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Information geometry in optimization,machine learning and statistical inference

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Frontiers of Electrical and Electronic Engineering in China 2010年第3期5卷 241-260页

作者： Shun-ichi AMARI RIKEN Brain Science Institute Saitama 351-0198Japan

The present article gives an introduction to information geometry and surveys its applications in the area of machine learning,optimization and statistical *** geometry is explained intuitively by using divergence functions introduced in a manifold of probability distributions and other general *** give a Riemannian structure together with a pair of dual flatness *** manifolds are dually *** a manifold is dually flat,a generalized Pythagorean theorem and related projection theorem are *** provide useful means for various approximation and optimization *** apply them to alternative minimization problems,Ying-Yang machines and belief propagation algorithm in machine learning.

关键词： information geometry machine learning optimization statistical inference divergence graphical model Ying-Yang machine

Autoregressive moving average model for matrix time series

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statistical Theory and Related Fields 2023年第4期7卷 318-335页

作者： Shujin Wu Ping Bi College of Liberal Arts and Sciences China University of Petroleum-Beijing at KaramayKaramayPeople’s Republic of China KLATASDS-MOE School of StatisticsEast China Normal UniversityShanghaiPeople’s Republic of China School of Mathematical Sciences Key Laboratory of Pure Mathematics and Mathematical PracticeEast China Normal UniversityShanghaiPeople’s Republic of China

In the paper,the autoregressive moving average model for matrix time series(MARMA)is *** properties of the MARMA model are investigated by using the conditional least square estimation,the conditional maximum likelihood estimation,the projection theorem in Hilbert space and the decomposition technique of time series,which include necessary and suf-ficient conditions for stationarity and invertibility,model parameter estimation,model testing and model forecasting.

关键词： Matrix time series autoregressive moving average model bilinear model statistical inference

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隐私规避的网络调查与间接估计方法

Effect of observation time on source identification of diffusion in complex networks

管理科学 2024年第1期

作者：吕欣刘楚楚蔡梦思陈洒然

在管理决策中，管理对象的真实状态往往因隐私、敏感等因素导致自我报告数据质量不高，样本数据存在较大偏差，进而难以掌握目标对象的真实情况。针对这一问题，同时为了满足数字经济时代下的数据隐私保护需求，本文开发了一类基于社交... 详细信息

在管理决策中，管理对象的真实状态往往因隐私、敏感等因素导致自我报告数据质量不高，样本数据存在较大偏差，进而难以掌握目标对象的真实情况。针对这一问题，同时为了满足数字经济时代下的数据隐私保护需求，本文开发了一类基于社交网络间接报告的数据采集方法，并在网络抽样与统计推断理论的基础上，设计了基于间接报告样本数据的总体估计方法（ECM）。该方法操作简单，可对调查对象进行随机采样或实施普查，除采集样本的自我陈述数据外，同时采集每个样本关于其密切社交对象的报告数据，从而避免了自身因敏感原因等不愿提供数据或提供不真实数据的问题，提出的估计方法能在样本报告数据的基础上实现对总体的高精度估计，并能实现自报告数据和他报告数据的交互验证。本文的研究方法在一个多达556627名活跃用户的难接触人群在线社交网络上进行了充分验证，抽样实验表明ECM对全网平均好友数和总体特征的估计误差低于3%。进一步地，本文开展了实证研究，通过设计自报告和他报告问卷，对某企业职员的一般和隐私性问题进行了问卷调查，并通过间接估计方法实现了对目标的总体估计，展示了该方法的实用性和有效性。

关键词：隐私数据真实性网络抽样间接估计统计推断 privacy data authenticity network sampling indirect estimation statistical inference

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Chinese Physics B 2022年第7期31卷 97-103页

作者：史朝义张琦楚天广 College of Engineering Peking UniversityBeijing 100871China School of Information Technology and Management University of International Business and EconomicsBeijing 100105China

This paper examines the effect of the observation time on source identification of a discrete-time susceptible-infectedrecovered diffusion process in a network with snapshot of partial *** formulate the source identification problem as a maximum likelihood(ML)estimator and develop a statistical inference method based on Monte Carlo simulation(MCS)to estimate the source location and the initial time of *** results in synthetic networks and real-world networks demonstrate evident impact of the observation time as well as the fraction of the observers on the concerned problem.

