稀疏组lasso罚向量自回归模型的大气污染物预测:京津冀案例研究

进行了大气污染物预测研究。针对传统的向量自回归模型方法所面临的过参数化问题,提出了稀疏组lasso罚向量自回归模型并应用近邻梯度下降法求解模型参数。为了验证模型的有效性,将其应用于2015年京津冀大气污染物数据中并对2016年1月1日北京6项大气污染物浓度进行预测。实验数据表明:基于稀疏组lasso罚模型的PM2.5预测归一化均方误差约为3.8%,预测精度高于向量自回归(VAR)模型、基于各种稀疏结构的向量自回归(VAR-L)模型、分层向量自回归(HVAR)模型。此外,京津冀不同城市对北京的空气质量影响程度不同,这可以通过组内稀疏模型参数进行解释。将凸优化概念与向量自回归模型结合应用于大气污染物浓度的预测中,对京津冀大气污染协同治理具有重要意义。     

在线Group Lasso学习

对高维流式数据的在线组变量选择问题进行了研究，提出了带Group Lasso惩罚的逻辑斯蒂回归在线估计方法，并给出了GFTPRL (Group Follow the Proximally Regularized Leader)算法。通过给出GFTPRL算法的缺憾界，证明了算法在理论上是有效的。实验结果表明，对于稀疏模型GFTPRL算法的预测分类准确率明显优于其他主流稀疏在线算法。     

基于改进LSSVM的动态测量误差实时预测方法

误差修正是提高动态测量精度的有效途径,其中误差的建模是关键.在分析现有动态测量误差预测技术不足的基础上,提出基于改进的最小二乘支持向量机的动态测量误差回归建模和预测方法.在最小二乘支持向量机的基础上,通过将价值函数改为最小二乘价值函数以及用等式约束代替不等式约束,将求解的二次规划问题转变为一组等式方程,减少了待定参数的个数,很大程度地缩短了支持向量机的训练时间;同时针对最小二乘支持向量机稀疏性丢失这一缺陷,采用剪枝算法改进其性能,使其具有更好的稀疏性.通过实例验证及与其他建模方法的对比,表明该方法具有优良的预测效果和动态性能,为动态测量误差预测提供了一种新的可行方法.     

变量选择集成方法

随着海量高维数据在众多研究和应用领域的不断涌现,如何利用数据的稀疏性特征,从中挖掘到有价值的信息显得至关重要．变量选择作为可解释性建模、提高统计推断和预测精度的有效工具,在高维数据的分析中发挥着愈来愈重要的作用．由于集成学习能显著提高选择精度、缓解变量选择过程的不稳定性、降低噪声变量被误选的机率,变量选择集成方法近年来得到了广泛研究．为了给相关方向的研究者提供一个系统的参考资料,论文对现有的变量选择集成方法进行了详细阐述,按照构建集成所用的不同策略将其分为两大类,分析了各类方法的特征,并采用数值试验研究了各类方法在变量选择、预测等方面的性能．最后,论文对变量选择集成方法在未来值得研究的方向进行了探讨．     

岭回归协助稀疏表示红外小目标检测

提出一种基于岭回归协助稀疏表示的红外小目标检测方法。该方法分别采用二维高斯模型和正态分布随机矩阵生成红外小目标样本和背景样本,继而建立超完备字典。红外小目标检测包括两个阶段,在第一阶段利用岭回归表示快速计算所有测试样本的岭回归重建误差;在第二阶段,根据岭回归重建误差自适应选择候选目标,并计算其稀疏表示重建误差实现目标检测。对提出的方法进行了实验验证,结果表明:提出的方法具有较快的速度和较强的鲁棒性。     

频域组稀疏滚动轴承特征提取方法

针对时域非平稳振动信号模式混叠、信噪比低,以及传统稀疏表示算法模型复杂、优化求解算法难以确定,导致故障特征提取难的问题,提出了频域组稀疏和群桥约束改进迭代收缩阈值优化的故障特征提取方法（Group Sparse Representation in Frequency Domain,GSRF）。将振动信号转换至频域并对变量分组,构造施加群桥约束的最小二乘回归模型,准确筛选冲击相关变量;引入迭代重加权系数简化方程,以软阈值收缩优化求解频域稀疏信号;对重构的时域稀疏信号进行包络频谱分析提取故障特征。试验结果表明,提出的频域组稀疏算法优于传统的结合L21范数约束的组稀疏索套方法,可有效提取微弱故障特征,实现稀疏域下的轴承故障诊断。     

