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arXiv 2023年

作者： Jiang, Alex Ziyu Rodriguez, Abel Department of Statistics University of Washington United States

Multivariate Hawkes Processes (MHPs) are a class of point processes that can account for complex temporal dynamics among event sequences. In this work, we study the accuracy and computational efficiency of three classes of algorithms which, while widely used in the context of Bayesian inference, have rarely been applied in the context of MHPs: stochastic gradient expectation-maximization, stochastic gradient variational inference and stochastic gradient Langevin Monte Carlo. An important contribution of this paper is a novel approximation to the likelihood function that allows us to retain the computational advantages associated with conjugate settings while reducing approximation errors associated with the boundary effects. The comparisons are based on various simulated scenarios as well as an application to the study of risk dynamics in the Standard & Poor’s 500 intraday index prices among its 11 sectors. © 2023, CC BY.

关键词： expectation maximization algorithm

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Matching prior pairs connecting Maximum A Posteriori estimation and posterior expectation

arXiv

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arXiv 2023年

作者： Okudo, Michiko Yano, Keisuke Department of Mathematical Informatics Graduate School of Information Science and Technology The University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo113-8656 Japan The Institute of Statistical Mathematics 10-3 Midori cho Tokyo Tachikawa190-8562 Japan

Bayesian statistics has two common measures of central tendency of a posterior distribution: posterior means and Maximum A Posteriori (MAP) estimates. In this paper, we discuss a connection between MAP estimates and posterior means. We derive an asymptotic condition for a pair of prior densities under which the posterior mean based on one prior coincides with the MAP estimate based on the other prior. A sufficient condition for the existence of this prior pair relates to α-flatness of the statistical model in information geometry. We also construct a matching prior pair using α-parallel priors. Our result elucidates an interesting connection between regularization in generalized linear regression models and posterior expectation. Copyright © 2023, The Authors. All rights reserved.

关键词： expectation maximization algorithm

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Robust algorithm for attack detection based on time-varying hidden Markov model subject to outliers

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INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING 2020年第10期34卷 1537-1558页

作者： Lu, Genghong Feng, Dongqin Huang, Biao Zhejiang Univ Inst Cyber Syst & Control State Key Lab Ind Control Technol Zheda Rd 38 Hangzhou Zhejiang Peoples R China Univ Alberta Dept Chem & Mat Engn Edmonton AB Canada

The problem of robust attack detection and prediction for networked control systems in the presence of outliers is discussed in this article. The conventional hidden Markov model (HMM) is trained to learn the system behavior (ie, transitions between different operating modes) in the nominal process. The HMM with time-varying transition probabilities is used to track the attack behavior in which the adversary triggers more hazard modes to hasten fatigue of control devices by injecting attack signals with random magnitude and frequency. For different operating modes, the observations are assumed to follow different multivariate Student'stdistributions instead of Gaussian distributions and thus address the robust estimation problem. The expectation maximization algorithm is used to estimate parameters. Finally, simulations are conducted to verify the effectiveness of the proposed method.

关键词： expectation maximization algorithm hidden Markov models outliers robust attack detection time-varying transition probabilities

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Identification of nonlinear state-space time-delay system

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ASSEMBLY AUTOMATION 2020年第1期40卷 22-30页

作者： Liu, Xin Zhang, Hang Zhu, Pengbo Yang, Xianqiang Du, Zhiwei Harbin Inst Technol Harbin Peoples R China North China Inst Sci & Technol Langfang Peoples R China

Purpose This paper aims to investigate an identification strategy for the nonlinear state-space model (SSM) in the presence of an unknown output time-delay. The equations to estimate the unknown model parameters and output time-delay are derived simultaneously in the proposed strategy. Design/methodology/approach The unknown integer-valued time-delay is processed as a latent variable which is uniformly distributed in a priori known range. The estimations of the unknown time-delay and model parameters are both realized using the expectation-maximization (EM) algorithm, which has a good performance in dealing with latent variable issues. Moreover, the particle filter (PF) with an unknown time-delay is introduced to calculated the Q-function of the EM algorithm. Findings Although amounts of effective approaches for nonlinear SSM identification have been developed in the literature, the problem of time-delay is not considered in most of them. The time-delay is commonly existed in industrial scenario and it could cause extra difficulties for industrial process modeling. The problem of unknown output time-delay is considered in this paper, and the validity of the proposed approach is demonstrated through the numerical example and a two-link manipulator system. Originality/value The novel approach to identify the nonlinear SSM in the presence of an unknown output time-delay with EM algorithm is put forward in this work.

