Facial Landmark Localization by Gibbs Sampling

In this paper, we introduce a novel method for facial landmark detection. We localize facial landmarks according to the MAP crite rion. Conventional gradient ascent algorithms get stuck at the local optimal solution. Gibbs sampling is a kind of Markov Chain Monte Carlo （MCMC） algorithm. We choose it for optimization because it is easy to implement and it guarantees global conver gence. The posterior distribution is obtained by learning prior distribution and likelihood function. Prior distribution is assumed Gaussian. We use Principle Component Analysis （PCA） to reduce the dimensionality and learn the prior distribution. Local Linear Support Vector Machine （LLSVM） is used to get the likelihood function of every key point. In our experiment, we compare our de tector with some other wellknown methods. The results show that the proposed method is very simple and efficient. It can avoid trapping in local optimal solution.

基于LightGBM-Gibbs Sampling的特征选择算法研究

针对数据维度较高、数据的冗余性导致模型训练带来的复杂性和挖掘不足的问题,创新性地提出了一种基于轻量梯度提升机(light gradient boosting machine,LightGBM)算法的吉布斯采样(Gibbs Sampling)方法,获取近似于目标分布的样本数据集,对样本数据集进行分析得到每个特征的重要度,选取一定的特征实现特征选择,实现降维。为验证这种方法的有效性,选取一些典型的特征选择算法进行对比,通过交叉验证的方法,与之进行比较,发现基于Gibbs Sampling的特征选择算法会取得更好的准确率,与原始数据集相比,能有效降低特征,同时提高了模型预测能力。

基于吉布斯采样的稀疏水声信道估计方法

The estimation of sparse underwater acoustic(UWA)channels can be regarded as an inference problem involving hidden variables within the Bayesian framework.While the classical sparse Bayesian learning(SBL),derived through the expectation maximization(EM)algorithm,has been widely employed for UWA channel estimation,it still differs from the real posterior expectation of channels.In this paper,we propose an approach that combines variational inference(VI)and Markov chain Monte Carlo(MCMC)methods to provide a more accurate posterior estimation.Specifically,the SBL is first re-derived with VI,allowing us to replace the posterior distribution of the hidden variables with a variational distribution.Then,we determine the full conditional probability distribution for each variable in the variational distribution and then iteratively perform random Gibbs sampling in MCMC to converge the Markov chain.The results of simulation and experiment indicate that our estimation method achieves lower mean square error and bit error rate compared to the classic SBL approach.Additionally,it demonstrates an acceptable convergence speed.

A Bayesian Mixture Model Approach to Disparity Testing

The topic of this article is one-sided hypothesis testing for disparity, i.e., the mean of one group is larger than that of another when there is uncertainty as to which group a datum is drawn. For each datum, the uncertainty is captured with a given discrete probability distribution over the groups. Such situations arise, for example, in the use of Bayesian imputation methods to assess race and ethnicity disparities with certain insurance, health, and financial data. A widely used method to implement this assessment is the Bayesian Improved Surname Geocoding (BISG) method which assigns a discrete probability over six race/ethnicity groups to an individual given the individual’s surname and address location. Using a Bayesian framework and Markov Chain Monte Carlo sampling from the joint posterior distribution of the group means, the probability of a disparity hypothesis is estimated. Four methods are developed and compared with an illustrative data set. Three of these methods are implemented in an R-code and one method in WinBUGS. These methods are programed for any number of groups between two and six inclusive. All the codes are provided in the appendices.

Bayesian Computation for the Parameters of a Zero-Inflated Cosine Geometric Distribution with Application to COVID-19 Pandemic Data

A new three-parameter discrete distribution called the zero-inflated cosine geometric(ZICG)distribution is proposed for the first time herein.It can be used to analyze over-dispersed count data with excess zeros.The basic statistical properties of the new distribution,such as the moment generating function,mean,and variance are presented.Furthermore,confidence intervals are constructed by using the Wald,Bayesian,and highest posterior density(HPD)methods to estimate the true confidence intervals for the parameters of the ZICG distribution.Their efficacies were investigated by using both simulation and real-world data comprising the number of daily COVID-19 positive cases at the Olympic Games in Tokyo 2020.The results show that the HPD interval performed better than the other methods in terms of coverage probability and average length in most cases studied.

