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A new Bayesian–inspired statistic for hypothesis testing is proposed which compares two posterior distributions; the observed posterior and the expected posterior under the null model. The Kullback–Leibler divergence between the two posterior distributions yields a test statistic which can be interpreted as a penalized log–Bayes factor with the penalty term converging to a constant as the sample size increases. Hence, asymptotically, the statistic behaves as a Bayes factor. Viewed as a penalized Bayes factor, this approach solves the long standing issue of using improper priors with the Bayes factor, since only posterior summaries are needed for the new statistic. Further motivation for the new statistic is a minimal move from the Bayes factor which requires no tuning nor splitting of data into training and inference, and can use improper priors. Critical regions for the test can be assessed using frequentist notions of Type I error.

In this paper, we use Bayesian nonparametric learning to estimate the skill of actively managed mutual funds and also to estimate the population distribution of skill. A nonparametric hierarchical prior, where the hyperprior distribution is unknown and modeled with a Dirichlet Process prior, is used to model the skill parameter, with its posterior predictive distribution being an estimate of the population distribution. Our nonparametric approach is equivalent to an infinitely ordered mixture of normals where we resolve the uncertainty in the number of mixture components by learning how to partition the funds into groups according to the average ability and the variability in the skill of a group. By resolving the mixture’s uncertainty, our nonparametric prior avoids having to sequentially estimate and test an array of pre-specified, finite ordered, mixture priors. Applying our Bayesian nonparametric learning approach to a panel of actively managed, domestic equity funds, we find the population distribution of skill to be fat-tailed, skewed towards higher levels of performance, with two distinct modes – a primary mode where the average ability covers the average fees charged by funds, and a secondary mode at a performance level where a fund loses money for its investors.

We consider the design of a robust procurement mechanism for an assembler who must procure multiple complementary components under limited information regarding the unit production costs of the potential suppliers. We abandon the standard assumption that there exists a common prior distribution for the suppliers’ costs and we employ the max-min criterion in which we design a mechanism to maximize the assembler’s worst-case expected profit when only the means of the suppliers’ costs are known. We formulate this problem using a linear semi-infinite programming model and we apply a primal-dual approach to reduce the problem to a single joint optimization model. We characterize the optimal procurement mechanism (payments and ordering quantities) under the assumption of balanced ordering and uncertain end-customer demand. We use these results to compare the performance of component production, under which the components are sourced from separate suppliers, and integrated production, under which the components are sourced from the same supplier. We find that component production is preferred when the production costs of the components are heterogeneous. We also propose two heuristic mechanisms which are easier to compute and implement in practice, particularly when the number of components is large. Finally, we extend our analysis to the case in which the average and variance of the suppliers’ costs are known.

We propose a likelihood-based Bayesian method that exploits up-to-date sequential Monte Carlo methods to efficiently estimate long-run risk models in which the conditional variance of consumption growth follows either an autoregressive (AR) process or an autoregressive gamma (ARG) process. We use the U.S. quarterly consumption and asset returns data from the postwar period to implement estimation. Our findings are: (1) informative priors on the preference parameters can help to improve model performance; (2) expected consumption growth has a very persistent component, whereas consumption volatility is less persistent; (3) while the ARG-based model performs better than the AR-based one statistically, the latter could fit asset returns better; and (4) the solution method matters more for estimation in the AR-based model than in the ARG-based model.

Civil unrest can range from peaceful protest to violent furor, and researchers are working to monitor, forecast, and assess such events to allocate resources better. Twitter has become a real-time data source for forecasting civil unrest because millions of people use the platform as a social outlet. Daily word counts are used as model features, and predictive terms contextualize the reasons for the protest. To forecast civil unrest and infer the reasons for the protest, we consider the problem of Bayesian variable selection for the dynamic logistic regression model and propose using penalized credible regions to select parameters of the updated state vector. This method avoids the need for shrinkage priors, is scalable to high-dimensional dynamic data, and allows the importance of variables to vary in time as new information becomes available. A substantial improvement in both precision and F1-score using this approach is demonstrated through simulation. Finally, we apply the proposed model fitting and variable selection methodology to the problem of forecasting civil unrest in Latin America. Our dynamic logistic regression approach shows improved accuracy compared to the static approach currently used in event prediction and feature selection.

Given a Wiener process with unknown and unobservable drift, we try to estimate this drift as effectively but also as quickly as possible, in the presence of a quadratic penalty for the estimation error and of a fixed, positive cost per unit of observation time. In a Bayesian framework, where the unobservable drift is assumed to have a known “prior” distribution, this question reduces to choosing judiciously a stopping time for an appropriate diffusion process in natural scale. We establish structural properties of the solution for the corresponding problem of optimal stopping. In particular, we show that, regardless of the prior distribution, the continuation region is monotonically shrinking in time. Moreover, we provide conditions on the prior distribution that guarantee a one-sided stopping region. Lastly, some concrete prior distributions are studied to illustrate the theoretical results.

We present an accurate and automatic bottom-up floorplan reconstruction method by leveraging geometric priors extracted from raw point clouds of indoor scenes. Compared to two state-of-the-art methods which adopt point density as priors only, our designed geometric priors integrate point density with indoor area recognition and normal information. These geometric priors are used to calculate the confidence score for each unit region as part of the external boundaries. A cost function is developed according to the confidence scores and the normals along a certain edge, as well as the edge length. By minimizing the cost function, we can automatically estimate candidate edges, and connect them edge by edge to generate rough external boundaries. After diminishing the redundant edges, we can finally solve for a fine closed-loop external boundary path via an efficient heuristic method. We validate our method on intensive real indoor scenes. Experimental results show that our method outperforms two state-of-the-art methods in terms of reconstructing accurate external floorplan boundaries.