关键词： Particle filter expectation maximization algorithm Latent variables Nonlinear system identification State-space time-delay model

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Metro passenger's path choice model estimation with travel time correlations derived from smart card data

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TRANSPORTATION PLANNING AND TECHNOLOGY 2020年第2期43卷 141-157页

作者： Zhang, Yongsheng Yao, Enjian Zheng, Kangning Xu, Hao Beijing Jiaotong Univ Sch Traff & Transportat 3 Shangyuancun Beijing 100044 Peoples R China Univ Nevada Dept Civil & Environm Engn Reno NV 89557 USA

Smart card data provides a new perspective for estimating a metro passenger's path choice model in a large-scale urban rail transit network with multiple alternative paths between origin-destination pairs. However, existing research does not consider correlations of path travel times among alternative paths when using smart card data for estimation purposes, leading to biased estimations. This paper proposes an approach to estimating the path choice model considering path travel time correlations. In particular, a simplified form of measuring path travel time correlations caused by shared links is proposed to improve estimation efficiency. Then a framework for a linking path choice model and smart card data is developed based on a Gaussian mixture model;an expectation maximization-based estimation algorithm is also provided. Finally, taking the Guangzhou Metro in China as an example, the superiority of estimations based on smart card data considering correlations is observed in both statistical terms and predictions.

关键词： Urban rail transit path choice model smart card data travel time correlation expectation maximization algorithm application

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Estimation and diagnostic tools in reparameterized slashed Rayleigh regression model. An application to chemical data

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CHEMOMETRICS AND INTELLIGENT LABORATORY SYSTEMS 2020年 207卷 104189-104189页

作者： Gallardo, Diego I. Gomez-Deniz, Emilio Leao, Jeremias Gomez, Hector W. Univ Atacama Fac Ingn Dept Matemat Copiapo Chile Univ Las Palmas Gran Canaria Dept Quantitat Methods Econ Las Palmas Gran Canaria Spain Univ Las Palmas Gran Canaria TiDES Inst Las Palmas Gran Canaria Spain Univ Fed Amazonas Dept Estatist Manaus AM Brazil Univ Antofagasta Fac Ciencias Basicas Dept Matemat Antofagasta Chile

In this paper, we introduce a regression model where the response variable is reparameterized slashed Rayleigh (RSR) distributed and which is indexed by mean and precision parameters. The proposed regression model is useful for situations where the variable of interest is continuous and restricted to the positive real line and is related to other variables through the mean and precision parameters. In addition, the RSR model has properties that its competitor distributions of the exponential family do not have. Estimation is performed by expectation maximization (EM) and extensions. Furthermore, we discuss residuals and influence diagnostic tools. Finally, we also carry out two applications to real-world data that demonstrate the usefulness of the proposed model.

关键词： expectation maximization algorithm Linear regression Reparameterized Rayleigh distribution Monte Carlo simulation

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On the use of the modified power series family of distributions in a cure rate model context

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STATISTICAL METHODS IN MEDICAL RESEARCH 2020年第7期29卷 1831-1845页

作者： Gallardo, Diego I. Gomez, Yolanda M. Gomez, Hector W. de Castro, Mario Univ Atacama Fac Ingn Dept Matemat Copiapo Chile Univ Antofagasta Fac Ciencias Basicas Dept Matemat Ave Angamos 601 Antofagasta Chile Univ Sao Paulo Inst Ciencias Matem & Comp Sao Paulo Brazil

In this paper, we propose a generalization of the power series cure rate model for the number of competing causes related to the occurrence of the event of interest. The model includes distributions not yet used in the cure rate models context, such as the Borel, Haight and Restricted Generalized Poisson distributions. The model is conveniently parameterized in terms of the cure rate. Maximum likelihood estimation based on the expectation maximization algorithm is discussed. A simulation study designed to assess some properties of the estimators is carried out, showing the good performance of the proposed estimation procedure in finite samples. Finally, an application to a bone marrow transplant data set is presented.