异方差随机系数回归模型的最优设计

最优设计方法在工程技术领域和工农业生产中具有广泛的应用．随机系数模型的最优设计研究中通常假定随机误差项具有相同的方差,实际中误差的产生往往与观测点有关,从而具有异方差性质．本文研究一般闭区间设计域上异方差随机系数回归模型的最优近似设计问题．我们获得了最优设计可以在设计域的两个端点处得到的一组充分条件,并进一步证明了当误差项方差具有对称结构且设计域是对称区间时,设计域两个对称端点处的等权重设计同时具有多重最优性质,这时最优设计不依赖于模型中随机误差项的方差结构及随机系数项的方差．     

基于正则化稀疏滤波的轴承声信号故障诊断方法

基于声信号的故障诊断由于其所具有的非接触、易安装等优点开始逐渐在机械故障诊断领域中得到广泛应用,但声信号的信噪比低导致其诊断准确率较差,因此急需有效的智能方法以实现噪声背景下的信号特征提取。稀疏滤波算法是一种基于无监督学习的智能特征提取算法,它能够优化特征分布的稀疏性从而得到好的特征表达。为了实现轴承声信号的特征提取和故障诊断,采用稀疏滤波算法从声信号频谱中提取特征,通过对其目标函数添加L2 范数约束以减少过拟合现象,然后采用Softmax 回归函数作为分类器,实现对不同轴承故障类型的精准识别。最后通过一组特殊设计的轴承故障诊断实验验证了所提方法的有效性。     

爆破振动对民房破坏效应预测的BDA模型及应用

爆破振动危险程度的预测与控制是爆破工程中不容忽视的重要内容。基于Bayes判别分析理论,建立爆破振动对民房破坏效应预测的Bayes判别分析模型(BDA);选用爆破振动幅值、主频率、主频率持续时间、灰缝强度、砖墙面积率、房屋高度、屋盖形式、圈梁构造柱、施工质量、场地条件等10个影响因素作为判别因子;将该方法应用到铜绿山矿露天采场爆破振动对民房破坏效应预测问题中,对现场实测的64组爆破振动数据作为学习样本进行训练,建立相应线性判别函数并利用回代估计方法进行回检,误判率为0.0938;用另外12组现场数据作为预测样本进行测试。研究结果表明:经过训练后的BDA模型预测结果与实际情况吻合较好,预测精度高,回代估计的误判率低,为露天采矿爆破振动对民房破坏效应的预测提供了一种新思路。     

基于正则化稀疏滤波的轴承声信号故障诊断方法

基于声信号的故障诊断由于其所具有的非接触、易安装等优点开始逐渐在机械故障诊断领域中得到广泛应用，但声信号的信噪比低导致其诊断准确率较差，因此急需有效的智能方法以实现噪声背景下的信号特征提取。稀疏滤波算法是一种基于无监督学习的智能特征提取算法，它能够优化特征分布的稀疏性从而得到好的特征表达。为了实现轴承声信号的特征提取和故障诊断，采用稀疏滤波算法从声信号频谱中提取特征，通过对其目标函数添加L2 范数约束以减少过拟合现象，然后采用Softmax 回归函数作为分类器，实现对不同轴承故障类型的精准识别。最后通过一组特殊设计的轴承故障诊断实验验证了所提方法的有效性。     

Adaptive modelling of gene regulatory network using Bayesian information criterion‐guided sparse regression approach

Inferring gene regulatory networks (GRNs) from microarray expression data are an important but challenging issue in systems biology. In this study, the authors propose a Bayesian information criterion (BIC)‐guided sparse regression approach for GRN reconstruction. This approach can adaptively model GRNs by optimising the l ₁ ‐norm regularisation of sparse regression based on a modified version of BIC. The use of the regularisation strategy ensures the inferred GRNs to be as sparse as natural, while the modified BIC allows incorporating prior knowledge on expression regulation and thus avoids the overestimation of expression regulators as usual. Especially, the proposed method provides a clear interpretation of combinatorial regulations of gene expression by optimally extracting regulation coordination for a given target gene. Experimental results on both simulation data and real‐world microarray data demonstrate the competent performance of discovering regulatory relationships in GRN reconstruction.Inspec keywords: genetics, Bayes methods, genomics, regression analysis, inference mechanisms, bioinformaticsOther keywords: adaptive modelling, gene regulatory network, Bayesian information criterion‐guided sparse regression approach, GRN, microarray expression data, systems biology, GRN reconstruction, optimisation, l₁ ‐norm regularisation     

