Mixtures Of T-distributions Research Articles

Unsupervised health indicator construction by a new Gaussian-student’s t-distribution mixture model and its application

The equipment’s remaining useful life (RUL) must be accurately estimated to guarantee its reliable operation. As a crucial part of data-driven RUL prediction, the health indicator (HI) construction method employing the distribution discrepancies can represent the variation trend of health conditions. However, the existing Gaussian mixture model based HI construction method cannot accurately estimate the long-tail distribution characteristics in some degradation data. Moreover, it cannot comprehensively mine the distribution characteristics of degradation data by leveraging different types of distributions. A novel Gaussian-student’s t-distribution mixture model (GSMM) that simultaneously considers Gaussian distribution and student’s t-distribution is developed in this work to estimate the distributions of normal and degradation data. Next, the distribution contact ratio metric (DCRM) is applied to measure the discrepancies between the baseline distribution of normal data and the distributions of test data at different moments. The bearing HI can be constructed with the acquired DCRMs. Finally, the effectiveness and merit of the developed HI construction approach are validated by two bearing life-cycle datasets. The experimental results illustrate that the GSMM-based HI performs better than other classical and state-of-the-art HIs. Additionally, the constructed HI is more suitable for bearing RUL prediction.

Research on Student's T-Distribution Point Cloud Registration Algorithm Based on Local Features.

LiDAR offers a wide range of uses in autonomous driving, remote sensing, urban planning, and other areas. The laser 3D point cloud acquired by LiDAR typically encounters issues during registration, including laser speckle noise, Gaussian noise, data loss, and data disorder. This work suggests a novel Student's t-distribution point cloud registration algorithm based on the local features of point clouds to address these issues. The approach uses Student's t-distribution mixture model (SMM) to generate the probability distribution of point cloud registration, which can accurately describe the data distribution, in order to tackle the problem of the missing laser 3D point cloud data and data disorder. Owing to the disparity in the point cloud registration task, a full-rank covariance matrix is built based on the local features of the point cloud during the objective function design process. The combined penalty of point-to-point and point-to-plane distance is then added to the objective function adaptively. Simultaneously, by analyzing the imaging characteristics of LiDAR, according to the influence of the laser waveform and detector on the LiDAR imaging, the composite weight coefficient is added to improve the pertinence of the algorithm. Based on the public dataset and the laser 3D point cloud dataset acquired in the laboratory, the experimental findings demonstrate that the proposed algorithm has high practicability and dependability and outperforms the five comparison algorithms in terms of accuracy and robustness.

Clustering trends of melanoma incidence and mortality: Aworldwide assessment from 1995 to 2019.

Melanoma is a skin cancer that has higher mortality among cutaneous malignant tumours. Tumour incidence in most world regions is rising. Here, we intend to highlight these trends in the world. We used the global burden of disease dataset to assess the incidence and mortality of melanoma from 1995 to 2019 in 204 countries/territories. To identify country/territory groups with similar trends of melanoma incidence and mortality, a model-based clustering with a mixture of multivariate t-distributions was used. Australia and New Zealand had the largest incidence and mortality rates. Men in Egypt and women in Sri Lanka and Guam had the lowest incidence and mortality rates. The clustering analysis revealed 4 classes of incidence in both gender and 3 and 2 classes of mortality in male and female, respectively. All groups had a growing incidence rate in both gender, similar to the worldwide trend. In 10% of the countries/territories, central and Western Europe, the incidence increase rate was greater than in the countries/territories with the greatest incidence. The total mortality rate for men was steadily growing, although it was decreasing in Asian and African countries/territories. Overall, the mortality rate for women remained relatively steady over time. Due to the increasing trend of melanoma in the world, primary and secondary prevention of this disease, especially in areas with higher incidence and mortality, is essential. Raising awareness about the disease is helpful in prevention and early detection of melanoma.

Multivariate process control chart based on sign and signed-rank tests for mixture distributions

The development and application of the traditional multivariate parametric control charts have been distribution-based procedures. This is because the process output is assumed to come from some specified probability distributions. However, in many quality/ process control applications, these distributional assumptions are either not satisfied or there is simply lack of enough information to verify the assumptions and this condition drops the performance of the charts. The purpose of this paper is to develop nonparametric control charts for mixture of multivariate normal and t-distributions with the view to evaluating the performance of the charts in simulation study. The results show that the charts are effective in monitoring process variability.

How has the relationship between safe haven assets and the US stock market changed after the global financial crisis?