关键词： expectation maximization algorithm long-term survival models maximum likelihood promotion time cure rate model survival analysis

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Modelling the patient accrual with truncated Gaussian mixture distribution for the accurate estimation of sample size in survival trials

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STATISTICAL METHODS IN MEDICAL RESEARCH 2020年第10期29卷 2972-2987页

作者： Hu, Haixia Wang, Ling Li, Chen Ge, Wei Wu, Kejian Xia, Jielai Air Force Med Univ Fac Prevent Med Dept Hlth Stat 169 Changle West Rd Xian 710032 Peoples R China Air Force Med Univ Sch Basic Med Dept Math & Phys Xian Peoples R China

In survival trials with fixed trial length, the patient accrual rate has a significant impact on the sample size estimation or equivalently, on the power of trials. A larger sample size is required for the staggered patient entry. During enrollment, the patient accrual rate changes with the recruitment publicity effect, disease incidence and many other factors and fluctuations of the accrual rate occur frequently. However, the existing accrual models are either over-simplified for the constant rate assumption or complicated in calculation for the subdivision of the accrual period. A more flexible accrual model is required to represent the fluctuant patient accrual rate for accurate sample size estimation. In this paper, inspired by the flexibility of the Gaussian mixture distribution in approximating continuous densities, we propose the truncated Gaussian mixture distribution accrual model to represent different variations of accrual rate by different parameter configurations. The sample size calculation formula and the parameter setting of the proposed accrual model are discussed further.

关键词： Truncated Gaussian mixture distribution accrual model expectation maximization algorithm sample size estimation survival trials

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The Log Private Company Valuation Model

arXiv

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arXiv 2022年

作者： Gankhuu, Battulga Department of Applied Mathematics National University of Mongolia Ulaanbaatar Mongolia

For a public company, pricing and hedging models of options and equity–linked life insurance products have been sufficiently developed. However, for a private company, because of unobserved prices, pricing and hedging models of the European options and life insurance products are in their early stages of development. For this reason, this paper introduces a log private company valuation model, which is based on the dynamic Gordon growth model. In this paper, we obtain closed–form pricing and hedging formulas of the European options and equity–linked life insurance products for private companies. Also, the paper provides Maximum Likelihood (ML) estimations of our model, expectation maximization (EM) algorithm, and valuation formula for private companies. © 2022, CC BY.

关键词： expectation maximization algorithm

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Speech Enhancement Based on Approximate Message Passing

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China Communications 2020年第8期17卷 187-198页

作者： Chao Li Ting Jiang Sheng Wu School of Information and Communication Engineering Beijing University of Posts and TelecommunicationsBeijing 100876China

To overcome the limitations of conventional speech enhancement methods, such as inaccurate voice activity detector(VAD) and noise estimation, a novel speech enhancement algorithm based on the approximate message passing(AMP) is adopted. AMP exploits the difference between speech and noise sparsity to remove or mute the noise from the corrupted speech. The AMP algorithm is adopted to reconstruct the clean speech efficiently for speech enhancement. More specifically, the prior probability distribution of speech sparsity coefficient is characterized by Gaussian-model, and the hyper-parameters of the prior model are excellently learned by expectation maximization(EM) algorithm. We utilize the k-nearest neighbor(k-NN) algorithm to learn the sparsity with the fact that the speech coefficients between adjacent frames are correlated. In addition, computational simulations are used to validate the proposed algorithm, which achieves better speech enhancement performance than other four baseline methods-Wiener filtering, subspace pursuit(SP), distributed sparsity adaptive matching pursuit(DSAMP), and expectation-maximization Gaussian-model approximate message passing(EM-GAMP) under different compression ratios and a wide range of signal to noise ratios(SNRs).

关键词： speech enhancement approximate message passing Gaussian model expectation maximization algorithm

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