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A new approach to parameter estimation of mixture of two normal distributions

COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2024年第3期53卷 1161-1187页

作者： Li, Yinan Fang, Kai-Tai BNU HKBU United Int Coll Div Sci & Technol Zhuhai Peoples R China Hong Kong Baptist Univ Dept Math Kowloon Hong Kong Peoples R China Chinese Acad Sci Key Lab Random Complex Structures & Data Anal Beijing Peoples R China

Mixtures of two-component normal distributions (MixN) have various applications in statistical inference with flexibility in density fitting. The best estimation of the five model parameters still represents a challenge. This article proposes more accurate density fittings given a random sample in both the moment-based and likelihood-based estimation frameworks. Motivated by the excellent performance of the Quasi-Monte Carlo method in quantile estimations, we propose an innovative approach to improve the accuracy of parameter estimations by reinforcing the representativeness of observed data via the distribution-free Harrell-Davis quantile estimators. The revision on the penalized maximum likelihood method is also considered due to the unpleasant properties of the original likelihood function under MixN. The bootstrap bias-corrected moment estimators are given as another revision. A sequential algorithm for optimization (SNTO) is conducted in finding numerical solutions for the two types of parameter estimation methods. SNTO is more adapted to MixN and shows strong advantages in the likelihood-based estimation compared to the famous EM algorithm. Simulation results show that our proposed approach can effectively improve estimation accuracy and increase resistance to small sample sizes and/or high percent overlaps between two mixture components. A real data example is given to illustrate the efficiency of our proposed methods.

关键词： Maximum likelihood estimation Mixture normal distributions Moment estimation Penalized maximum likelihood estimation Quasi-Monte Carlo SNTO algorithm

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An Adjusted Gray Map Technique for Constructing Large Four-Level Uniform Designs

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Journal of Systems science & complexity 2023年第1期36卷 433-456页

作者： ELSAWAH A M VISHWAKARMA G K MOHAMED H S FANG Kai-Tai Department of Statistics and Data Science Faculty of Science and TechnologyBeijing Normal University-Hong Kong Baptist University United International CollegeZhuhai 519087China Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science BNU-HKBU United International CollegeZhuhai 519087China Department of Mathematics Faculty of ScienceZagazig UniversityZagazig 44519Egypt Department of Mathematics&Computing Indian Institute of Technology DhanbadDhanbad 826004India College of Transportation and Civil Engineering Fujian Agriculture and Forestry UniversityFuzhou 350002China The Key Lab of Random Complex Structures and Data Analysis The Chinese Academy of SciencesBeijing 100190China

A uniform experimental design(UED)is an extremely used powerful and efficient methodology for designing experiments with high-dimensional inputs,limited resources and unknown underlying models.A UED enjoys the following two significant advantages:(i)It is a robust design,since it does not require to specify a model before experimenters conduct their experiments;and(ii)it provides uniformly scatter design points in the experimental domain,thus it gives a good representation of this domain with fewer experimental trials(runs).Many real-life experiments involve hundreds or thousands of active factors and thus large UEDs are *** large UEDs using the existing techniques is an NP-hard problem,an extremely time-consuming heuristic search process and a satisfactory result is not *** paper presents a new effective and easy technique,adjusted Gray map technique(AGMT),for constructing(nearly)UEDs with large numbers of four-level factors and runs by converting designs with s two-level factors and n runs to(nearly)UEDs with 2^(t−1)s four-level factors and 2tn runs for any t≥0 using two simple transformation *** justifications for the uniformity of the resulting four-level designs are given,which provide some necessary and/or sufficient conditions for obtaining(nearly)uniform four-level *** results show that the AGMT is much easier and better than the existing widely used techniques and it can be effectively used to simply generate new recommended large(nearly)UEDs with four-level factors.

