm was developed. The prior is a multi-level logistic Markov random field enforcing local continuity in a statistical sense. The smoothness parameter controlling the degree of homo…
Spatial connectivity is an important consideration when modelling infectious disease data across a geographical region. Connectivity can arise for many reasons, including shared characteristics between regions, and human or vector movement. Bayesian hierarchical models include structured random effects to account for spatial connectivity. However, conventional approaches require the spatial structure to be fully defined prior to model fitting. By applying penalised smoothing splines to coordinates, we create 2-dimensional smooth surfaces describing the spatial structure of the data whilst maki…
Conditional heteroscedastic (CH) models are routinely used to analyze financial datasets. The classical models such as ARCH-GARCH with time-invariant coefficients are often inadequate to describe frequent changes over time due to market variability. However we can achieve significantly better insight by considering the time-varying analogues of these models. In this paper, we propose a Bayesian approach to the estimation of such models and develop computationally efficient MCMC algorithm based on Hamiltonian Monte Carlo (HMC) sampling. We also established posterior contraction rates with incre…
Generalized additive models (GAMs) are flexible non-linear regression models, which can be fitted efficiently using the approximate Bayesian methods provided by the mgcv R package. While the GAM methods provided by mgcv are based on the assumption that the response distribution is modelled parametrically, here we discuss more flexible methods that do not entail any parametric assumption. In particular, this article introduces the qgam package, which is an extension of mgcv providing fast calibrated Bayesian methods for fitting quantile GAMs (QGAMs) in R. QGAMs are based on a smooth version of …