关键词： complex network source identification statistical inference partial observation

inference and optimal design on step-stress partially accelerated life test for hybrid system with masked data

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Journal of Systems Engineering and Electronics 2018年第5期29卷 1089-1100页

作者： SHI Xiaolin LU Pu SHI Yimin School of Electronic Engineering Xi'an University of Posts and Telecommunications Department of Applied Mathematics Northwestern Polytechnical University

Under Type-Ⅱ progressively hybrid censoring, this paper discusses statistical inference and optimal design on stepstress partially accelerated life test for hybrid system in presence of masked data. It is assumed that the lifetime of the component in hybrid systems follows independent and identical modified Weibull distributions. The maximum likelihood estimations(MLEs)of the unknown parameters, acceleration factor and reliability indexes are derived by using the Newton-Raphson algorithm. The asymptotic variance-covariance matrix and the approximate confidence intervals are obtained based on normal approximation to the asymptotic distribution of MLEs of model parameters. Moreover,two bootstrap confidence intervals are constructed by using the parametric bootstrap method. The optimal time of changing stress levels is determined under D-optimality and A-optimality ***, the Monte Carlo simulation study is carried out to illustrate the proposed procedures.

关键词： hybrid system step-stress partially accelerated life test Type-Ⅱ progressively hybrid censored and masked data statistical inference optimal test plan

Informative subsampling of big data for statistical inferences

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Informative subsampling of big data for statistical inferenc...

Estimating the basic reproduction number for single-strain dengue fever epidemics

第十届海峡两岸统计与概率研讨会

作者： Wei Zheng Indiana University-Purdue University

For many tasks of data analysis,a large database of explanatory variables is readily available, while the responses are missing and very expensive to obtain. A natural remedy is to judiciously select a subset of the population for which the measurement of the response is to be obtained. In the machine learning community, this problem termed as active learning has been extensively studied. It has applications in marketing, banking, health care, etc. Recently, the subsampling problem for the statistical inference has been explored by Ouyang, Apley and Mehrotra(2015a, 2015 b, 2016). However, the main focus was on the logistic regression for model validation and on the linear model with the interaction term in the study of precision medicine. Here, we propose a generic framework to approximate this N-P hard problem by a continuous problem for which efficient algorithms can be developed. It has three advantages:(i) The information efficiency of the derived subsample can be evaluated without knowing the exact optimal subsample;(ii) It can cope with a very general class of nonlinear models;(iii) The computational cost of the new method is only a small fraction of the existing method.

关键词： subsampling big data design of experiments algorithm statistical inference

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Infectious Diseases of Poverty 2014年第1期3卷 100-116页

作者： Adnan Khan Muhammad Hassan Mudassar Imran Department of Mathematics Lahore University of Management SciencesDHALahorePakistan Department of Mathematics Swiss Federal Institute of Technology(ETH)ZurichRämistrasse 1018092 ZurichSwitzerland

Background:Dengue,an infectious tropical disease,has recently emerged as one of the most important mosquito-borne viral diseases in the *** perform a retrospective analysis of the 2011 dengue fever epidemic in Pakistan in order to assess the transmissibility of the *** obtain estimates of the basic reproduction number R0 from epidemic data using different methodologies applied to different epidemic models in order to evaluate the robustness of our ***:We first estimate model parameters by fitting a deterministic ODE vector-host model for the transmission dynamics of single-strain dengue to the epidemic data,using both a basic ordinary least squares(OLS)as well as a generalized least squares(GLS)***,we perform the same analysis for a direct-transmission ODE model,thereby allowing us to compare our results across different *** addition,we formulate a direct-transmission stochastic model for the transmission dynamics of dengue and obtain parameter estimates for the stochastic model using Markov chain Monte Carlo(MCMC)*** each of the cases we have considered,the estimate for the basic reproduction number R0 is initially greater than unity leading to an epidemic ***,control measures implemented several weeks after the initial outbreak successfully reduce R0 to less than unity,thus resulting in disease ***,it is observed that there is strong agreement in our estimates for the pre-control value of R0,both across different methodologies as well across different ***,there are also significant differences between our estimates for the post-control value of the basic reproduction number across the two different ***:In conclusion,we have obtained robust estimates for the value of the basic reproduction number R0 associated with the 2011 dengue fever epidemic before the implementation of public health control ***,we have shown that there is close agreement

关键词： Epidemiology Dengue fever statistical inference Stochastic model Markov chain Monte Carlo

inference of Online Approach to Non-parametric Smoothing of Big Data

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中国科学技术大学学报 2021年

作者： CHENZiyu GUOXiao DepartmentofStatisticsandFinance SchoolofManagementUniversityofScienceandTechnologyofChina InternationalInstituteofFinance SchoolofManagementUniversityofScienceandTechnologyofChina

The online updating method(ONLINE) is an efficient analysis approach applied to big *** establish the asymptotic properties and conduct statistical inference of the ONLINE models in kernel density and regression. Several algorithms are constructed to solve the difficulties of the bandwidth h selection in kernel density and regression respectively. We verify the asymptotic normality of the ONLINE density model in simulation and apply the methods to the Volatility Index(VIX) prediction using the ONLINE linear kernel regression. The empirical results show the model achieves a comparable performance in continuously arriving option data streams prediction with significantly lower complexity than the classical local linear regression model.

关键词： bandwidth parameter kernel estimator online updating estimation statistical inference VIX prediction

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跳出传统假设检验方法的陷阱