This paper introduces a Bayesian multilevel model based on the age-period-cohort framework to examine Chinese happiness. Using 8 waves of the Chinese General Social Survey (CGSS) data between 2005–2015, the model not only solves the co-linearity problem with weakly informative priors and explicit assumptions, it also produces more computationally stable results. Our estimation results show how Chinese happiness changes in an individual’s life circle and how one’s life experience is accumulated to her/his happiness with cognitive development. We identify some different generation patterns and explain generation differences in happiness across the various birth years with narratives of historical events. This paper contributes to existing studies both theoretically and methodologically. The novel modeling strategy and the analytical framework which assisted with historical narratives altogether explain better the age, period, and cohort effects on Chinese happiness.

The elicitation of power priors, based on the availability of historical data, is realized by raising the likelihood function of the historical data to a fractional power δ , which quantifies the degree of discounting of the historical information in making inference with the current data. When δ is not pre-specified and is treated as random, it can be estimated from the data using Bayesian updating paradigm. However, in the original form of the joint power prior Bayesian approach, certain positive constants before the likelihood of the historical data could be multiplied when different settings of sufficient statistics are employed. This would change the power priors with different constants, and hence the likelihood principle is violated. In this article, we investigate a normalized power prior approach which obeys the likelihood principle and is a modified form of the joint power prior. The optimality properties of the normalized power prior in the sense of minimizing the weighted Kullback–Leibler divergence are investigated. By examining the posteriors of several commonly used distributions, we show that the discrepancy between the historical and the current data can be well quantified by the power parameter under the normalized power prior setting. Efficient algorithms to compute the scale factor is also proposed. In addition, we illustrate the use of the normalized power prior Bayesian analysis with three data examples, and provide an implementation with an R package NPP.

Segmentation of knee articular cartilage tissue (ACT) from 3D magnetic resonance images (MRIs) is a fundamental task in assessing knee osteoarthritis (KOA). However, automated ACT segmentation of knee cartilage is complicated by (1) the variability of pathological structures in terms of shape, size, spatial resolution and (2) the uncertainties in delineating inter- and intra-cartilage boundaries (possibly touching inter-cartilage surfaces, intensity inhomogeneity, cartilage loss due to disease progression). To address these problems, we propose a novel joint deep and hand-crafted learning-based (JD-HCl) framework. The fully automated segmentation pipeline is a combination of three main steps: 3D convolutional neural networks (CNNs), diffeomorphic mapping, and a conventional hand-crafted feature-based classification model. Firstly, the initial segmentation of knee ACT was drawn from preprocessed knee MRIs using 3D U-Net. Secondly, the spatial alignment in the image domain was carried out using diffeomorphic image registration derived from an estimate of the anatomical correspondences between the subjects and population-specific template. Finally, a tissue-specific hand-crafted feature set was extracted from the spatially aligned pre-segmented ACT region and combined with the semantic context priors obtained from 3D CNN model to develop the second-stage learning model. The proposed method was evaluated with two publicly available Osteoarthritis Initiative (OAI) datasets and one in-house MRI sequences from the Alfred hospital, Melbourne, Australia. The proposed JD-HCl framework produced strong Dice similarity coefficient (DSC), ranging between 97.4% and 98.5% (95% confidence interval) for all cartilage compartments at baseline to 97.2% and 98.5% (the 1-year follow-up) for OAI(-Imorphics) dataset, and 89.3% and 94.6% for OAI-ZIB validation dataset, respectively. Average correlations of cartilage volumes between manual and automatic segmentations were 0.9 and 0.83 for OAI-ZIB dataset, respectively, and 0.975, 0.995, and 0.99 for OAI(-Imorphics) validation datasets, respectively. In longitudinal studies, accurate segmentation of knee ACT using the proposed method produces reproducible cartilage volume, thickness measurements valuable for the study of KOA progression.

A Bayesian treatment of the proportional hazard (PH) model is revisited using Dirichlet process and gamma process priors for the baseline survival and cumulative hazard functions respectively. Such priors, due to their discrete support, conflict with the absolutely continuous nature of survival responses expressed through the hazard function structure that defines the PH model. We resolve this conflict through the use of a proposed e -grid likelihood approach which we apply to the PH model to consider marginal inference for the regression parameter β using expansions as e ↓ 0 . Using Dirichlet process priors, the e -grid likelihood approach leads to a new explicit marginal posterior density expansion for β which accommodates the most general setting with arbitrary ties and right censoring. In the previously considered case of gamma process priors, the approach extends the results of Kalbfleisch (1978) to deal with arbitrary arrangements of ties and also provides a rigorous justification for his posterior expressions. As in Kalbfleisch (1978), we show that the leading terms of both expansions approximate Cox’s partial likelihood when there are no ties and the process priors are diffuse. The e -grid likelihood approach is similar in concept to the grouped data likelihood approach of Sinha et al. (2003) but differs in the likelihood approximation. Whereas our expansions are Poincare expansions (with relative error O ( e ) as e ↓ 0 ), those of Sinha et al. (2003) are stochastic expansions and not proper Poincare expansion (as we show), so that they lack relative error O ( e ) . Using a flat improper prior for β , the two marginal posterior expressions for β are shown to be integrable for general arrangements of ties and censoring under weak conditions on the design and failures.

Reducing noise is an urgent problem that solved in practical application, so designing robust signal recovery approach based on compressive sensing (CS) theory is critical for the multichannel electroencephalogram (EEG) signals. However, almost all the algorithms seldom regard noise or just take Gaussian noise emerged in transmission into account. When the original signal is affected by noise before compression and transmission, all these CS approaches will be out of effect. In order to abase the impact of impulsive noise, a new robust CS approach based on cosparse and low-rank priors is proposed to recover the clean original signal near perfectly. Specially, our model employs Welsch estimator to retrain the impulsive noise, and weighted schatten- p norm to efficiently utilize low-rank prior knowledge. Moreover, we present an iterative optimization strategy to reconstruct the signals. Experimental results have demonstrated that the proposed algorithm can exactly reconstruct the multichannel EEG signals under the impact of impulsive noise.