In this paper, I investigate how the relationship between safe haven assets and the US stock market has changed since the global financial crisis. To do so, I propose a new concept of bear-market correlation which allows us to see the effectiveness of the safe haven asset as a hedge and portfolio diversification tool. I compute the bear-market correlation of five safe haven assets during two sample periods, pre-financial crisis (1995–2009) and post-financial crisis (2010–2018). My findings are as follows: First, I find that the empirical bear-market correlations are not explained by multivariate normal and t-distributions. Second, I document that the bear-market correlations of both the Japanese yen and gold show notable changes after the crisis. Third, I estimate a multivariate normal mixture, a multivariate t-distribution mixture, and a generalized dynamic conditional correlation model. I document that these mixture models outperform the dynamic conditional correlation model in most cases. Finally, I discuss the economic impact of failing to capture the bear-market correlation for portfolio optimization.

Student Mixture and Its Machine Learning Applications to PVT Properties of Reservoir Fluids

Distribution mixture models are widely used in cluster analysis. Particularly, a mixture of Student t-distributions is mostly applied for robust data clustering. In this paper, we introduce EM algorithm for a mixture of Student distributions, where at the E-step, we apply variational Bayesian inference for parameters estimation. Based on a mixture of Student distributions, a machine learning method is constructed that allows solving regression problems for any set of features, clustering, and anomaly detection within one model. Each of these problems can be solved by the model even if there are missing values in the data. The proposed method was tested on real data describing the PVT properties of reservoir fluids. The results obtained by the model do not contradict the basic physical properties. In majority of conducted experiments our model gives more accurate results than well-known machine learning methods in terms of MAPE and RMSPE metrics.

An Automatic Background Filtering Method for Detection of Road Users in Heavy Traffics Using Roadside 3-D LiDAR Sensors With Noises

Background filtering for roadside Light Detecting and Ranging (LiDAR) data could benefit detection of road users with high frequency and accuracy. But existing methods are unsatisfactory under traffic congestions and neglect noises of LiDAR sensors. This paper attempts to develop background identification and filtering methods for heavy traffics and LiDAR noises. In particular, a 3-D space-time diagram of the LiDAR's detection space over frames is divided into plenty of subspace-frames, where one subspace-frame refers to one subspace from the isometric division of detection space in one frame. For subspace-frames at the same position, an unsupervised clustering method with unknown number of clusters is applied for classifying subspace-frames into different groups and the background group is identified based on background characteristics. The proposed clustering method is a t-distribution mixture model with constraints, where weights follow a Dirichlet distribution so that some weights have the possibility to be 0. A Bayesian estimation framework is developed to carry out the clustering. Then each background subspace-frame is divided into cubes with equal lengths. By aggregating points over frames in the same cube, the cube with aggregated points is regarded as background cube. For background filtering, points in background cubes are background points and excluded. Finally, examined by data from a Velodyne VLP-32 LiDAR sensor, the proposed approach has better filtering results no matter under free-flow conditions or congestions. Using background filtering results for road users' detection is introduced as well.

Robust Task Learning Based on Nonlinear Regression With Mixtures of Student-t Distributions

We propose a robust task learning method based on nonlinear regression model with mixtures of t-distributions. The model can adaptively reduce the effects of complex noises and accurately learn the nonlinear structure of targets. By introducing latent variables, the model is expressed into a hierarchical structure, which helps explain the advantage of flexibility compared to the traditional Gaussian based learning model. We develop a two-stage efficient estimation procedure to obtain penalized likelihood estimator of the parameters combined an expectation-maximization algorithm with Lagrange multiplier method. The learning performances of the model are investigated through experiments on both synthetic and real data sets.

Generative adversarial networks with mixture of t-distributions noise for diverse image generation

Image generation is a long-standing problem in the machine learning and computer vision areas. In order to generate images with high diversity, we propose a novel model called generative adversarial networks with mixture of t-distributions noise (tGANs). In tGANs, the latent generative space is formulated using a mixture of t-distributions. Particularly, the parameters of the components in the mixture of t-distributions can be learned along with others in the model. To improve the diversity of the generated images in each class, each noise vector and a class codeword are concatenated as the input of the generator of tGANs. In addition, a classification loss is added to both the generator and the discriminator losses to strengthen their performances. We have conducted extensive experiments to compare tGANs with a state-of-the-art pixel by pixel image generation approach, pixelCNN, and related GAN-based models. The experimental results and statistical comparisons demonstrate that tGANs perform significantly better than pixleCNN and related GAN-based models for diverse image generation.

