基于贝叶斯权函数的模型无关元学习算法

模型无关的元学习(MAML)是一种多任务的元学习算法,能使用不同的模型,并快速地在不同任务之间进行适应,但MAML在训练速度与准确率上还亟待提高.从高斯随机过程的角度出发对MAML的原理进行分析,提出一种基于贝叶斯权函数的模型无关元学习(BW-MAML)算法,该权函数利用贝叶斯分析设计并用于损失的加权.训练过程中,BW...     

Variational Bayesian methods for spatial data analysis

With scientific data available at geocoded locations, investigators are increasingly turning to spatial process models for carrying out statistical inference. However, fitting spatial models often involves expensive matrix decompositions, whose computational complexity increases in cubic order with the number of spatial locations. This situation is aggravated in Bayesian settings where such computations are required once at every iteration of the Markov chain Monte Carlo (MCMC) algorithms. In this paper, we describe the use of Variational Bayesian (VB) methods as an alternative to MCMC to approximate the posterior distributions of complex spatial models. Variational methods, which have been used extensively in Bayesian machine learning for several years, provide a lower bound on the marginal likelihood, which can be computed efficiently. We provide results for the variational updates in several models especially emphasizing their use in multivariate spatial analysis. We demonstrate estimation and model comparisons from VB methods by using simulated data as well as environmental data sets and compare them with inference from MCMC.     

Bayesian multiscale analysis of images modeled as Gaussian Markov random fields

A Bayesian multiscale technique for the detection of statistically significant features in noisy images is proposed. The prior is defined as a stationary intrinsic Gaussian Markov random field on a toroidal graph, which enables efficient computation of the relevant posterior marginals. Hence the method is applicable to large images produced by modern digital cameras. The technique is demonstrated in two examples from medical imaging.     

Variational Bayesian method for speech enhancement

In this paper, we propose to use variational Bayesian (VB) method to learn the clean speech signal from noisy observation directly. It models the probability distribution of clean signal using a Gaussian mixture model (GMM) and minimizes the misfit between the true probability distributions of hidden variables and model parameters and their approximate distributions. Experimental results demonstrate that the performance of the proposed algorithm is better than that of some other methods.     

Similarity analysis in Bayesian random partition models

This work proposes a method to assess the influence of individual observations in the clustering generated by any process that involves random partitions. We call it Similarity Analysis. It basically consists of decomposing the estimated similarity matrix into an intrinsic and an extrinsic part, coupled with a new approach for representing and interpreting partitions. Individual influence is associated with the particular ordering induced by individual covariates, which in turn provides an interpretation of the underlying clustering mechanism. We present applications in the context of Species Sampling Mixture Models (SSMMs), including Bayesian density estimation and dependent linear regression models.     

Model validation and predictive capability for the thermal challenge problem

We address the thermal problem posed at the Sandia Validation Challenge Workshop. Unlike traditional approaches that confound calibration with validation and prediction, our approach strictly distinguishes these activities, and produces a quantitative measure of model-form uncertainty in the face of available data. We introduce a general validation metric that can be used to characterize the disagreement between the quantitative predictions from a model and relevant empirical data when either or both predictions and data are expressed as probability distributions. By considering entire distributions, this approach generalizes traditional approaches to validation that focus only on the mean behaviors of predictions and observations. The proposed metric has several desirable properties that should make it practically useful in engineering, including objectiveness and robustness, retaining the units of the data themselves, and generalizing the deterministic difference. The metric can be used to assess the overall performance of a model against all the experimental observations in the validation domain and it can be extrapolated to express predictive capability of the model under conditions for which direct experimental observations are not available. We apply the metric and the scheme for characterizing predictive capability to the thermal problem.     

A Bayesian multilevel model for fMRI data analysis

Bayesian approaches have been proposed by several functional magnetic resonance imaging (fMRI) researchers in order to overcome the fundamental limitations of the popular statistical parametric mapping method. However, the difficulties associated with subjective prior elicitation have prevented the widespread adoption of the Bayesian methodology by the neuroimaging community. In this paper, we present a Bayesian multilevel model for the analysis of brain fMRI data. The main idea is to consider that all the estimated group effects (fMRI activation patterns) are exchangeable. This means that all the collected voxel time series are considered manifestations of a few common underlying phenomena. In contradistinction to other Bayesian approaches, we think of the estimated activations as multivariate random draws from the same distribution without imposing specific prior spatial and/or temporal information for the interaction between voxels. Instead, a two-stage empirical Bayes prior approach is used to relate voxel regression equations through correlations between the regression coefficient vectors. The adaptive shrinkage properties of the Bayesian multilevel methodology are exploited to deal with spatial variations, and noise outliers. The characteristics of the proposed model are evaluated by considering its application to two real data sets.     

