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A unified Minorization-Maximization approach for estimation of general mixture models

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Applied Mathematics(A Journal of Chinese Universities) 2024年第2期39卷 343-362页

作者： HUANG Xi-fen LIU Deng-ge ZHOU Yun-peng ZHU Fei School of Mathematics Yunnan Normal UniversityKunming 650092China department of statistics and actuarial science The University of Hong KongHong KongChina

The mixed distribution model is often used to extract information from heteroge-neous data and perform modeling analysis.When the density function of mixed distribution is complicated or the variable dimension is high,it usually brings challenges to the parameter es-timation of the mixed distribution model.The application of MM algorithm can avoid complex expectation calculations,and can also solve the problem of high-dimensional optimization by decomposing the objective function.In this paper,MM algorithm is applied to the parameter estimation problem of mixed distribution model.The method of assembly and decomposition is used to construct the substitute function with separable parameters,which avoids the problems of complex expectation calculations and the inversion of high-dimensional matrices.

关键词： MM algorithm mixed distribution model parameter estimation assembly decomposition tech-nology parameter separation

Flexible, efficient, and accurate tests for epidemics

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science China Mathematics 2024年第8期67卷 1881-1898页

作者： Linjiajie Fang Bing-Yi Jing Shen Ling Qiyue Wang Qing Yang Data science and Analytics Thrust The Hong Kong University of Science and Technology department of statistics and Data science Southern University of Science and Technology department of Mathematics and statistics Dalhousie University department of Mathematics The Hong Kong University of Science and Technology

Group testing involves discovering a small subset of distinguished subjects from a large population while efficiently reducing the total number of tests. It has been widely used for industrial testing, information technology, and biology, especially epidemic screening. Tests, in reality, are noisy for the presence of false outcomes. Some tests are accurate but time-consuming, while others are cheaper but less accurate. Exactly which test to use is constrained by various considerations, such as availability, cost, accuracy, and efficiency.In this paper, we propose flexible, efficient, and accurate tests(FEATs). FEATs are based on group testing with simple but careful designs by incorporating ideas such as close contact cliques and repeated tests. FEATs could dramatically improve the efficiency or accuracy of existing tests. For example, for accurate but slow tests, the FEAT can improve efficiency multiple times without compromising accuracy. On the other hand,for fast but inaccurate tests, the FEAT can sharply reduce the false-negative rate(FNR) and significantly increase efficiency. Theoretical justifications are provided. We point out some scenarios where the FEAT can be effectively employed.

关键词： epidemiology control blood testing testing efficiency testing accuracy

Recent trends in the epidemiology and clinical outcomes of inflammatory bowel disease in South Korea,2010-2018

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World Journal of Gastroenterology 2024年第9期30卷 1154-1163页

作者： Seulji Kim Hyun Jung Lee Seung Woo Lee Sanghyun Park Seong-Joon Koh Jong Pil Im Byeong Gwan Kim Kyung-Do Han Joo Sung Kim department of Internal Medicine Korea Institute of Radiological and Medical SciencesSeoul 01812South Korea department of Internal Medicine and Liver Research Institute Seoul National University College of MedicineSeoul 03080South Korea department of statistics and actuarial science Soongsil UniversitySeoul 06978South Korea

BACKGROUND Inflammatory bowel disease(IBD)was previously regarded as a Western disease;however,its incidence is increasing in the East.The epidemiology of IBD in Asia differs significantly from the patterns in the West.AIM To comprehensively investigate the epidemiology of IBD in South Korea,inclu-ding its incidence,prevalence,medication trends,and outcomes.METHODS We analyzed claims data from the Health Insurance Review and Assessment Service and Rare and Intractable Diseases(RIDs),operated by the National Health Insurance Service of South Korea.Patients with IBD were identified based on the International Classification of Diseases,Tenth Revision,and RID diagnostic codes for Crohn’s disease(CD)and ulcerative colitis(UC)from 2010 to 2018.RESULTS In total,14498 and 31409 patients were newly diagnosed with CD and UC,respectively,between 2010 and 2018.The annual average incidence of CD was 3.11 cases per 105 person-years,and that of UC was 6.74 cases per 10^(5) person-years.Since 2014,the incidence rate of CD has been stable,while that of UC has steadily increased,shifting the peak age group from 50-year-olds in 2010 to 20-year-olds in 2018.The CD and UC prevalence increased consistently over the study period;the use of 5-aminosali-cylates and corticosteroids gradually decreased,while that of immunomodulators and biologics steadily increased in both CD and UC.The clinical outcomes of IBD,such as hospitalization and surgery,decreased during the study period.CONCLUSION The CD incidence has been stable since 2014,but that of UC has increased with a shift to a younger age at peak incidence between 2010 and 2018.IBD clinical outcomes improved over time,with increased use of immunomodu-lators and biologics.