The aim of network embedding is to learn compact node representations. This has been shown to be effective in various downstream learning tasks, such as link prediction and node classification . Most methods focus on preserving different network structures and properties , ignoring the fact that networks are usually noisy and incomplete, thus such methods potentially lack robustness and suffer from the overfitting issue. Recently, generative adversarial networks based methods have been exploited to impose a prior distribution on node embeddings to encourage a global smoothness, but their model architecture is very complicated and they suffer from the non-convergence problem. Here, we propose adversarial training (AdvT), a more succinct and effective local regularization method, for negative-sampling-based network embedding to improve model robustness and generalization ability . Specifically, we first define the adversarial perturbations in the embedding space instead of in the discrete graph domain to circumvent the challenge of generating discrete adversarial examples. Then, to enable more effective regularization, we design the adaptive l 2 norm constraints on adversarial perturbations that depend upon the connectivity pattern of node pairs. We integrate AdvT into several famous models including D eep W alk , LINE and node2vec, and conduct extensive experiments on benchmark datasets to verify its effectiveness.

Meta-learning aims to leverage experience from previous tasks to achieve an effective and fast adaptation ability when encountering new tasks. However, it is unclear how the generalization property applies to new tasks. Probably approximately correct (PAC) Bayes bound theory provides a theoretical framework to analyze the generalization performance for meta-learning with an explicit numerical generalization error upper bound. A tighter upper bound may achieve better generalization performance. However, for the PAC-Bayes meta-learning bound, the prior distribution is selected randomly which results in poor generalization performance. In this paper, we derive three novel generalization error upper bounds for meta-learning based on the PAC-Bayes relative entropy bound. Furthermore, in order to avoid randomly prior distribution, based on the empirical risk minimization (ERM) method, a data-dependent prior for the PAC-Bayes meta-learning bound algorithm is developed and the sample complexity and computational complexity are analyzed. The experiments illustrate that the proposed three PAC-Bayes bounds for meta-learning achieve a competitive generalization guarantee, and the extended PAC-Bayes bound with a data-dependent prior can achieve rapid convergence ability.

We study probabilistic voting rules in a two-voter model. The notion of incentive compatibility we consider is ordinal Bayesian incentive compatibility (OBIC) as introduced in d’Aspremont and Peleg (1988). We show that there exist anonymous and ex-post efficient probabilistic voting rules that are not random dictatorships and at the same time are OBIC with respect to an independently distributed generic prior. This contrasts with the results obtained for deterministic voting mechanisms obtained in Majumdar and Sen (2004) and in Mishra (2016). In case of neutral and efficient rules, there are two kinds of results. First we show that imposing OBIC with respect to some generic prior leads to random dictatorship when there are three alternatives. Second, we show that the result is no longer true when there are four or more alternatives and consequently we provide sufficient conditions on the priors for the result to be true.

HLA haplotype frequencies are estimated from ambiguous unphased HLA genotyping data using Expectation-Maximization (EM) algorithms. Current population genetics methods require independent EM frequency estimates for each population, and assume that each population is in Hardy-Weinberg Equilibrium (HWE). The HWE assumption of EM has thus far resulted in the exclusion of individuals from mixed or unknown ethnic backgrounds from reference datasets. Multi-region populations are currently poorly served by stem cell donor registry HLA imputation and matching implementations due to the inability of such algorithms to incorporate admixture into their population genetics models. To address this unmet need, we have expanded the imputation component of our GRaph IMputation and Matching (GRIMM) framework, where imputation becomes the expectation step in an iterative EM algorithm. Our novel multi-region EM implementation considers region as a Bayesian prior, enabling integration of HLA information from multiple single-region population groups, and for the first time including individuals with ambiguous or mixed ethnic backgrounds. We show that our multi-region EM produces much higher likelihood values and better haplotype recovery as measured by Kullback-Leibler divergence than all evaluated EM implementations when tested on real datasets of US donor registry HLA typings as well as simulated multi-region datasets of ambiguous HLA typings.

Sparse Bayesian learning (SBL) provides state-of-the-art performance in accuracy, sparsity and probabilistic prediction for classification. In SBL, the regularization priors are automatically determined that avoids an exhaustive hyperparameter selection by cross-validation. However, scalability to large problems is a drawback of SBL because of the inversion of a potentially enormous covariance matrix for updating the regularization priors in every iteration. This paper develops an approximate SBL algorithm called ARP-SBL, where the regularization priors are approximated without inverting the covariance matrix. Therefore, our approach can easily scale up to problems with large data size or feature dimension. It alleviates the long training time and high memory complexity in SBL. Based on ARP-SBL, two scalable nonlinear SBL models: scalable relevance vector machine (ARP-RVM) and scalable sparse Bayesian extreme learning machine (ARP-SBELM) are developed for problems of large data size and large feature size respectively. Experiments on a variety of benchmarks have shown that the proposed models are with competitive accuracy compared to existing methods while i) converging faster; ii) requiring thousands of times less memory; iii) without exhaustive regularized hyperparameter selection; and iv) easily scaling up to large data size and high dimensional features.

Multi-view clustering, which utilizes the ample information provided by multiple sources to obtain better performance, has attracted much attention. However, existing clustering algorithms either have no ability to offer confidence for each assignment or suffer from the disturbance of outliers. To address these problems, in this paper, we propose a novel multi-view fuzzy clustering method via transferring softmin to fuzzy models. To obtain fuzzy assignments, we utilize the softmin with temperature and further develop an efficient algorithm to solve the non-convex problem approximately. We also show another explanation for the algorithm from the aspect of the prior distribution of various views. Besides, we design a scalable robust loss function, which interpolates between l2-norm and the squared l2-norm, to enhance the robustness to outliers. Extensive experiments show the superiority of our model under different clustering metrics.