关键词： Aberration adjusted Gray map technique Gray map technique Hamming distance moment aberration threshold accepting algorithm uniform design

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Cross-Entropy Loss for Recommending Efficient Fold-Over Technique

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Journal of Systems science & complexity 2021年第1期34卷 402-439页

作者： WENG Lin-Chen ELSAWAH A M FANG Kai-Tai Division of Science and Technology Beijing Normal University-Hong Kong Baptist University United International CollegeZhuhai 519085China Department of Mathematics Faculty of ScienceZagazig UniversityZagazig 44519Egypt The Key Lab of Random Complex Structures and Data Analysis Chinese Academy of SciencesBeijing 100190China

Due to the limited resources and budgets in many real-life projects, it is unaffordable to use full factorial experimental designs and thus fractional factorial(FF) designs are used instead. The aliasing of factorial effects is the price we pay for using FF designs and thus some significant effects cannot be estimated. Therefore, some additional observations(runs) are needed to break the linages among the factorial effects. Folding over the initial FF designs is one of the significant approaches for selecting the additional runs. This paper gives an in-depth look at fold-over techniques via the following four significant contributions. The first contribution is on discussing the adjusted switching levels foldover technique to overcome the limitation of the classical one. The second contribution is on presenting a comparison study among the widely used fold-over techniques to help experimenters to recommend a suitable fold-over technique for their experiments by answering the following two fundamental questions:Do these techniques dramatically lessen the confounding of the initial designs, and do the resulting combined designs(combining initial design with its fold-over) via these techniques have considerable difference from the optimality point of view considering the markedly different searching domains in each technique? The optimality criteria are the aberration, confounding, Hamming distance and uniformity. Many of these criteria are given in sequences(patterns) form, which are inconvenient and costly to represent and compare, especially when the designs have many factors. The third innovation is on developing a new criterion(dictionary cross-entropy loss) to simplify the existing criteria fromsequence to scalar. The new criterion leads to a more straightforward and easy comparison study. The final contribution is on establishing a general framework for the connections between initial designs and combined designs based on any fold-over technique.

关键词： Aberration confounding cross-entropy dictionary ordering fold-over Hamming distance loss function uniformity

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Towards understanding residual and dilated dense neural networks via convolutional sparse coding

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National science Review 2021年第3期8卷 127-139页

作者： Zhiyang Zhang Shihua Zhang National Center for Mathematics and Interdisciplinary Sciences Center for Excellence in Mathematical Science Key Laboratory of Random Complex Structures and Data ScienceAcademy of Mathematics and Systems ScienceChinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences Center for Excellence in Animal Evolution and Genetics Chinese Academy of Sciences Key Laboratory of Systems Biology Hangzhou Institute for Advanced Study University of Chinese Academy of Sciences Chinese Academy of Sciences

Convolutional neural network(CNN) and its variants have led to many state-of-the-art results in various ***,a clear theoretical understanding of such networks is still ***,a multilayer convolutional sparse coding(ML-CSC) model has been proposed and proved to equal such simply stacked networks(plain networks).Here,we consider the initialization,the dictionary design and the number of iterations to be factors in each layer that greatly affect the performance of the ML-CSC *** by these considerations,we propose two novel multilayer models:the residual convolutional sparse coding(Res-CSC) model and the mixed-scale dense convolutional sparse coding(MSD-CSC) *** are closely related to the residual neural network(ResNet) and the mixed-scale(dilated) dense neural network(MSDNet),***,we derive the skip connection in the ResNet as a special case of a new forward propagation rule for the ML-CSC *** also find a theoretical interpretation of dilated convolution and dense connection in the MSDNet by analyzing the MSD-CSC model,which gives a clear mathematical understanding of *** implement the iterative soft thresholding algorithm and its fast version to solve the Res-CSC and MSD-CSC *** unfolding operation can be employed for further ***,extensive numerical experiments and comparison with competing methods demonstrate their effectiveness.

关键词： convolutional neural network convolutional sparse coding residual neural network mixed-scale dense neural network dilated convolution dense connection

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Construction of Uniform Designs over Continuous Domain in Computer Experiments

arXiv

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arXiv 2023年

作者： Lai, Jianfa Fang, Kai-Tai Peng, Xiaoling Lin, Yuxuan Department of Mathematics Hong Kong Baptist University Kowloon Tong Hong Kong Division of Science and Technology BNU-HKBU United International College Zhuhai519085 China The Key Lab of Random Complex Structures and Data Analysis The Chinese Academy of Sciences Beijing China

Construction of uniform designs (UDs) has received much attention in computer experiments over the past decades, but most of previous works obtain uniform designs over a U-type by lattice domain. Due to increasing demands for continuous factors, UDs over continuous domain is in lack. Moreover, the uniformity can be further improved over a continuous domain. In this paper, we use coordinate descent methods with an initialization derived by threshold accepting (TA) algorithm to construct UDs over continuous domain with Centered L2-discrepancy. The new UDs perform better than the recorded ones in several computer experiments by the Kriging *** Codes 62K05 (Primary), 62K15 (Secondary) Copyright © 2023, The Authors. All rights reserved.