关键词： Inflammatory bowel disease Crohn’s disease Ulcerative colitis Incidence Prevalence

Optimal investment and consumption with forward preferences and uncertain parameters

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Probability, Uncertainty and Quantitative Risk 2024年第1期9卷 65-84页

作者： Wing Fung Chong Gechun Liang Marwell Institute for Mathematical sciences and department of actuarial Mathematics and statistics Heriot-Watt UniversityEdinburgh EH144ASUK department of statistics The University of WarwickCoventry CV47ALUK

We introduce and analyze a class of forward performance criteria in incomplete markets in the presence of model ambiguity.Incompleteness stems from general investment constraints,while model uncertainty is represented by a convex and compact set of plausible model parameter processes.Following the max-min criteria in traditional(backward)robust control,we formulate similar criteria for the robust forward performance processes and focus on the rich class of time-monotone processes.We provide a novel PDE characterization and a semi-explicit saddle-point construction of the robust forward performance criteria and their optimal policies.Furthermore,we present additional results within the class of homothetic constant relative risk aversion(CRRA)processes.Within this class,we investigate the relationship between forward performance processes on wealth and those on consumption,establishing an interesting dominance through time.

关键词： Robust forward performance criteria Portfolio constraints Consumption Saddle points Constant relative risk aversion

Ambarzumyan's Theorem for the Dirac Operator on Equilateral Tree Graphs

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 568-576页

作者： Dong-Jie WU Xin-Jian XU Chuan-Fu YANG department of Mathematics School of Mathematics and StatisticsNanjing University of Science and TechnologyNanjing 210094China

The classical Ambarzumyan’s theorem states that if the Neumann eigenvalues of the Sturm-Liouville operator-d^(2)/dx^(2)+q with an integrable real-valued potential q on[0,π] are {n^(2):n≥0},then q=0 for almost all x∈[0,π].In this work,the classical Ambarzumyan’s theorem is extended to the Dirac operator on equilateral tree graphs.We prove that if the spectrum of the Dirac operator on graphs coincides with the unperturbed case,then the potential is identically zero.

关键词： dirac operator quantum graph Ambarzumyan’s theorem inverse spectral problem

SPARSE RECOVERY BASED ON THE GENERALIZED ERROR FUNCTION

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Journal of Computational Mathematics 2024年第3期42卷 679-704页

作者： Zhiyong Zhou department of statistics and Data science and Institute of Digital FinanceHangzhou City UniversityHangzhou 310015China

In this paper,we offer a new sparse recovery strategy based on the generalized error function.The introduced penalty function involves both the shape and the scale parameters,making it extremely flexible.For both constrained and unconstrained models,the theoretical analysis results in terms of the null space property,the spherical section property and the restricted invertibility factor are established.The practical algorithms via both the iteratively reweighted■_(1)and the difference of convex functions algorithms are presented.Numerical experiments are carried out to demonstrate the benefits of the suggested approach in a variety of circumstances.Its practical application in magnetic resonance imaging(MRI)reconstruction is also investigated.