Multimodal functional neuroimaging by integrating functional magnetic resonance imaging (fMRI) and electroencephalography (EEG) has the promise of recovering brain activities with high spatiotemporal resolution, which is crucial for neuroscience research and clinical diagnosis. However, the misalignment of the localizations between fMRI and EEG activities may degrade the accuracy of the fMRI-constrained EEG source imaging (ESI) technique. To leverage the complementary spatiotemporal resolution of fMRI and EEG in a data-driven fashion, we propose an asymmetric approach for EEG/fMRI fusion, termed fMRI-informed source imaging based on spatiotemporal basis functions (fMRI-SI-STBF). fMRI-SI-STBF employs the covariance components (CCs) derived from clusters defined by fMRI and EEG signals as spatial priors within the empirical Bayesian framework. Additionally, fMRI-SI-STBF represents the current source matrix as a linear combination of several unknown temporal basis functions (TBFs) by matrix decomposition. The relative contribution of each of the fMRI-informed and EEG-informed CCs, as well as the number and profiles of the TBFs, are all automatically determined based on the EEG data using variational Bayesian inference. Our results demonstrate that fMRI-SI-STBF can effectively utilize valid fMRI information for ESI and is robust to invalid fMRI priors. This robustness is essential for practical ESI since the validity of fMRI priors is often unclear considering that fMRI is an indirect measure of neural activity. Moreover, fMRI-SI-STBF can achieve performance improvement by incorporating temporal constraints compared to methods that use spatial constraints only. For the numerical simulations, fMRI-SI-STBF reconstructs the source extents, locations and time courses more accurately than existing EEG-fMRI ESI methods (i.e., fwMNE, fMRI-SI-SBF) and ESI methods without fMRI priors (i.e., wMNE, LORETA, SBL, SI-STBF, SI-SBF), indicated by the smaller spatial dispersion (average SD 5 mm), distance of localization error (average DLE 2 mm), shape error (average SE 0.9 ) and larger model evidence values.

The Bayesian compressive sensing (BCS) is an available approach for data compressions based on compressed sensing framework. Moreover, the priors of sparse signals play a key role in BCS. Various studies that exploit the priors only via models generating, which exist the low prior utilizations. Therefore, to fully use the priors for signals recovering, we propose a novel deep heterogeneous optimization framework which can completely express the priors in a data-model double driven manner. Our work can be briefly summarized by the following aspects. As the heterogeneous handles benefiting recovery solutions, we firstly exploit the available heterogeneous arrangements for traditional BCS recovery models. Secondly, inspired by the deep neural networks (DNNs), we do researches on adding a deep optimization scheme for the scale parameters of heterogeneous prior functions via supervised learning. In addition to developing the three complete algorithms with that merge the prior parameters learning and signal recoveries. Finally, Experimental results show that for both synthetic data and images data our proposed double driven framework achieves the superior performances compared with that of the other well-known compressed recovery algorithms no matter in noise-free or noisy measurement environments.

Automatic ultrasound image segmentation is crucial for clinical diagnosis and treatment. However, ultrasound image segmentation is challenging because of the ambiguous structure, incomplete boundary and analogous appearance among different categories. To address above challenges, we propose a flexibly plug-and-play module called vector self-attention layer (VSAL) to conduct long-range spatial and channels reasoning simultaneously. Moreover, it also preserves translational equivariance and considers multi-scale information, by using geometric priors and multi-scale calibration. Besides, a novel context aggregation loss (CAL) is designed to consider the contextual dependences between inter-classes and intra-classes based on context prior. The proposed methods, VSAL and CAL, are flexible enough to be integrated in any CNN-based methods. We validate the effectiveness of the modules on two different ultrasound datasets, multi-target Fetal Apical Four-chamber dataset and one-target Fetal Head dataset. Experiment results reveal significant performance gain when using the proposed modules.

In the diversity of contemporary decision-making tasks, where the data is no longer static and changes over time, data stream processing has become an important issue in the field of pattern recognition. In addition, most of the real problems are not balanced, representing their classes in various improportions. Following paper proposes the Prior Imbalance Compensation method, modifying on-the-fly predictions made by the base classifier, aiming at mapping prior probability in the statistics of assigned classes. It is intended to be a less computationally complex competition for popular algorithms such as smote , solving this problem by oversampling the training set. The proposed method has been tested using computer experiments on the example of a set of various data streams, leading to promising results, suggesting its usefulness in solving this type of problems.

Intra-speaker variability, caused by emotional speech, is a real threat to the performance of speaker recognition systems. In fact, as human beings, we are constantly changing our emotional state. While many efforts have been made to increase automatic speaker verification (ASV) robustness towards channel effects or spoofing attacks, only a handful of studies have addressed the detrimental consequences of affective speech. In this paper, we propose a new method to minimize the mismatch between neutral and affective speech. To this end, a Gaussian mixture model is used to learn a prior probability distribution of the neutral speech for a given speaker (i.e., characterizing his/her source space). This knowledge is then used to minimize the differences between target (affective) and source (neutral) spaces. The proposed method is validated across four multi-lingual emotional datasets. Experimental results show a consistent improvement in performance across eight emotional states, with significant reductions of equal error rate relative to the baseline.

To address the ill-posed nature of image compressive sensing (CS) recovery, it is of great importance to properly exploit image priors. In this paper, we propose a novel group residual based nonlocal low-rank regularization for image CS recovery, namely GRNLR-CS, which performs nonlocal low-rank modeling based on the residual of patch group rather than on the patch group itself as conventional methods. In our GRNLR-CS, the weighted Schatten p-norm is adopted as a non-convex surrogate function to estimate the rank of the group residual. To make our GRNLR-CS method tractable and robust, the split Bregman iteration technique is employed to develop an efficient algorithm to solve the optimization problem of GRNLR-CS. Extensive experimental results demonstrate that our GRNLR-CS method outperforms some state-of-the-art optimization based or deep learning based methods for image CS recovery.