关键词： Interpolation

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A catalog of optimal foldover plans for constructing U-uniform minimum aberration four-level combined designs

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JOURNAL OF APPLIED STATISTICS 2019年第7期46卷 1288-1322页

作者： Elsawah, A. M. Fang, Kai-Tai Zagazig Univ Dept Math Fac Sci Zagazig 44519 Egypt BNU HKBU United Int Coll Div Sci & Technol Zhuhai 519085 Peoples R China Chinese Acad Sci Key Lab Random Complex Structures & Data Anal Beijing Peoples R China

The foldover plan is a transformation map for adding a foldover design to the initial design, thus resulting in a combined design which can be used for breaking the links between aliased effects. This paper discusses the optimality of foldover plans for four-level designs via the most common criteria: the generalized word-length pattern (GWLP), Lee discrepancy (LD), wrap-around discrepancy (WD), centered discrepancy (CD) and mixture discrepancy (MD). We prove that the LD, WD and GWLP are equivalent for: any initial design and the corresponding foldover designs;any foldover design and its complementary foldover design;and any combined design and its complementary combined design. However, these interesting properties do not necessarily take place in the cases of the CD and MD. New analytical expressions and lower bounds of these discrepancies are given for initial and combined designs, which can be used as benchmarks for constructing uniform designs. For illustration of the usage of our theoretical results, a catalog of optimal foldover plans for constructing U-uniform minimum aberration four-level combined designs that involve factors with run is tabulated, which can be used for investigating either qualitative or quantitative factors.

关键词： Foldover plan Foldover design combined design optimal foldover plan discrepancy generalized word-length pattern

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A joint call for actions to advance taxonomy in China

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Zoological Systematics 2022年第3期47卷 188-197页

作者： Chaodong Zhu Arong Luo Ming Bai Michael COrr Zhonge Hou Siqin Ge Jun Chen Yibo Hu Xuming Zhou Gexia Qiao Hongzhi Kong Limin Lu Xiaohua Jin Lei Cai Xinli Wei Ruilin Zhao Wei Miao Qingfeng Wang Zhongli Sha Qiang Lin Meng Qu Jianping Jiang Jiatang Li Jing Che Xuelong Jiang Xiaoyong Chen Lianming Gao Zongxin Ren Chunlei Xiang Shixiao Luo Donghui Wu Dong Liu Yanqiong Peng Tao Su Chenyang Cai Tianqi Zhu Wanzhi Cai Xingyue Liu Hu Li Huaijun Xue Zhen Ye Xuexin Chen Pu Tang Shujun Wei Hong Pang Qiang Xie Feng Zhang Feng Zhang Xianjin Peng Aibing Zhang Taiping Gao Changfa Zhou Chen Shao Libin Ma Zhaoming Wei Yunxia Luan Ziwei Yin Wu Dai Cong Wei Xiaolei Huang Jingxian Liu Xiangsheng Chen Tianci Yi Zhisheng Zhang Zhulidezi Aishan Qin Li Hongying Hu CAS Key Laboratory of Zoological Systematics and Evolution Institute of ZoologyChinese Academy of SciencesBeijing 100101China CAS Key Laboratory of Animal Ecology and Conservation Biology Institute of ZoologyChinese Academy of SciencesBeijing 100101China State Key Laboratory of Systematic and Evolutionary Botany Institute of BotanyChinese Academy of SciencesBeijing 100093China State Key Laboratory of Mycology(SKLM) Institute of MicrobiologyChinese Academy of SciencesBeijing 100101China CAS Key Laboratory of Aquatic Biodiversity and Conservation Institute of HydrobiologyChinese Academy of SciencesWuhan 430072China Wuhan Botanical Garden Chinese Academy of SciencesWuhan 430074China Department of Marine Organism Taxonomy&Phylogeny Institute of OceanologyChinese Academy of SciencesQingdao 266071China CAS Key Laboratory of Tropical Marine Bio-resources and Ecology South China Sea Institute of OceanologyChinese Academy of SciencesGuangzhou 510301China CAS Key Laboratory of Mountain Ecological Restoration and Bioresource Utilization&Ecological Restoration and Biodiversity Conservation Key Laboratory of Sichuan Province Chengdu Institute of BiologyChinese Academy of SciencesChengdu 610041China State Key Laboratory of Genetic Resources and Evolution&Yunnan Key Laboratory of Biodiversity and Ecological Security of Gaoligong Mountain Kunming Institute of ZoologyChinese Academy of SciencesKunming 650221China CAS Key Laboratory for Plant Diversity and Biogeography of East Asia Kunming Institute of BotanyChinese Academy of SciencesKunming 650201China CAS Key Laboratory of Plant Resource Conservation and Sustainable Utilization South China Botanical GardenChinese Academy of SciencesGuangzhou 510650China CAS Key Laboratory of Wetland Ecology and Environment Northeast Institute of Geography and AgroecologyChinese Academy of SciencesChangchun 130102China CAS Key Laboratory of Tropical Forest Ecology Xishuangbanna Tropical Botanical GardenChinese Academy of SciencesMenglunMenglaYunnan 66630