关键词： Sparse recovery Generalized error function Nonconvex regularization Itera-tive reweighted Li Difference of convex functions algorithms

Automated Machine Learning Algorithm Using Recurrent Neural Network to Perform Long-Term Time Series Forecasting

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Computers, Materials & Continua 2024年第3期78卷 3529-3549页

作者： Ying Su Morgan C.Wang Shuai Liu department of statistics and Data science University of Central FloridaOrlandoFL32816-2370USA School of Mathematics and statistics Beijing Technology and Business UniversityBeijing100048China

Long-term time series forecasting stands as a crucial research domain within the realm of automated machine learning(AutoML).At present,forecasting,whether rooted in machine learning or statistical learning,typically relies on expert input and necessitates substantial manual involvement.This manual effort spans model development,feature engineering,hyper-parameter tuning,and the intricate construction of time series models.The complexity of these tasks renders complete automation unfeasible,as they inherently demand human intervention at multiple junctures.To surmount these challenges,this article proposes leveraging Long Short-Term Memory,which is the variant of Recurrent Neural Networks,harnessing memory cells and gating mechanisms to facilitate long-term time series prediction.However,forecasting accuracy by particular neural network and traditional models can degrade significantly,when addressing long-term time-series tasks.Therefore,our research demonstrates that this innovative approach outperforms the traditional Autoregressive Integrated Moving Average(ARIMA)method in forecasting long-term univariate time series.ARIMA is a high-quality and competitive model in time series prediction,and yet it requires significant preprocessing efforts.Using multiple accuracy metrics,we have evaluated both ARIMA and proposed method on the simulated time-series data and real data in both short and long term.Furthermore,our findings indicate its superiority over alternative network architectures,including Fully Connected Neural Networks,Convolutional Neural Networks,and Nonpooling Convolutional Neural Networks.Our AutoML approach enables non-professional to attain highly accurate and effective time series forecasting,and can be widely applied to various domains,particularly in business and finance.

关键词： Automated machine learning autoregressive integrated moving average neural networks time series analysis

THE LONG TIME BEHAVIOR OF THE FRACTIONAL ORNSTEIN-UHLENBECK PROCESS WITH LINEAR SELF-REPELLING DRIFT

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Acta Mathematica Scientia 2024年第2期44卷 671-685页

作者：夏晓宇闫理坦杨晴 College of Information science and Technology Donghua UniversityShanghai201620China department of statistics College of ScienceDonghua UniversityShanghai201620China

Let B^(H) be a fractional Brownian motion with Hurst index 1/2≤H<1.In this paper,we consider the equation(called the Ornstein-Uhlenbeck process with a linear self-repelling drift)dX_(t)^(H)=dB_(t)^(H)+σ X_(t)^(H)dt+vdt-θ(∫_(0)^(t)(X_(t)^(H)-X_(s)^(H))ds)dt,whereθ<0,σ,v∈ℝ.The process is an analogue of self-attracting diffusion(Cranston,Le Jan.Math Ann,1995,303:87–93).Our main aim is to study the large time behaviors of the process.We show that the solution X^(H)diverges to infinity as t tends to infinity,and obtain the speed at which the process X^(H)diverges to infinity.

关键词： fractional Brownian motion stochastic difference equations rate of convergence asymptotic

Asymptotic Inference in the Random Coefficient Autoregressive Model with Time-functional Variance Noises

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 320-346页

作者： En-wen ZHU Zi-wei DENG Han-jun ZHANG Jun CAO Xiao-hui LIU department of Mathematics and statistics Changsha University of Science and TechnologyChangsha 410114China School of Mathematics and Computational science Xiangtan UniversityXiangtan 411105China School of statistics and Data science and Key Laboratory of Data Science in Finance and EconomicsJiangxi University of Finance and EconomicsNanchang 330013China

This paper considers the random coefficient autoregressive model with time-functional variance noises,hereafter the RCA-TFV model.We first establish the consistency and asymptotic normality of the conditional least squares estimator for the constant coefficient.The semiparametric least squares estimator for the variance of the random coefficient and the nonparametric estimator for the variance function are constructed,and their asymptotic results are reported.A simulation study is presented along with an analysis of real data to assess the performance of our method in finite samples.

关键词： random coefficient autoregressive model time-functional variance conditional least squares semiparametric least squares