In state-of-the-art text-independent speaker verification systems, a discriminative deep neural network (DNN) model learns speaker-discriminative representations (x-vectors) for utterances using labeled data. For the verification task, a Probabilistic Linear Discriminant Analysis (PLDA) model is used to decide whether two x-vectors come from the same speaker. The PLDA scoring model assumes Gaussian priors and conditional distributions across speakers, which is not the case for x-vectors. This work introduces a variational-based regularization term that encourages the network to generate embeddings that follow a desired prior distribution. The regularization function performs a non-parametric match between the embeddings generated in the mini-batch training and a sample from the desired distribution. Unlike Variational Auto Encoders (VAEs), no distribution parameter is necessary to be learned, and no sampling schema is employed, which makes the proposed method flexible for different desired distributions. Our experiments compared the proposed method with the standard x-vectors system jointly with other approaches recently proposed to generate Gaussianized representations. We assessed the verification performance of the systems using the Fisher English Training Speech - Part II database in eight test conditions based on the gender of the speakers and the duration of the speech segments. Besides using the standard Gaussian distribution as prior, we also applied a less strict distribution (uniform). The proposed method outperformed others in all test conditions for both distributions, with gains of performance between 7.68% and 20.49% when compared to the standard x-vectors. To understand the effect of the regularizations into the embeddings space, we also conducted a 2-dimensional visual comparison, which showed clusters with better quality when the regularizations were applied.

The goal of visual mapless navigation is to navigate from a random starting point in a scene to a specified target in an unknown environment. A fundamental challenge in visual mapless navigation is generalizing to a novel environment, where the layout of the scenes and appearance of targets are unfamiliar. Furthermore, traditional navigation models are frozen during inference resulting in poor adaptability. To address these issues, we propose a multi goals and multi scenes visual mapless navigation model, which integrates meta learning with spatial relationships between different object categories. In this way, our method not only improves the generalization on multi goals in multi scenes but also encourages effective navigation. Experimental results on AI2-THOR dataset show that our approach significantly outperforms the state-of-the-art model SAVN by > 27.05 % for the average success rate and by > 31.7 % for the average SPL. Our source code and data of this paper are available at: https://github.com/zhiyu-tech/WHU-VMN.

This paper presents reference priors for non-regular model whose support depends on an unknown parameter. A multi-parameter family which includes both regular and non-regular structures is considered. The resulting priors are obtained by asymptotically maximizing the expected α -divergence between the prior and the corresponding posterior distribution. Some examples of reference priors for typical multi-parameter non-regular distributions such as the location-scale family of distributions and the truncated Weibull distribution are also given.

Existing recommender systems rely on user and item representations in a fixed continuous low-dimensional latent space. To predict ratings, they use only an implicit feedback matrix , whereas user and item side information is ignored. Furthermore, they use the same arbitrary priors for the user and item latent vectors, reducing the ability of the model to identify the actual latent vectors. Currently, the latent parameters should be learned directly for every user and movie. This is problematic, as it would require both model retraining and learning the latent vector representations when users or items are added to the underlying dataset. To address these issues, we propose a two-step hybrid variational Bayesian autoencoder to characterize the uncertainty of predicted ratings. An encoder is first trained to map data vectors to the latent space so that the latent representations can be dynamically computed. Subsequently, we use the generative process of users and items with their priors as side-specific information to handle matrix sparsity and better learn their latent vectors. Finally, we consider stochastic variational inference to approximate the posterior density of intractable user-item latent vectors. Experiments conducted on two real-world datasets demonstrate the effectiveness of the proposed method compared with state-of-the-art methods.

Number and brightness (N&B) analysis is useful for monitoring the spatial distribution of the concentration and oligomeric state of fluorescently labeled proteins in cells. N&B analysis is based on the statistical analysis of fluorescence images by using the method of moments (MoM). Furthermore, N&B analysis can determine the particle number and particle brightness, which indicate the concentration and oligomeric state, respectively. However, the statistical accuracy and precision are limited in actual experiments with fluorescent proteins, owing to low excitation and the limited number of images. In this study, we applied maximum likelihood (ML) estimation and maximum a posteriori (MAP) estimation coupled with the empirical Bayes (EB) method (referred to as EB-MAP). In EB-MAP, we constructed a simple prior distribution for a pixel to utilize the information of the surrounding pixels. To evaluate the accuracy and precision of our method, we conducted simulations and experiments and compared the results of MoM, ML, and EB-MAP. The results showed that MoM estimated the particle number with many outliers. The outliers hampered the visibility of the spatial distribution and cellular structure. In contrast, EB-MAP suppressed the number of outliers and improved the visibility notably. The precision of EB-MAP was better by an order of magnitude in terms of particle number and 1.5 times better in terms of particle brightness compared with those of MoM. The proposed method (EB-MAP-N&B) is applicable to studies on fluorescence imaging and would aid in accurately recognizing changes in the concentration and oligomeric state in cells. Our results hold significant importance because quantifying the concentration and oligomeric state would contribute to the understanding of dynamic processes in molecular mechanism in cells.

This paper proposes a novel forecast reconciliation framework using Bayesian state-space methods. It allows for the joint reconciliation at all forecast horizons and uses predictive distributions rather than past variation of forecast errors. Informative priors are used to assign weights to specific predictions, which makes it possible to reconcile forecasts such that they accommodate specific judgmental predictions or managerial decisions. The reconciled forecasts adhere to hierarchical constraints, which facilitates communication and supports aligned decision-making at all levels of complex hierarchical structures. An extensive forecasting study is conducted on a large collection of 13,118 time series that measure Swiss merchandise exports, grouped hierarchically by export destination and product category. We find strong evidence that in addition to producing coherent forecasts, reconciliation also leads to substantial improvements in forecast accuracy. The use of state-space methods is particularly promising for optimal decision-making under conditions with increased model uncertainty and data volatility. © 2020 Elsevier B.V., European Journal of Operational Research, 291 (2), ISSN:0377-2217, ISSN:1872-6860