Semi-supervised Gaussian and t-distribution hybrid mixture model for water leak detection

The last few years have seen a great number of announcements and projections on cities of the future, where technological interconnected metering infrastructure is the main smart-grid unit, promoting higher sustainability due to its more efficient management capability. The water supply network is one of the grids that has been given additional attention due to the problem of waste caused by water leakage, usually requiring rapid detection for fast intervention to prevent high costs. With centralised information coming from the grid, like the measurement of pressure and flow, it is revealed that anomaly detection could be an important tool for quick automatic detection without needing permanent analysis by a human operator. However, there is a need for a more robust approach, especially when noisy data are present. In this paper, we propose the implementation of a new approach based on a hybrid expectation maximization (EM) Gaussian model combined with a t-distribution mixture. This approach is compared to both a pure EM Gaussian mixture model and a t-distribution mixture model that can use labelled data or not. Each EM algorithm was applied to real data acquired from a water supply grid with the aim of automatically detecting water leaks. Using the newly developed approach, the results show that detection is both possible and more accurate for this type of database.

Registration of vascular structures using a hybrid mixture model.

Morphological changes to anatomy resulting from invasive surgical procedures or pathology, typically alter the surrounding vasculature. This makes it useful as a descriptor for feature-driven image registration in various clinical applications. However, registration of vasculature remains challenging, as vessels often differ in size and shape, and may even miss branches, due to surgical interventions or pathological changes. Furthermore, existing vessel registration methods are typically designed for a specific application. To address this limitation, we propose a generic vessel registration approach useful for a variety of clinical applications, involving different anatomical regions. A probabilistic registration framework based on a hybrid mixture model, with a refinement mechanism to identify missing branches (denoted as HdMM+) during vasculature matching, is introduced. Vascular structures are represented as 6-dimensional hybrid point sets comprising spatial positions and centerline orientations, using Student's t-distributions to model the former and Watson distributions for the latter. The proposed framework is evaluated for intraoperative brain shift compensation, and monitoring changes in pulmonary vasculature resulting from chronic lung disease. Registration accuracy is validated using both synthetic and patient data. Our results demonstrate, HdMM+ is able to reduce more than [Formula: see text] of the initial error for both applications, and outperforms the state-of-the-art point-based registration methods such as coherent point drift and Student's t-distribution mixture model, in terms of mean surface distance, modified Hausdorff distance, Dice and Jaccard scores. The proposed registration framework models complex vascular structures using a hybrid representation of vessel centerlines, and accommodates intricate variations in vascular morphology. Furthermore, it is generic and flexible in its design, enabling its use in a variety of clinical applications.

基于T分布混合模型的多光谱人脸图像配准

基于T分布混合模型的多光谱人脸图像配准

On Fractionally-Supervised Classification: Weight Selection and Extension to the Multivariate t-Distribution

Recent work on fractionally-supervised classification (FSC), an approach that allows classification to be carried out with a fractional amount of weight given to the unlabelled points, is further developed in two respects. The primary development addresses a question of fundamental importance over how to choose the amount of weight given to the unlabelled points. The resolution of this matter is essential because it makes FSC more readily applicable to real problems. Interestingly, the resolution of the weight selection problem opens up the possibility of a different approach to model selection in model-based clustering and classification. A secondary development demonstrates that the FSC approach can be effective beyond Gaussian mixture models. To this end, an FSC approach is illustrated using mixtures of multivariate t-distributions.

不同类型数据下混合模型参数估计效果的对比研究

混合高斯模型在描述数据方面应用较多，但它易受离群点的影响，其参数的极大似然估计不是稳健估计。混合t-分布模型由于其重尾分布的特性，相对于混合高斯分布，在分析重尾数据上更具稳健性。文章首先研究一元混合t-分布模型，利用标准EM算法给出了该模型参数极大似然估计的迭代步骤，并分别在三类模拟数据下与混合高斯模型进行了对比分析，验证了该模型的有效性以及在拟合重尾数据上的优势。算法初始化采用k-means方法。 The normal mixture model has more applications in describing data. But it is easily influenced by the outlier, and the maximum likelihood estimation of parameters is not robust estimation. T-distribution mixture model has better robustness than Gauss mixture model to analyze data with longer time than normal tails because of its heavy-tails. In this paper, we studied a univariate t mixture model primarily. Based on EM algorithm, we derived the iteration steps of maximum li-kelihood estimation of the model’s unknown parameters. Furthermore, we did a comparative analysis by three types of simulated data. Simulation study shows that this model has an advantage in fitting data with longer time than normal tails. The initial value is given by k-means method.