Reliability enhancement of mixed-domain seismic inversion with bounding constraints

Seismic inversion works as one of pragmatic and effective approaches to estimate the subsurface parameters. One robust Bayesian sparse inversion method incorporating the mixed-domain convolution with model bounding constraints is proposed in this study. The time-domain response and partial frequency components are utilized in mixed-domain seismic inversion to improve the resolution and stability of seismic inversion. First, the objective updated function is yielded with Bayesian inference in joint time and frequency domain. And, the sparse constraint is incorporated into the objective function to improve robustness of inversion algorithm. Conventional seismic inversion methods always don’t focus on the lower and upper bounding constraints on subsurface model parameters, due to which unrealistic predicted results may arise. To get rid of the problem, the bounding constraints on P-wave impedance elaborated by logarithmic or inverse hyperbolic tangent formulas is introduced in mixed-domain seismic inversion as it renders to reduce the unrealistic parameters and enhance the reliability of prediction effectively. In addition, the synthetic examples demonstrate the effectiveness and robustness of the proposed inversion algorithm. Finally, one field case is studied carefully and the estimated parameters with bounding constraints at the borehole-side location can preserve a high degree of agreements with real logging data to verify the practicability of the bounding-constraining mixed-domain Bayesian inversion.     

Prediction of Compressive Strength of Various SCC Mixes Using Relevance Vector Machine

This paper discusses the applicability of relevance vector machine (RVM) based regression to predict the compressive strength of various self compacting concrete (SCC) mixes. Compressive strength data various SCC mixes has been consolidated by considering the effect of water cement ratio, water binder ratio and steel fibres. Relevance vector machine (RVM) is a machine learning technique that uses Bayesian inference to obtain parsimonious solutions for regression and classification. The RVM has an identical functional form to the support vector machine, but provides probabilistic classification and regression. RVM is based on a Bayesian formulation of a linear model with an appropriate prior that results in a sparse representation. Compressive strength model has been developed by using MATLAB software for training and prediction. About 75% of the data has been used for development of model and 30% of the data is used for validation. The predicted compressive strength for SCC mixes is found to be in very good agreement with those of the corresponding experimental observations available in the literature.     

Remaining Life Prediction Based on Wiener Processes with ADT Prior Information

Precisely predicting the remaining life for an individual plays an important role in condition‐based maintenance, so Bayesian inference method, which can integrate useful data from several sources to improve the prediction accuracy, has became a research hot. Aiming at the situation that accelerated degradation tests have been widely applied to assess the reliability of products, a remaining life prediction method based on Bayesian inference by taking accelerated degradation data as prior information is proposed. A Wiener process with random drift, diffusion parameters is used to model degradation data, and conjugate prior distributions of random parameters are adopted. To solve the problem that it is hard to estimate the hyper parameters from accelerated degradation data using an Expectation Maximization algorithm, a data extrapolation method is developed. With acceleration factors, degradation data are extrapolated from accelerated stress levels to the normal use stress level. Acceleration factor constant hypothesis is used to deduce the expression of acceleration factor for a Wiener degradation model. Besides, simulation tests are designed to validate the proposed method. The method of constructing the confidence levels for the remaining life predictions is also provided. Finally, a case study is used to illustrate the application of our developed method. Copyright © 2015 John Wiley & Sons, Ltd.     

Seismic fragility analysis of structures based on Bayesian linear regression demand models

Bayesian linear regression (BLR) based demand prediction models are proposed for efficient seismic fragility analysis (SFA) of structures utilizing limited numbers of nonlinear time history analyses results. In doing so, two different BLR models i.e. one based on the classical Bayesian least squares regression and another based on the sparse Bayesian learning using Relevance Vector Machine are explored. The proposed models integrate both the record-to-record variation of seismic motions and uncertainties due to structural model parameters. The magnitude of uncertainty involved in the fragility estimate is represented by providing a confidence bound of the fragility curve. The effectiveness of the proposed BLR models are compared with the commonly used cloud method and the maximum likelihood estimates methods of SFA by considering a nonlinear single-degree-of-freedom system and a five-storey reinforced concrete building frame. It is observed that both the BLR models can estimate fragility with improved accuracy compared to those common analytical SFA approaches considering direct Monte Carlo simulation based fragility results as the benchmark.     