Akaike’s Bayesian information criterion (ABIC) has been widely used in inverse ill-posed problems. Little has been done to investigate its statistical aspects. We present an alternative derivation of the marginal distribution of measurements for ABIC under the assumption of normal distributions and show that the principle of ABIC is to statistically estimate the variances of measurements and prior data by maximizing the marginal distribution of measurements. The determination of the regularization parameter with ABIC is essentially equivalent to estimating the relative weighting between measurements and prior data. We prove that ABIC theoretically would produce a biased estimate of the variance of measurements. Since the prior mean is generally unknown but arbitrarily treated as zero in inverse ill-posed problems, ABIC is shown to fail to produce any reasonable estimate for the prior variance. Although ABIC is constructed under the Bayesian framework, it essentially plays more or less the same role as biased regularization from the frequentist’s point of view. ABIC error evaluation cannot be performed under the Bayesian framework but should be more appropriately done with the frequentist’s standpoint in terms of mean squared errors. ABIC is sensitive to prior distributions. In the case of non-informative prior distribution, ABIC leads to the conventional weighted least squares (LS) estimate of parameters and cannot be used to solve inverse ill-posed problems. It is not linked to the regularization parameter but only straightforwardly produces an unbiased estimator for the noise level of measurements, which is only applicable numerically for well-posed problems but not for inverse ill-posed problems. Numerical simulated examples are used to demonstrate the statistical performances of ABIC.

Compressive sensing is an impressive approach for fast MRI. It aims at reconstructing MR image using only a few under-sampled data in k-space, enhancing the efficiency of the data acquisition. In this study, we propose to learn priors based on undecimated wavelet transform and an iterative image reconstruction algorithm. At the stage of prior learning, transformed feature images obtained by undecimated wavelet transform are stacked as an input of denoising autoencoder network (DAE). The highly redundant and multi-scale input enables the correlation of feature images at different channels, which allows a robust network-driven prior. At the iterative reconstruction, the transformed DAE prior is incorporated into the classical iterative procedure by means of proximal gradient algorithm. Experimental comparisons on different sampling trajectories and ratios validated the great potential of the presented algorithm.

Investigation of past accidents has shown that LPG tank accidents cause significant damage to the industry due to the storage of large volumes of flammable materials in them. This study aimed for developing a predictive accident model for dynamic risk assessment of propane storage tanks of the refinery. Hazards and safety barriers were identified using MIMAH methodology. The basis of MIMAH methodology is Bow-tie method. To construct the Bow-tie diagram, first, accidents that occurred on LPG tanks were extracted from the databases of accidents and valid sources. The top events of the accidents were identified and analyzed by the fault tree. The Bow-tie diagrams were constructed and the barriers on the diagrams were identified and verified by refinery experts. According to the SHIPP model, safety barriers were categorized into seven main barriers. The failure rates of the fault tree basic events were extracted from reliable sources and the prior probability of barriers was calculated. Based on the failure or success of safety barriers, 6 levels of severity of consequences, safe, near miss, mishap, incident, and catastrophic accident were considered. Using the prior probability of failure of the barriers, the probability of occurrence of each level of severity of consequences was calculated with the event tree. In the next step, this paper employed LPG storage tanks past accidents to construct a likelihood function and update prior probability using the Bayesian equation. Finally, the posterior probability of occurrence of the consequences was calculated using the posterior probability of failure of the barriers. Because LPG accidents occur with low probability and high severity, predicting accidents dynamically helps people to always be prepared to prevent their occurrence.

The anomaly zoo has caused many to question whether researchers are using the right tests of statistical significance. But even if researchers are using the right tests, they will still draw the wrong conclusions from their econometric analyses if they start out with the wrong priors (i.e., if they start out with incorrect beliefs about the ex ante probability of encountering a tradable anomaly, the “anomaly base rate”). We propose a way to estimate it by combining two key insights: Empirical Bayes methods capture the implicit process by which researchers form priors about the likelihood that a new variable is a tradable anomaly based on their past experience, and under certain conditions, a one-to-one mapping exists between these prior beliefs and the best-fit tuning parameter in a penalized regression. The anomaly base rate varies substantially over time, and we study trading-strategy performance to verify our estimation results.

HighLights • Explore maximum entropy minimum elaborations of simpler maximum entropy models. • Compare maximum entropy priors with parametric modes fitted to elicited quantiles. • Measure uncertainty and disagreement of forecasters with elicited probabilities. • Include the maximizing profit quantile in the newsvendor?s demand distribution., Graphical abstract, Quantiles are available in various problems for developing probability distributions. In some problems quantiles are elicited from experts and used for fitting parametric models, which induce non-elicited information. In some other problems comparisons are made with a quantile of an assumed model which is noncommittal to the quantile information. The maximum entropy (ME) principle provides models that avoid these issues. However, the information theory literature has been mainly concerned about models based on moment information. This paper explores the ME models that are the minimum elaborations of the uniform and moment-based ME models by quantiles. This property provides diagnostics for the utility of elaboration in terms of the information value of each type of information over the other. The ME model with quantiles and moments is represented as the mixture of truncated distributions on consecutive intervals whose shapes and existence are determined by the moments. Elaborations of several ME distributions by quantiles are presented. The ME model based only on quantiles elicited by the fixed interval method possesses a useful property for pooling information elicited from multiple experts. The elaboration of Laplace distribution is an extension of the information theory connection with minimum risk under symmetric loss functions to the asymmetric linear loss. This extension produces a new Asymmetric Laplace distribution. Application examples compare ME priors with a parametric model fitted to elicited quantiles, illustrate measuring uncertainty and disagreement of economic forecasters based on elicited probabilities, and adjust ME models for a fundamental quantile in an inventory management problem.

We introduce a variant of Milgrom and Weber’s (1985) model of n -person games with incomplete information (games for short) and define a correspondence that maps each game to its α -core (the α -core correspondences). Our main objective is to prove such a correspondence to be generically lower semicontinuous. For a multi-valued solution correspondence, the lower semicontinuity is relevant as a theoretical base for predicting outcomes using game-theoretic models. We introduce a family of games parametrized by both payoff functions and information structures (common priors), which allows simultaneous perturbations in those two parameters. We then appeal to Fort’s (1951) theorem to conclude that generic games are essential relative to the parameter space.

