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The Journal of Machine Learning Research 2022年第1期23卷 134-167页

作者： Lorenzo Rimella Nick Whiteley Department of Mathematics and Statistics Lancaster University Lancaster UK Institute for Statistical Science School of Mathematics University of Bristol Bristol UK and the Alan Turing Institute UK

We propose algorithms for approximate filtering and smoothing in high-dimensional Factorial hidden Markov models. The approximation involves discarding, in a principled way, likelihood factors according to a notion of locality in a factor graph associated with the emission distribution. This allows the exponential-in-dimension cost of exact filtering and smoothing to be avoided. We prove that the approximation accuracy, measured in a local total variation norm, is "dimension-free" in the sense that as the overall dimension of the model increases the error bounds we derive do not necessarily degrade. A key step in the analysis is to quantify the error introduced by localizing the likelihood function in a Bayes' rule update. The factorial structure of the likelihood function which we exploit arises naturally when data have known spatial or network structure. We demonstrate the new algorithms on synthetic examples and a London Underground passenger ow problem, where the factor graph is effectively given by the train network.

关键词： factorial hidden Markov models filtering smoothing em algorithm high-dimensions

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Detection of Rapidly Spreading Hashtags via Social Networks

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IEEE ACCESS 2020年 8卷 39847-39860页

作者： Kim, Younghoon Seo, Jiwon Hanyang Univ Devis Comp Sci Ansan 15588 South Korea Hanyang Univ Dept Comp Sci Seoul 04763 South Korea

Social network services (SNSs) such as Twitter and Facebook have emerged as a new medium for communication. They offer a unique mechanism of sharing information by allowing users to receive all messages posted by those whom they & x201C;follow& x201D;. As information in today& x2019;s SNSs often spreads in the form of hashtags, detecting rapidly spreading hashtags in SNSs has recently attracted much attention. In this paper, we propose realistic epidemic models to describe the probabilistic process of hashtag propagation. Our models take into account the way how users communicate in SNSs;moreover the models consider the influence of external media and separate it from internal diffusion within networks. Based on the proposed models, we develop efficient inference algorithms that measure the propagation rates of hashtags in social networks. With real-life social network data including hashtags and synthetic data obtained by simulating information diffusion, we show that the proposed algorithms find fast-spreading hashtags more accurately than existing algorithms. Moreover, our in-depth case study demonstrates that our algorithms correctly find internal diffusion rates of hashtags as well as external media influences.

关键词： Twitter Tagging Media Inference algorithms Probabilistic logic Facebook Social network information diffusion hashtag probabilistic modeling em algorithm

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Adaptive stochastic-filter-based failure prediction model for complex repairable systems under uncertainty conditions

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RELIABILITY ENGINEERING & SYSTem SAFETY 2020年 204卷 107190-107190页

作者： Peng Yizhen Wang Yu Xie Jingsong Zi Yanyang ChongQing Univ Coll Mech Engn Shazheng St 174 Chongqing 400044 Peoples R China ChongQing Univ State Key Lab Mech Transmiss Shazheng St 174 Chongqing 400044 Peoples R China Xi An Jiao Tong Univ Sch Mech Engn Xianning Xi Rd 28 Xian 710049 Peoples R China Cent South Univ Coll Traff & Transportat Engn Shaoshan Nan Rd 22 Changsha 410075 Peoples R China

Dynamical reliability assessment and failure prediction are effective tools for ensuring the efficiency, availability, and safety of repairable systems. To achieve better assessment performance, accurate modeling failure recurrence data are the core of prediction approaches. However, because of the uncertainties from the environmental conditions and repair activities, the failure counting model is usually not well established. To solve this problem, in this paper, we propose an adaptive recursive-filter-based dynamical failure prediction approach for complex repairable systems. First, based on the framework of the state space model, a fusion model that fuses Brownian motion into a nonhomogeneous Poisson process is proposed to characterize failure process under multiple uncertainty conditions. Then, an adaptive statistical inference method based on a Bayesian recursive filter and the em algorithm is derived to update the model parameters and estimate the initial states adaptively. To verify the effectiveness of the proposed approach, a real gas pipeline compressors reliability prediction problem was implemented.