Sensibility of Bayesian inference methods for reliability prediction of ageing systems,case of Diesel locomotives

This paper addresses the problem of reliability analysis of in-service identical systems when a limited number of lifetime data is available compared to censored ones. Lifetime (resp. censored) data characterise the life of failed (resp. non-failed) systems in the sample. Because, censored data induce biassed estimators of reliability model parameters, a methodology approach is proposed to overcome this inconvenience and improve the accuracy of the parameter estimation based on Bayesian inference methods. These methods combine, in an effective way, system’s life data and expert opinions learned from failure diagnosis of similar systems. Three Bayesian inference methods are considered: Classical Bayesian, Extended Bayesian and Bayesian Restoration Maximisation methods. Given a sample of lifetime data, simulated according to prior opinions of maintenance expert, a sensibility analysis of each Bayesian method is performed. Reliability analysis of critical subsystems of Diesel locomotives is established under the proposed methodology approach. The relevance of each Bayesian inference methods with respect to collected reliability data of critical subsystems and expert opinions is discussed.     

Model validation under epistemic uncertainty

This paper develops a methodology to assess the validity of computational models when some quantities may be affected by epistemic uncertainty. Three types of epistemic uncertainty regarding input random variables - interval data, sparse point data, and probability distributions with parameter uncertainty - are considered. When the model inputs are described using sparse point data and/or interval data, a likelihood-based methodology is used to represent these variables as probability distributions. Two approaches - a parametric approach and a non-parametric approach - are pursued for this purpose. While the parametric approach leads to a family of distributions due to distribution parameter uncertainty, the principles of conditional probability and total probability can be used to integrate the family of distributions into a single distribution. The non-parametric approach directly yields a single probability distribution. The probabilistic model predictions are compared against experimental observations, which may again be point data or interval data. A generalized likelihood function is constructed for Bayesian updating, and the posterior distribution of the model output is estimated. The Bayes factor metric is extended to assess the validity of the model under both aleatory and epistemic uncertainty and to estimate the confidence in the model prediction. The proposed method is illustrated using a numerical example.     

A joint-probability approach to crash prediction models

Many road safety researchers have used crash prediction models, such as Poisson and negative binomial regression models, to investigate the associations between crash occurrence and explanatory factors. Typically, they have attempted to separately model the crash frequencies of different severity levels. However, this method may suffer from serious correlations between the model estimates among different levels of crash severity. Despite efforts to improve the statistical fit of crash prediction models by modifying the data structure and model estimation method, little work has addressed the appropriate interpretation of the effects of explanatory factors on crash occurrence among different levels of crash severity. In this paper, a joint probability model is developed to integrate the predictions of both crash occurrence and crash severity into a single framework. For instance, the Markov chain Monte Carlo (MCMC) approach full Bayesian method is applied to estimate the effects of explanatory factors. As an illustration of the appropriateness of the proposed joint probability model, a case study is conducted on crash risk at signalized intersections in Hong Kong. The results of the case study indicate that the proposed model demonstrates a good statistical fit and provides an appropriate analysis of the influences of explanatory factors.     

计量中回归模型参数值及其不确定度评估

针对计量领域中广泛应用的数据回归处理方法,阐述了在基于正态分布噪声条件下,最小二乘法与贝叶斯推断法用于回归模型参数估计以及相应不确定度评估的过程。GUM系列不确定度评估准则中没有明确指出如何对回归参数进行不确定度评估,同时有些回归模型也无法唯一地转化为相应的测量方程。通过计量校准的实例说明了如何处理相应参数的确定等问题,以此说明2种方法的相同与不同之处。最小二乘方法计算简单直接且便于使用;而基于贝叶斯推断的方法则能充分利用计量校准中的经验和历史数据等信息,但由于其参数后验分布计算通常较为复杂,需采用马尔科夫链-蒙特卡罗(MCMC)法通过数值计算得到关注参数的结果。     

Bayesian model robustness via disparities

This paper develops a methodology for robust Bayesian inference through the use of disparities. Metrics such as Hellinger distance and negative exponential disparity have a long history in robust estimation in frequentist inference. We demonstrate that an equivalent robustification may be made in Bayesian inference by substituting an appropriately scaled disparity for the log likelihood to which standard Monte Carlo Markov Chain methods may be applied. A particularly appealing property of minimum-disparity methods is that while they yield robustness with a breakdown point of 1/2, the resulting parameter estimates are also efficient when the posited probabilistic model is correct. We demonstrate that a similar property holds for disparity-based Bayesian inference. We further show that in the Bayesian setting, it is also possible to extend these methods to robustify regression models, random effects distributions and other hierarchical models. These models require integrating out a random effect; this is achieved via MCMC but would otherwise be numerically challenging. The methods are demonstrated on real-world data.