We propose a social learning model where agents choose who to communicate with based on the trade-off between collecting information and influencing others' actions. Like-minded people reveal more truthful information, but talking to someone different makes an agent more likely to influence another person's action, because like-minded people will take similar actions anyway. In our model agents start with heterogeneous priors about an unknown state of the world. First agents form coalitions of communication partners. Then everyone observes a private i.i.d. signal and sends a message to her partner. Finally everyone takes an action based on her prior, her private signal, and her partner's message. Our main finding is that when signals and actions are binary, agents form assortative coalitions, even though assortative coalitions are inefficient for social welfare.

Light field (LF) imaging has generated considerable interest owing to its ability to capture both spatial and angular information of light rays simultaneously. However, the extremely large volume of data associated with LF imaging poses challenges to both data storage and transmission. This study addresses this issue by proposing a view synthesis-based LF image compression method using a generative adversarial network (GAN). The primary basis of compression relies on the fact that adjacent sub-aperture images (SAIs) are highly correlated. Accordingly, only sparsely sampled SAIs are transmitted and the others are reconstructed at the decoder side. The proposed sparse SAI sampling method enhances the quality of reconstructed SAIs by considering a fair trade-off between the number of SAIs available for use as priors in the synthesis process and SAI redundancy. The quality of reconstructed SAIs is further enhanced by a GAN-based SAI synthesis method, where the synthesis procedure is broken into disparity estimation and un-sampled SAI estimation components, and the adversarial nature of the jointly trained generative and discriminative networks results in a more accurate generative model. Furthermore, more texture details can be preserved in the synthesized SAIs by adopting a loss function in the GAN model based on perceptual quality. Extensive experimental results demonstrate the superiority of the proposed method relative to several other state-of-the-art compression methods in terms of standard quality metrics and the perceptual quality of the synthetic SAIs at the decoder side.

Exploiting prior/human knowledge is an effective way to enhance Bayesian models, especially in cases of sparse or noisy data, for which building an entirely new model is not always possible. There is a lack of studies on the effect of external prior knowledge in streaming environments, where the data come sequentially and infinitely. In this work, we show the problem of vanishing prior knowledge in streaming variational Bayes. This is a serious drawback in various applications. We then develop a simple framework to boost the external prior when learning a Bayesian model from data streams. By boosting, the prior knowledge can be maintained and efficiently exploited through each minibatch of streaming data. We evaluate the performance of our framework in four scenarios: streaming in synthetic data, streaming sentiment analysis, streaming learning for latent Dirichlet allocation, and streaming text classification, in comparison with the methods that do not keep priors. From extensive experiments, we find that when provided good external knowledge, our framework can improve the performance of a Bayesian model, often by a significant margin for noisy and short text streams.

Introduction: It has been demonstrated that weather conditions have significant impacts on freeway safety. However, when employing an econometric model to examine freeway crash injury severity, most of the existing studies tend to categorize several different adverse weather conditions such as rainy, snowy, and windy conditions into one category, “adverse weather,” which might lead to a large amount of information loss and estimation bias. Hence, to overcome this issue, real-time weather data, the value of meteorological elements when crashes occurred, are incorporated into the dataset for freeway crash injury analysis in this study. Methods: Due to the possible existence of spatial correlations in freeway crash injury data, this study presents a new method, the spatial multinomial logit (SMNL) model, to consider the spatial effects in the framework of the multinomial logit (MNL) model. In the SMNL model, the Gaussian conditional autoregressive (CAR) prior is adopted to capture the spatial correlation. In this study, the model results of the SMNL model are compared with the model results of the traditional multinomial logit (MNL) model. In addition, Bayesian inference is adopted to estimate the parameters of these two models. Result: The result of the SMNL model shows the significance of the spatial terms, which demonstrates the existence of spatial correlation. In addition, the SMNL model has a better model fitting ability than the MNL model. Through the parameter estimate results, risk factors such as vertical grade, visibility, emergency medical services (EMS) response time, and vehicle type have significant effects on freeway injury severity. Practical Application: According to the results, corresponding countermeasures for freeway roadway design, traffic management, and vehicle design are proposed to improve freeway safety. For example, steep slopes should be avoided if possible, and in-lane rumble strips should be recommended for steep down-slope segments. Besides, traffic volume proportion of large vehicles should be limited when the wind speed exceeds a certain grade.

Recent Bayesian reanalyses of prominent trials in critical illness have generated controversy by contradicting the initial conclusions based on conventional frequentist analyses. Many clinicians might be sceptical that Bayesian analysis, a philosophical and statistical approach that combines prior beliefs with data to generate probabilities, provides more useful information about clinical trials than the frequentist approach. In this Personal View, we introduce clinicians to the rationale, process, and interpretation of Bayesian analysis through a systematic review and reanalysis of interventional trials in critical illness. In the majority of cases, Bayesian and frequentist analyses agreed. In the remainder, Bayesian analysis identified interventions where benefit was probable despite the absence of statistical significance, where interpretation depended substantially on choice of prior distribution, and where benefit was improbable despite statistical significance. Bayesian analysis in critical care medicine can help to distinguish harm from uncertainty and establish the probability of clinically important benefit for clinicians, policy makers, and patients.

Group decision-making combined with uncertainty theory is verified as a more conclusive theory, by building a bridge between deterministic and indeterministic group decision-making in this paper. Due to the absence of sufficient historical data, reliability of decisions are mainly determined by experts rather than some prior probability distributions, easily leading to the problem of subjectivity. Thus, belief degree and uncertainty distribution are used in this paper to fit individual preferences, and five scenarios of uncertain chance-constrained minimum cost consensus models are further discussed from the perspectives of the moderator, individual decision-makers and non-cooperators. Through deduction, reaching conditions for consensus and analytic formulas of the minimum total cost are both theoretically given. Finally, with the application in carbon quota negotiation, the proposed models are demonstrated as a further extension of the crisp number or interval preference-based minimum cost consensus models. In other words, the basic conclusions of the traditional models are some special cases of the uncertain minimum cost consensus models under different belief degrees.