关键词： Repairable systems Failure prediction Multiple uncertainties Bayesian recursive filter em algorithm

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A Variational Image Segmentation Model Based on Normalized Cut with Adaptive Similarity and Spatial Regularization

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SIAM JOURNAL ON IMAGING SCIENCES 2020年第2期13卷 651-684页

作者： Wang, Faqiang Zhao, Cuicui Liu, Jun Huang, Haiyang Beijing Normal Univ Sch Math Sci Minist Educ China Lab Math & Complex Syst Beijing 100875 Peoples R China

Image segmentation is a fundamental research topic in image processing and computer vision. In recent decades, researchers developed a large number of segmentation algorithms for various applications. Among these algorithms, the normalized cut (Ncut) segmentation method is widely applied due to its good performance. The Ncut segmentation model is an optimization problem whose energy is defined on a specifically designed graph. Thus, the segmentation results of the existing Ncut method are largely dependent on a preconstructed similarity measure on the graph since this measure is usually given empirically by users. This flaw will lead to some undesirable segmentation results. In this paper, we propose an Ncut-based segmentation algorithm by integrating an adaptive similarity measure and spatial regularization. The proposed model combines the Parzen-Rosenblatt window method, nonlocal weights entropy, Ncut energy, and regularizer of phase field in a variational framework. Our method can adaptively update the similarity measure function by estimating some parameters. This adaptive procedure enables the proposed algorithm to find a better similarity measure for classification than the Ncut method. We provide some mathematical interpretation of the proposed adaptive similarity from multiple viewpoints, such as statistics and convex optimization. In addition, the regularizer of phase field can guarantee that the proposed algorithm has a robust performance in the presence of noise, and it can also rectify the similarity measure with a spatial priori. The well-posed theory such as the existence of the minimizer for the proposed model is given in the paper. Compared with some existing segmentation methods such as the traditional Ncutbased model and the classical Chan-Vese model, the numerical experiments show that our method can provide promising segmentation results.

关键词： normalized cut Parzen-Rosenblatt window em algorithm regularization convex optimization adaptive similarity duality

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A bivariate joint frailty model with mixture framework for survival analysis of recurrent events with dependent censoring and cure fraction

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BIOMETRICS 2020年第3期76卷 753-766页

作者： Tawiah, Richard McLachlan, Geoffrey J. Ng, Shu Kay Griffith Univ Sch Med Nathan Qld 4111 Australia Griffith Univ Menzies Hlth Inst Queensland Nathan Qld 4111 Australia Univ New South Wales Sch Psychol Sydney NSW Australia Univ Queensland Dept Math St Lucia Qld Australia

In the study of multiple failure time data with recurrent clinical endpoints, the classical independent censoring assumption in survival analysis can be violated when the evolution of the recurrent events is correlated with a censoring mechanism such as death. Moreover, in some situations, a cure fraction appears in the data because a tangible proportion of the study population benefits from treatment and becomes recurrence free and insusceptible to death related to the disease. A bivariate joint frailty mixture cure model is proposed to allow for dependent censoring and cure fraction in recurrent event data. The latency part of the model consists of two intensity functions for the hazard rates of recurrent events and death, wherein a bivariate frailty is introduced by means of the generalized linear mixed model methodology to adjust for dependent censoring. The model allows covariates and frailties in both the incidence and the latency parts, and it further accounts for the possibility of cure after each recurrence. It includes the joint frailty model and other related models as special cases. An expectation-maximization (em)-type algorithm is developed to provide residual maximum likelihood estimation of model parameters. Through simulation studies, the performance of the model is investigated under different magnitudes of dependent censoring and cure rate. The model is applied to data sets from two colorectal cancer studies to illustrate its practical value.

关键词： bivariate frailty cure proportion em algorithm informative censoring joint model mixture model random effect terminal event

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Cure Rate-Based Step-Stress Model

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JOURNAL OF STATISTICAL THEORY AND PRACTICE 2023年第1期17卷 15-15页

作者： Pal, Ayan Samanta, Debashis Kundu, Debasis Univ Burdwan Dept Stat Burdwan 713104 W Bengal India Aliah Univ Dept Math & Stat 2-A-27Act Area 2 Kolkata 700156 W Bengal India Indian Inst Technol Kanpur Dept Math & Stat Kanpur 208016 India

In this article, we consider step-stress accelerated life testing (SSALT) models assuming that the time-to-event distribution belongs to the proportional hazard family and the underlying population consists of long-term survivors. Further, with an increase in stress levels, it is natural that the mean time to the event of interest gets shortened and hence a method of obtaining order-restricted maximum likelihood estimators (MLEs) of the model parameters is proposed based on expectation maximization (em) algorithm coupled with the reparametrization technique. To illustrate the effectiveness of the proposed method, extensive simulation experiments are performed and a real-life data example is analyzed in detail.

关键词： Step-stress model Failure rate-based SSALT model Cure rate em algorithm Maximum likelihood estimator Reparametrization technique Confidence interval

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On the joint Type-II progressive censoring scheme

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2020年第4期49卷 958-976页

作者： Mondal, Shuvashree Kundu, Debasis Indian Inst Technol Kanpur Dept Math & Stat Kanpur Uttar Pradesh India

Recently the progressive censoring scheme has been extended for two or more populations. In this article we consider the joint Type-II progressive censoring (JPC) scheme for two populations when the lifetime distributions of the experimental units of the two populations follow two-parameter generalized exponential distributions with the same scale parameter but different shape parameters. The maximum likelihood estimators of the unknown parameters cannot be obtained in explicit forms. We propose to use the expectation maximization (em) algorithm to compute the maximum likelihood estimators. The observed information matrix based on missing value principles is derived. We study the Bayesian inference of the unknown parameters based on a beta-gamma prior for the shape parameters, and an independent gamma prior for the common scale parameter. The Bayes estimators with respect to the squared error loss function cannot be obtained in explicit form. We propose to use the importance sampling technique to compute the Bayes estimates and the associated credible intervals of the unknown parameters. Extensive simulation experiments have been performed to study the performances of the different methods. Finally a real data set has been analyzed for illustrative purposes.