Monte-Carlo based random passive energy beamforming for reconfigurable intelligent surface assisted wireless power transfer

Reconfigurable intelligent surface(RIS)employs passive beamforming to control the wireless propagation channel,which benefits the wireless communication capacity and the received energy efficiency of wireless power transfer(WPT)systems.Such beamforming schemes are classified as discrete and non-convex integer program-ming problems.In this paper,we propose a Monte-Carlo(MC)based random energy passive beamforming of RIS to achieve the maximum received power of electromagnetic(EM)WPT systems.Generally,the Gibbs sampling and re-sampling methods are employed to generate phase shift vector samples.And the sample with the maximum received power is considered the optimal solution.In order to adapt to the application scenarios,we develop two types of passive beamforming algorithms based on such MC sampling methods.The first passive beamforming uses an approximation of the integer programming as the initial sample,which is calculated based on the channel information.And the second one is a purely randomized algorithm with the only total received power feedback.The proposed methods present several advantages for RIS control,e.g.,fast convergence,easy implementation,robustness to the channel noise,and limited feedback requirement,and they are applicable even if the channel information is unknown.According to the simulation results,our proposed methods outperform other approxi-mation and genetic algorithms.With our methods,the WPT system even significantly improves the power effi-ciency in the nonline-of-sight(NLOS)environment.

Synthetic security assessment for incomplete interval-valued information system

In order to understand the security conditions of the incomplete interval-valued information system （IllS） and acquire the corresponding solution of security problems, this paper proposes a multi-attribute group decision- making （MAGDM） security assessment method based on the technique for order performance by similarity to ideal solution （TOPSIS）. For IllS with preference information, combining with dominance-based rough set approach （DRSA）, the effect of incomplete interval-valued information on decision results is discussed. For the imprecise judgment matrices, the security attribute weight can be obtained using Gibbs sampling. A numerical example shows that the proposed method can acquire some valuable knowledge hidden in the incomplete interval-valued information. The effectiveness of the proposed method in the synthetic security assessment for IIIS is verified.

A Phrase Topic Model Based on Distributed Representation

Traditional topic models have been widely used for analyzing semantic topics from electronic documents.However,the obvious defects of topic words acquired by them are poor in readability and consistency.Only the domain experts are possible to guess their meaning.In fact,phrases are the main unit for people to express semantics.This paper presents a Distributed Representation-Phrase Latent Dirichlet Allocation(DR-Phrase LDA)which is a phrase topic model.Specifically,we reasonably enhance the semantic information of phrases via distributed representation in this model.The experimental results show the topics quality acquired by our model is more readable and consistent than other similar topic models.

Scheduling Check-in Staff with Hierarchical Skills and Weekly Rotation Shifts

The paper aims to schedule check-in staff with hierarchical skills as well as day and night shifts in weekly rotation.That shift ensures staff work at day in a week and at night for the next week.The existing approaches do not deal with the shift constraint.To address this,the proposed algorithm firstly guarantees the day and night shifts by designing a data copy tactic,and then introduces two algorithms to generate staff assignment in a polynomial time.The first algorithm is to yield an initial solution efficiently,whereas the second incrementally updates that solution to cut off working hours.The key idea of the two algorithms is to utilize a block Gibbs sampling with replacement to simultaneously exchange multiple staff assignment.Experimental results indicate that the proposed algorithm reduces at least 15.6 total working hours than the baselines.

Posterior propriety in nonparametric mixed efects model

It is well known that spline smoothing estimator relates to the Bayesian estimate under partially informative normal prior. In this paper, we derive the conditions for the pro- priety of the posterior in the nonparametric mixed effects model under this class of partially informative normal prior for fixed effect with inverse gamma priors on the variance compo- nents and hierarchical priors for covariance matrix of random effect, then we explore the Gibbs sampling procedure.