Face recognition has become a widely adopted biometric in forensics, security and law enforcement thanks to the high accuracy achieved by systems based on convolutional neural networks (CNNs). However, to achieve good performance, CNNs need to be trained with very large datasets which are not always available. In this paper we investigate the feasibility of using synthetic data to augment face datasets. In particular, we propose a novel generative adversarial network (GAN) that can disentangle identity-related attributes from non-identity-related attributes. This is done by training an embedding network that maps discrete identity labels to an identity latent space that follows a simple prior distribution, and training a GAN conditioned on samples from that distribution. A main novelty of our approach is the ability to generate both synthetic images of subjects in the training set and synthetic images of new subjects not in the training set, both of which we use to augment face datasets. By using recent advances in GAN training, we show that the synthetic images generated by our model are photo-realistic, and that training with datasets augmented with those images can lead to increased recognition accuracy. Experimental results show that our method is more effective when augmenting small datasets. In particular, an absolute accuracy improvement of 8.42% was achieved when augmenting a dataset of less than 60k facial images.

Many data-driven control design methods require the a-priori selection of a reference model to be tracked. In case of limited priors on the plant, such a blind choice might ultimately compromise the overall performance. In this work, we propose a nested strategy for the direct design of Linear Parameter Varying (LPV) controllers from data, in which the reference model is treated as a hyperparameter to be tuned. The proposed approach allows one to jointly optimize the reference model and learn an LPV controller, solely based on soft specifications on the desired closed-loop. The effectiveness of the proposed technique is assessed on a benchmark case study, with the obtained results showing its potential advantages over a state-of-the-art method.

Bayesian clinical trials are becoming popular owing to their adaptive, flexible, and versatile nature. Such trials typically require specification of the prior distribution and construction of the likelihood function; subsequently, inference is made on the basis of the posterior distribution. In comparison with frequentist trial designs, there are less established guidelines on how to report Bayesian trials. We provide a general overview on key components of the design, conduct, and analysis of Bayesian trials and elaborate on the reporting guidelines dos and don'ts.

In some recent works, the authors have proposed and developed an Empirical Bayes framework for frequency estimation. The unknown frequencies in a noisy oscillatory signal are modeled as uniform random variables supported on narrow frequency bands. The bandwidth and the relative band centers are known as hyperparameters which can be efficiently estimated using techniques from subspace identification. In the current paper, we examine carefully how the estimated frequency prior can be used to produce a Bayesian estimate of the unknown frequencies based on the same data (for hyperparameter estimation). To this end, we formulate the Bayesian Maximum A Posteriori (MAP) optimization problem and propose an iterative algorithm to compute its solution. Then, we do extensive simulations under various parameter configurations, showing that the MAP estimate of the frequencies are asymptotically close to the band centers of the frequency priors. These results provide an attractive link between the conventional Bayesian method and the Empirical Bayes method for frequency estimation, and in retrospect justify the use of the latter.

Vehicle loads such as those due to vehicle mass and road grade need to be determined from measurements. However, due to the uncertainties of measurements, the corresponding estimations are uncertain as well. This paper addresses parallel vehicle mass and road grade estimation problems with a Bayesian inversion-based approach, intending to give estimations in a statistical sense. The parallel estimation problem is firstly reformulated as a statistical inverse problem. Then, the assumption is made on the prior probability distribution of vehicle mass and road grade. The posterior is updated by feeding measured data and the best estimation is determined according to the obtained posterior distribution. Comprehensive validation of the estimation performance is conducted statistically for the proposed method with a comparison with least squares approach. The results indicate that the Bayesian inversion approach gives a parallel estimation with higher statistical reliability than least squares method.

This paper attempts to bridge the gap between standard engineering practice and machine learning when modelling stochastic processes. For a number of physical processes of interest, derivation of the (auto)covariance is achievable. This paper suggests their use as priors in a standard Gaussian process regression as a means of enhancing predictive capability in situations where they are reflective of the process of interest. A covariance function of a linear oscillator under random load is derived and used in a regression context to predict the displacements of a vibratory system. A simulation case study is used to demonstrate the enhancement over a standard Gaussian process regression model.

This article addresses the estimation of differential entropy of the Weibull distribution based on different non-informative prior distributions. We first derive non-informative priors using formal rules, such as Jeffreys prior and maximal data information prior based on Fisher information and entropy, respectively. We also develop reference prior and probability matching prior for the differential entropy. Next, we investigate the effects of these priors in the Bayes estimates of the differential entropy of the Weibull distribution based on complete sample. The Bayes estimates are computed using random-walk Metropolis-Hastings algorithms. We use Monte Carlo simulation to evaluate the performance of the Bayes estimates of differential entropy in terms of bias and root mean-squared error, while highest posterior density credible intervals are assessed in terms of average width and coverage probabilities. Finally, a real data set has been analyzed for illustrative purposes.

An object can be consisting of various attributes, such as illuminance, appearance, shape, orientation, etc. Separately extract these attributes has enormous value in visual effects modeling, attribute-specific retrieval and recognition. Essentially, these attributes can be fairly abstract and thus need labels to extract. However, sometimes the labels of these attributes may not be available with training data. A solution to this problem is projecting the observed data into a lower dimension latent subspace, such that each observed data can be represented by a latent variable. After that, the dimensions of a latent variable can be segmented into different parts by weighting the kernel automatic relevance determination (ARD) parameters. Consequently, the latent variable is segmented into different parts each of which corresponds to the main attribute. In real life scenery, the attributes of an object may vary significantly from case to case. For instance, a single face can probably be under different illuminance conditions. Taking into account the diversity of these attribute variations, we propose the Diversified Shared Latent Variable Model (DSLVM) to extract and manipulate object attributes in an unsupervised way. More specifically, we initially set up two views that share the same latent variables. Then, two Diversity Encouraging (DE) priors are applied to the inducing points of each model view. Here, the inducing points are a small representative dataset that explains the observed data in its entirety. Meanwhile, the exploited diversity encouraging priors are able to cover more diverse characteristics of the attributes. The defined objective function is computed by variational inference. Extensive experiments on different datasets demonstrate that our method can accurately deal with various object.