关键词： Progressive censoring scheme Joint progressive censoring scheme Generalized Exponential distribution em algorithm Fisher Information Bayes estimator Importance sampling Credible interval

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A two-phase Bayesian methodology for the analysis of binary phenotypes in genome-wide association studies

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BIOMETRICAL JOURNAL 2020年第1期62卷 191-201页

作者： Joyner, Chase McMahan, Christopher Baurley, James Pardamean, Bens Clemson Univ Sch Math & Stat Sci O-110 Martin HallBox 340975 Clemson SC 29634 USA BioRealm LLC Walnut CA USA Bina Nusantara Univ Bioinformat & Data Sci Res Ctr Kebon Jeruk Indonesia

Recent advances in sequencing and genotyping technologies are contributing to a data revolution in genome-wide association studies that is characterized by the challenging large p small n problem in statistics. That is, given these advances, many such studies now consider evaluating an extremely large number of genetic markers (p) genotyped on a small number of subjects (n). Given the dimension of the data, a joint analysis of the markers is often fraught with many challenges, while a marginal analysis is not sufficient. To overcome these obstacles, herein, we propose a Bayesian two-phase methodology that can be used to jointly relate genetic markers to binary traits while controlling for confounding. The first phase of our approach makes use of a marginal scan to identify a reduced set of candidate markers that are then evaluated jointly via a hierarchical model in the second phase. Final marker selection is accomplished through identifying a sparse estimator via a novel and computationally efficient maximum a posteriori estimation technique. We evaluate the performance of the proposed approach through extensive numerical studies, and consider a genome-wide application involving colorectal cancer.

关键词： Bayes factors em algorithm GWAS MAP estimator shrinkage prior

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Semiparametric mixtures of regressions with single-index for model based clustering

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ADVANCES IN DATA ANALYSIS AND CLASSIFICATION 2020年第2期14卷 261-292页

作者： Xiang, Sijia Yao, Weixin Zhejiang Univ Finance & Econ Sch Data Sci Hangzhou 310018 Zhejiang Peoples R China Univ Calif Riverside Dept Stat Riverside CA 92521 USA

In this article, we propose two classes of semiparametric mixture regression models with single-index for model based clustering. Unlike many semiparametric/nonparametric mixture regression models that can only be applied to low dimensional predictors, the new semiparametric models can easily incorporate high dimensional predictors into the nonparametric components. The proposed models are very general, and many of the recently proposed semiparametric/nonparametric mixture regression models are indeed special cases of the new models. Backfitting estimates and the corresponding modified em algorithms are proposed to achieve optimal convergence rates for both parametric and nonparametric parts. We establish the identifiability results of the proposed two models and investigate the asymptotic properties of the proposed estimation procedures. Simulation studies are conducted to demonstrate the finite sample performance of the proposed models. Two real data applications using the new models reveal some interesting findings.

关键词： em algorithm Kernel regression Mixture regression model Model based clustering Single-index model

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Mixture modeling of data with multiple partial right-censoring levels

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ADVANCES IN DATA ANALYSIS AND CLASSIFICATION 2020年第2期14卷 355-378页

作者： Michael, Semhar Miljkovic, Tatjana Melnykov, Volodymyr South Dakota State Univ Dept Math & Stat Brookings SD 57007 USA Miami Univ Dept Stat Oxford OH 45056 USA Univ Alabama Dept Informat Syst Stat & Management Sci Tuscaloosa AL 35487 USA

In this paper, a new flexible approach to modeling data with multiple partial right-censoring points is proposed. This method is based on finite mixture models, flexible tool to model heterogeneity in data. A general framework to accommodate partial censoring is considered. In this setting, it is assumed that a certain portion of data points are censored and the rest are not. This situation occurs in many insurance loss data sets. A novel probability function is proposed to be used as a mixture component and the expectation-maximization algorithm is employed for estimating model parameters. The Bayesian information criterion is used for model selection. Additionally, an approach for the variability assessment of parameter estimates as well as the computation of quantiles commonly known as risk measures is considered. The proposed model is evaluated using a simulation study based on four common probability distribution functions used to model right skewed loss data and applied to a real data set with good results.

关键词： Finite mixture models em algorithm Right-censoring Partial censoring BIC Insurance loss modeling

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