财务欺诈风险特征筛选框架的建立和应用

本文从金融科技大数据出发,以人工智能的吉布斯随机搜索(Gibbs Sampling)算法为工具,在大数据框架下建立了针对公司财务欺诈风险的特征因子筛选的一般处理方法与特征提取推断原理,并结合上市公司的财务报表数据进行实证分析,结合从2017年1月到2018年12月证监会对上市公司财务报表信息披露违规的数据样本,筛选出刻画财务欺诈的特征因子并进行了验证测试,支持财务欺诈的识别。本文提出的框架和模型方法可以加强和提升对上市公司财务欺诈风险的识别能力,并实现对公司财务在欺诈方面的探测与预测(Detecting and Predicting)功能。

Statistical inference for zero-and-one-inflated poisson models

In this paper, a zero-and-one-inflated Poisson (ZOIP) model is studied. The maximum likelihoodestimation and the Bayesian estimation of the model parameters are obtained based on dataaugmentation method. A simulation study based on proposed sampling algorithm is conductedto assess the performance of the proposed estimation for various sample sizes. Finally, two realdata-sets are analysed to illustrate the practicability of the proposed method.

Study on segmented distribution for reliability evaluation

In practice, the failure rate of most equipment exhibits different tendencies at different stages and even its failure rate curve behaves a multimodal trace during its life cycle. As a result,traditionally evaluating the reliability of equipment with a single model may lead to severer errors.However, if lifetime is divided into several different intervals according to the characteristics of its failure rate, piecewise fitting can more accurately approximate the failure rate of equipment. Therefore, in this paper, failure rate is regarded as a piecewise function, and two kinds of segmented distribution are put forward to evaluate reliability. In order to estimate parameters in the segmented reliability function, Bayesian estimation and maximum likelihood estimation（MLE） of the segmented distribution are discussed in this paper. Since traditional information criterion is not suitable for the segmented distribution, an improved information criterion is proposed to test and evaluate the segmented reliability model in this paper. After a great deal of testing and verification,the segmented reliability model and its estimation methods presented in this paper are proven more efficient and accurate than the traditional non-segmented single model, especially when the change of the failure rate is time-phased or multimodal. The significant performance of the segmented reliability model in evaluating reliability of proximity sensors of leading-edge flap in civil aircraft indicates that the segmented distribution and its estimation method in this paper could be useful and accurate.

Bayesian analysis of series system with dependent causes of failure

Most studies of series system assume the causes of failure are independent,which may not hold in practice.In this paper,dependent causes of failure are considered by using a Marshall-Olkin bivariateWeibull distribution.We derived four reference priors based on several grouping orders.Gibbs sampling combined with the rejection sampling algorithm and Metropolis-Hastings algorithm is developed to obtain the estimates of the unknown parameters.The proposed approach is compared with the maximum-likelihood method via simulation.We find that the root-meansquared errors of the Bayesian estimates are much smaller for the case of small sample size,and that the coverage probabilities of the Bayesian estimates are much closer to the nominal levels.Finally,a real data-set is analysed for illustration.

Bayesian Planning of Optimal Step-stress Accelerated Life Test for Log-location-scale Distributions

This paper introduces some Bayesian optimal design methods for step-stress accelerated life test planning with one accelerating variable, when the acceleration model is linear in the accelerated variable or its function, based on censored data from a log-location-scale distributions. In order to find the optimal plan,we propose different Monte Carlo simulation algorithms for different Bayesian optimal criteria. We present an example using the lognormal life distribution with Type-I censoring to illustrate the different Bayesian methods and to examine the effects of the prior distribution and sample size. By comparing the different Bayesian methods we suggest that when the data have large（small） sample size B1（τ）（B2（τ）） method is adopted. Finally, the Bayesian optimal plans are compared with the plan obtained by maximum likelihood method.

Estimation and Prediction for Flexible Weibull Distribution Based on Progressive Type II Censored Data

In this work,we consider the problem of estimating the parameters and predicting the unobserved or removed ordered data for the progressive type II censored flexible Weibull sample.Frequentist and Bayesian analyses are adopted for conducting the estimation and prediction problems.The likelihood method as well as the Bayesian sampling techniques is applied for the inference problems.The point predictors and credible intervals of unobserved data based on an informative set of data are computed.Markov ChainMonte Carlo samples are performed to compare the so-obtained methods,and one real data set is analyzed for illustrative purposes.