Taxonomy plays an important role in understanding the origin, evolution, and ecological functionality of biodiversity. There are large number of unknown species yet to be described by taxonomists, which together with their ecosystem services cannot be effectively protected prior to description. Despite this, taxonomy has been increasingly underrated insufficient funds and permanent positions to retain young talents. Further, the impact factordriven evaluation systems in China exacerbate this downward trend, so alternative evaluation metrics are urgently necessary. When the current generation of outstanding taxonomists retires,there will be too few remaining taxonomists left to train the next generation. In light of these challenges, all co-authors worked together on this paper to analyze the current situation of taxonomy and put out a joint call for immediate actions to advance taxonomy in China.

关键词： Endangered taxonomists morphology-based taxonomy integrative taxonomy capacity building systematics

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A sharp threshold of propagation connectivity for mixed random hypergraphs

arXiv

引用

arXiv 2018年

作者： Zhou, Guangyan Wang, Bin Xu, Ke Department of Mathematics Beijing Technology and Business University China Key Laboratory of Random Complex Structures and Data Science Academy of Mathematics and Systems Science Chinese Academy of Sciences China State Key Laboratory of Software Development Environments Beihang University China

This paper studies the propagation connectivity of a random hypergraph G containing both 2-edges and 3-hyperedges. We find an exact threshold of the propagation connectivity of G: If Iϵ,r -1, then G is propagation connected with high probability, where Iϵ,r is a constant dependent on the parameters of 2 and 3-edge probabilities.68Q87, 05C65 Copyright © 2018, The Authors. All rights reserved.

关键词： Graph theory

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The Itô SDEs and Fokker–Planck equations with Osgood and Sobolev coefficients

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Stochastics 2018年第3期90卷 379-410页

作者： Luo, Dejun Key Laboratory of Random Complex Structures and Data Sciences Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China School of Mathematical Sciences University of the Chinese Academy of Sciences Beijing China

We study the degenerate Itô SDE on ℝd whose drift coefficient only fulfills a mixed Osgood and Sobolev regularity. Under suitable assumptions on the gradient of the diffusion coefficient and on the divergence of ... 详细信息

We study the degenerate Itô SDE on ℝ^d whose drift coefficient only fulfills a mixed Osgood and Sobolev regularity. Under suitable assumptions on the gradient of the diffusion coefficient and on the divergence of the drift coefficient, we prove the existence and uniqueness of generalized stochastic flows associated to such equations. We also prove the uniqueness of solutions to the corresponding Fokker–Planck equation by using the probabilistic method. © 2017 Informa UK Limited, trading as Taylor & Francis Group.

关键词： DiPerna–Lions theory Fokker–Planck equation Osgood and Sobolev condition Stochastic differential equation stochastic flow

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Euler-Lagrangian approach to 3D stochastic Euler equations

arXiv

引用

arXiv 2018年

作者： Flandoli, Franco Luo, Dejun Scuola Normale Superiore of Pisa Italy Key Laboratory of Random Complex Structures and Data Sciences Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of the Chinese Academy of Sciences Beijing100049 China

3D stochastic Euler equations with a special form of multiplicative noise are considered. A Constantin-Iyer type representation in Euler-Lagrangian form is given, based on stochastic characteristics. Local existence and uniqueness of solutions in suitable Hölder spaces is proved from the Euler-Lagrangian formulation. Copyright © 2018, The Authors. All rights reserved.

关键词： Stochastic systems

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