Robust Improper Maximum Likelihood: Tuning, Computation, and a Comparison With Other Methods for Robust Gaussian Clustering

ABSTRACTThe two main topics of this article are the introduction of the “optimally tuned robust improper maximum likelihood estimator” (OTRIMLE) for robust clustering based on the multivariate Gaussian model for clusters, and a comprehensive simulation study comparing the OTRIMLE to maximum likelihood in Gaussian mixtures with and without noise component, mixtures of t-distributions, and the TCLUST approach for trimmed clustering. The OTRIMLE uses an improper constant density for modeling outliers and noise. This can be chosen optimally so that the nonnoise part of the data looks as close to a Gaussian mixture as possible. Some deviation from Gaussianity can be traded in for lowering the estimated noise proportion. Covariance matrix constraints and computation of the OTRIMLE are also treated. In the simulation study, all methods are confronted with setups in which their model assumptions are not exactly fulfilled, and to evaluate the experiments in a standardized way by misclassification rates, a new model-based definition of “true clusters” is introduced that deviates from the usual identification of mixture components with clusters. In the study, every method turns out to be superior for one or more setups, but the OTRIMLE achieves the most satisfactory overall performance. The methods are also applied to two real datasets, one without and one with known “true” clusters. Supplementary materials for this article are available online.

Robust fuzzy clustering using nonsymmetric student׳s t finite mixture model for MR image segmentation

Accurate tissue segmentation from magnetic resonance (MR) images is an essential step in clinical practice. In this paper, we introduce a robust fuzzy clustering scheme for finite mixture model fitting, which exploits the merits of the mixture of the nonsymmetric Student׳s t-distribution and mean template to reduce the sensitivity of the segmentation results with respect to noise. This approach utilizes a fuzzy objective function regularized by the Kullback–Leibler (KL) divergence term and sets the dissimilarity function as the negative log-likelihood of the nonsymmetric Student׳s t-distribution and mean template. The advantage of this fuzzy clustering scheme is that the spatial relationships among neighbouring pixels are taken into account with the help of the mean template so that the proposed method is more robust to noise than several other existing fuzzy c-means (FCM)-based algorithms. Another advantage is that the application of the nonsymmetric Student׳s t-distribution mixture model allows the proposed model to fit different shapes of observed data. Experiments using synthetic and real MR images show that the proposed model has considerably better segmentation accuracy and robustness against noise compared with several well-known finite mixture models.

Using mixtures of [formula omitted] densities to make inferences in the presence of missing data with a small number of multiply imputed data sets

Strategies for making inference in the presence of missing data after conducting a Multiple Imputation (MI) procedure are considered. An approach which approximates the posterior distribution for parameters using a mixture of t-distributions is proposed. Simulated experiments show this approach improves inferences in some aspects, making them more stable over repeated analysis and creating narrower bounds for certain common statistics of interest. Extensions to the existing literature have been executed that provide further stability to inferences and also a strong potential to identify ways to make the analysis procedure more flexible. The competing methods have been first compared using simulated data sets and then a real data set concerning analysis of the effect of breastfeeding duration on children’s cognitive ability. R code to implement the methods used is available as online supplementary material.

Stringency-based ranking of normality tests

ABSTRACTMany parametric statistical inferential procedures in finite samples depend crucially on the underlying normal distribution assumption. Dozens of normality tests are available in the literature to test the hypothesis of normality. Availability of such a large number of normality tests has generated a large number of simulation studies to find a best test but no one arrived at a definite answer as all depends critically on the alternative distributions which cannot be specified. A new framework, based on stringency concept, is devised to evaluate the performance of the existing normality tests. Mixture of t-distributions is used to generate the alternative space. The LR-tests, based on Neyman–Pearson Lemma, have been computed to construct a power envelope for calculating the stringencies of the selected normality tests. While evaluating the stringencies, Anderson–Darling (AD) statistic turns out to be the best normality test.

Robust mixture regression using the [formula omitted]-distribution

The traditional estimation of mixture regression models is based on the normal assumption of component errors and thus is sensitive to outliers or heavy-tailed errors. A robust mixture regression model based on the t-distribution by extending the mixture of t-distributions to the regression setting is proposed. However, this proposed new mixture regression model is still not robust to high leverage outliers. In order to overcome this, a modified version of the proposed method, which fits the mixture regression based on the t-distribution to the data after adaptively trimming high leverage points, is also proposed. Furthermore, it is proposed to adaptively choose the degrees of freedom for the t-distribution using profile likelihood. The proposed robust mixture regression estimate has high efficiency due to the adaptive choice of degrees of freedom.

An Extension of the Student's t-distribution Mixture Model and the Gradient Descent method

A new Student's t-distribution finite mixture model is proposed which incorporates the local spatial information of the pixels. The pixels' label probability proportions are explicitly modelled as probability vectors in the proposed model. We use the gradient descend method to estimate the parameters of the proposed model. Compre- hensive experiments are performed for synthetic and natural grayscale images. The experimental results demonstrate that the superiority of the proposed model over some other models. Index Terms—Spatially variant finite mixture model, Stu- dent's t-distribution, Image segmentation, Gradient descent