基于贝叶斯通用背景模型的图像标注

在高斯图特征提取过程中,通用背景模型(Universal background model, UBM) 方法常用于根据总体分布估计每一幅图像中特征点分布的高斯混合模型(Gaussian mixture model, GMM)参数. 然而UBM估计的GMM权重参数中有很多接近零的数值,它们所对应的高斯分量对分布估计贡献小却又都参与了计算, 因此UBM的时间复杂度较高. 为解决这个问题,本文提出Bayes UBM方法. 通过引入受限的对称Dirichlet分布来描述GMM权重参数的先验分布,利用Bayes最大后验概率对GMM参数集进行估计. 实验表明Bayes UBM方法不仅有效地降低了时间复杂度,而且提高了Corel数据集上的图像标注精度.     

Being Bayesian About Network Structure. A Bayesian Approach to Structure Discovery in Bayesian Networks

In many multivariate domains, we are interested in analyzing the dependency structure of the underlying distribution, e.g., whether two variables are in direct interaction. We can represent dependency structures using Bayesian network models. To analyze a given data set, Bayesian model selection attempts to find the most likely (MAP) model, and uses its structure to answer these questions. However, when the amount of available data is modest, there might be many models that have non-negligible posterior. Thus, we want compute the Bayesian posterior of a feature, i.e., the total posterior probability of all models that contain it. In this paper, we propose a new approach for this task. We first show how to efficiently compute a sum over the exponential number of networks that are consistent with a fixed order over network variables. This allows us to compute, for a given order, both the marginal probability of the data and the posterior of a feature. We then use this result as the basis for an algorithm that approximates the Bayesian posterior of a feature. Our approach uses a Markov Chain Monte Carlo (MCMC) method, but over orders rather than over network structures. The space of orders is smaller and more regular than the space of structures, and has much a smoother posterior landscape. We present empirical results on synthetic and real-life datasets that compare our approach to full model averaging (when possible), to MCMC over network structures, and to a non-Bayesian bootstrap approach.     

BayesChess: A computer chess program based on Bayesian networks

In this paper, we introduce a chess program able to adapt its game strategy to its opponent, as well as to adapt the evaluation function that guides the search process according to its playing experience. The adaptive and learning abilities have been implemented through Bayesian networks. We show how the program learns through an experiment consisting on a series of games that point out that the results improve after the learning stage.     

面向图像复原的分层贝叶斯局部高斯混合模型

近年来使用高斯模型作为块先验的贝叶斯方法取得了优秀的图像去噪性能,但是这一方法在去噪之外的逆问题求解方面性能不太稳定。提出一种基于分层贝叶斯的高斯混合模型对图像块建模,对模型参数引入先验知识,利用Gaussian-Wishart分布对均值和协方差矩阵的概率分布建模,使得块估计过程更加稳定。基于邻近块的相干性,利用L2范数度量完成局部窗口中相似块的聚类,局部窗口相似块利用特定均值和协方差的多元高斯概率分布建模,利用累加平方图及快速傅里叶变换的数值优化方法,加快相似性度量的计算时间。使用基于马式距离的高斯分布相似度的聚合权重,结合图像上的空间域高斯相似度,更好地拟合自然图像的统计特性。通过实验验证了提出的模型在图像复原求解中的有效性。     

GP-BayesFilters: Bayesian filtering using Gaussian process prediction and observation models

Bayesian filtering is a general framework for recursively estimating the state of a dynamical system. Key components of each Bayes filter are probabilistic prediction and observation models. This paper shows how non-parametric Gaussian process (GP) regression can be used for learning such models from training data. We also show how Gaussian process models can be integrated into different versions of Bayes filters, namely particle filters and extended and unscented Kalman filters. The resulting GP-BayesFilters can have several advantages over standard (parametric) filters. Most importantly, GP-BayesFilters do not require an accurate, parametric model of the system. Given enough training data, they enable improved tracking accuracy compared to parametric models, and they degrade gracefully with increased model uncertainty. These advantages stem from the fact that GPs consider both the noise in the system and the uncertainty in the model. If an approximate parametric model is available, it can be incorporated into the GP, resulting in further performance improvements. In experiments, we show different properties of GP-BayesFilters using data collected with an autonomous micro-blimp as well as synthetic data.