Semiparametric Bayesian Inference for Accelerated Failure Time Models with Errors-in-Covariates and Doubly Censored Data

This paper proposes a Bayesian semiparametric accelerated failure time model for doubly censored data with errors-in-covariates. The authors model the distributions of the unobserved covariates and the regression errors via the Dirichlet processes. Moreover, the authors extend the Bayesian Lasso approach to our semiparametric model for variable selection. The authors develop the Markov chain Monte Carlo strategies for posterior calculation. Simulation studies are conducted to show the performance of the proposed method. The authors also demonstrate the implementation of the method using analysis of PBC data and ACTG 175 data.

Low-complexity single-channel blind source separation

For the time-frequency overlapped signals, a low-complexity single-channel blind source separation （SBSS） algorithm is proposed in this paper. The algorithm does not only introduce the Gibbs sampling theory to separate the mixed signals, but also adopts the orthogonal triangle decomposition-M （QRD-M） to reduce the computational complexity. According to analysis and simulation results, we demonstrate that the separation performance of the proposed algorithm is similar to that of the per-survivor processing （PSP） algorithm, while its computational complexity is sharply reduced.

Posterior propriety of an objective prior for generalized hierarchical normal linear models

Bayesian Hierarchical models has been widely used in modern statistical application.To deal with the data having complex structures,we propose a generalized hierarchical normal linear(GHNL)model which accommodates arbitrarily many levels,usual design matrices and'vanilla'covari-ance matrices.Objective hyperpriors can be employed for the GHNL model to express ignorance or match frequentist properties,yet the common objective Bayesian approaches are infeasible or fraught with danger in hierarchical modelling.To tackle this issue,[Berger,J,Sun,D.&Song,C.(2020b).An objective prior for hyperparameters in normal hierarchical models.Journal of Multi-variate Analysis,178,104606.https://doi.org/10.1016/jmva.2020.104606]proposed a particular objective prior and investigated its properties comprehensively.Posterior propriety is important for the choice of priors to guarantee the convergence of MCMC samplers.James Berger conjec-tured that the resulting posterior is proper for a hierarchical normal model with arbitrarily many levels,a rigorous proof of which was not given,however.In this paper,we complete this story and provide an user friendly guidance.One main contribution of this paper is to propose a new technique for deriving an elaborate upper bound on the integrated likelihood but also one uni-fied approach to checking the posterior propriety for linear models.An eficient Gibbs sampling method is also introduced and outperforms other sampling approaches considerably.

Algorithmic challenges in structure-based drug design and NMR structural biology

The three-dimensional structure of a biomolecule rather than its one-dimensionM sequence determines its biological function. At present, the most accurate structures are derived from experimental data measured mainly by two techniques： X-ray crystallog- raphy and nuclear magnetic resonance （NMR） spec- troscopy. Because neither X-ray crystallography nor NMR spectroscopy could directly measure the positions of atoms in a biomolecule, algorithms must be designed to compute atom coordinates from the data. One salient feature of most NMR structure computation algorithms is their reliance on stochastic search to find the lowest energy conformations that satisfy the experimentally- derived geometric restraints. However, neither the cor- rectness of the stochastic search has been established nor the errors in the output structures could be quantified. Though there exist exact algorithms to compute struc- tures from angular restraints, similar algorithms that use distance restraints remain to be developed. An important application of structures is rational drug design where protein-ligand docking plays a crit- ical role. In fact, various docking programs that place a compound into the binding site of a target protein have been used routinely by medicinal chemists for both lead identification and optimization. Unfortunately, de- spite ongoing methodological advances and some success stories, the performance of current docking algorithms is still data-dependent. These algorithms formulate the docking problem as a match of two sets of feature points. Both the selection of feature points and the search for the best poses with the minimum scores are accomplished through some stochastic search methods. Both the un- certainty in the scoring function and the limited sam- pling space attained by the stochastic search contribute to their failures. Recently, we have developed two novel docking algorithms： a data-driven docking algorithm and a general docking algorithm that does not rely on experimental data. Our algorithms search the pose space exhaustively with the pose space itself being limited to a set of hierarchical manifolds that represent, respectively, surfaces, curves and points with unique geometric and energetic properties. These algorithms promise to be es- pecially valuable for the docking of fragments and small compounds as well as for virtual screening.