Bayes网络学习的MCMC方法

基于Bayes统计理论, 提出了一种从数据样本中学习Bayes网络的Markov链Monte Carlo(MCMC)方法. 首先通过先验概率和数据样本的结合得到未归一化的后验概率, 然后使用此后验概率指导随机搜索算法寻找“好”的网络结构模型. 通过对Alarm网络的学习表明了本算法具有较好的性能.     

A study on the life of an innovative product using a Bayesian approach

In this paper, the life cycle of an innovative product is divided into three stages, where a nonhomogeneous Poisson process (NHPP) with a power law intensity function is employed to illustrate the entry process of rival firms in a competitive market. The effects of the competitors’ entry on the profits of the incumbent firm are taken into consideration, with an objective of deriving the optimal product life to maximize the incumbent’s profit. Furthermore, a case study of a new type of LCD (liquid–crystal display) TV is empirically investigated to examine the effectiveness of the proposed approach. The results of the posterior analysis suggest that the influence of the competitors’ entry on the optimal product life is overestimated in the prior analysis. The results of sensitivity analyses indicate that the effect of competition of the introduction and growth stages on the optimal product life is greater than that of the maturation stage on the optimal product life, which is subsequently greater than that of the decline stage on the optimal product life.     

Development of a computer game-based framework for cognitive behaviour identification by using Bayesian inference methods

In this work a novel technique for cognitive behavioural data acquisition via computer/console games is introduced by which the user feels more relax than s/he is in a formal environment (e.g., labs and clinics) and has less disruption as s/he provides cognitive data sequence by playing a game. The method can be adapted into any game and is based on the assumption that in this way more efficient analysis of mind can be made to unveil the cognitive or mental characteristics of an individual. In experiments of the proposed work a commercial console game was utilised by different users to complete the tasks in which each game player followed his/her own optional scenarios of the game for a certain period of time. The attributes were then extracted from the behavioural video data sequence by visual inspection where each one corresponds to user’s behavioural characteristics spotted throughout the game and then analysed by the Bayesian network utility. At the end of all the experiments, two types of results were obtained: semantic representation of behavioural attributes and classification of personal behavioural characteristics. The approach is proved to be a unique way and helped identify general and specific behavioural characteristics of the individuals and is likely to open new areas of applications.     

Distributed monitoring for large-scale processes based on multivariate statistical analysis and Bayesian method

Large-scale plant-wide processes have become more common and monitoring of such processes is imperative. This work focuses on establishing a distributed monitoring scheme incorporating multivariate statistical analysis and Bayesian method for large-scale plant-wide processes. First, the necessity of distributed monitoring is demonstrated by theoretical analysis on the impact of process decomposition on multivariate statistical process monitoring performance. Second, a stochastic optimization algorithm-based performance-driven process decomposition method is proposed which aims to achieve the best possible monitoring performance from process decomposition aspect. Based on the obtained sub-blocks, local monitors are established to characterize local process behaviors, and then a Bayesian fault diagnosis system is established to identify the underlying process status of the entire process. The proposed distributed monitoring scheme is applied on a numerical example and the Tennessee Eastman benchmark process. Comparison results to some state-of-the-art methods indicate the efficiency and feasibility.     

Variational Bayesian data analysis on manifold

In this paper, variational inference is studied on manifolds with certain metrics. To solve the problem, the analysis is first proposed for the variational Bayesian on Lie group, and then extended to the manifold that is approximated by Lie groups. Then the convergence of the proposed algorithm with respect to the manifold metric is proved in two iterative processes: variational Bayesian expectation (VB-E) step and variational Bayesian maximum (VB-M) step. Moreover, the effective of different metrics for Bayesian analysis is discussed.     

Bayesian semiparametric analysis of short- and long-term hazard ratios with covariates

A full Bayesian analysis is developed for an extension to the short-term and long-term hazard ratios model that has been previously introduced. This model is specified by two parameters, short- and long-term hazard ratios respectively, and an unspecified baseline function. Furthermore, the model also allows for crossing hazards in two groups and includes the proportional hazards, and the proportional odds models as particular cases. The model is extended to include covariates in both, the short- and long-term parameters, and uses a Bayesian nonparametric prior, based on increasing additive processes mixtures, to model the baseline function. Posterior distributions are characterized via their full conditionals. Latent variables are introduced wherever needed to simplify computations. The algorithm is tested with a simulation study and posterior inference is illustrated with a survival study of ovarian cancer patients who have undergone a treatment with erythropoietin stimulating agents.