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Finite mixture of varying coefficient model: Estimation and component selection

JOURNAL OF MULTIVARIATE ANALYSIS 2019年 171卷 452-474页

作者： Ye, Mao Lu, Zhao-Hua Li, Yimei Song, Xinyuan Purdue Univ Dept Stat 610 Purdue Mall W Lafayette IN 47907 USA St Jude Childrens Res Hosp Dept Biostat MS 768262 Danny Thomas Pl Memphis TN 38105 USA Chinese Univ Hong Kong Shenzhen Res Inst Shatin Hong Kong Peoples R China Chinese Univ Hong Kong Dept Stat Shatin Hong Kong Peoples R China

Heterogeneous longitudinal data have become prevalent in medical, biological, and social studies. This paper proposes a finite mixture of varying coefficient models for handling heterogeneous populations. Each component of the mixture is modeled by a varying coefficient mixed-effect model that characterizes the longitudinal relations among variables. The identifiability of the mixture model is studied. Regression splines with equally spaced knots are used to approximate the varying coefficient functions, and a nested expectation maximization algorithm is developed to obtain the maximum likelihood estimation. We propose a penalized likelihood method based on the smoothly clipped absolute deviation (SCAD) penalty for the component selection of finite mixture of varying coefficient model. A modified BIC-based criterion based on the SCAD penalty, the BICSCAD, is proposed for selecting the penalty parameter and spline space simultaneously. The asymptotic properties of parameter estimation and component selection consistency are studied under mild conditions. Simulation studies are conducted to illustrate the component selection, parameter estimation, and inference of the proposed method. The model is then applied to a heterogeneous longitudinal data set from a study of the treatment effect on the use of heroin in the California Civil Addict Program. (C) 2019 Elsevier Inc. All rights reserved.

关键词： expectation maximization algorithm Finite mixture model Model selection Random effects SCAD Varying coefficients

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Adaptive quantile low-rank matrix factorization

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PATTERN RECOGNITION 2020年 103卷 107310-107310页

作者： Xu, Shuang Zhang, Chun-Xia Zhang, Jiangshe Xi An Jiao Tong Univ Sch Math & Stat Xian 710049 Shaanxi Peoples R China

Low-rank matrix factorization (LRMF) has received much popularity owing to its successful applications in both computer vision and data mining. By assuming noise to come from a Gaussian, Laplace or mixture of Gaussian distributions, significant efforts have been made on optimizing the (weighted) L-1 or L-2-norm loss between an observed matrix and its bilinear factorization. However, the type of noise distribution is generally unknown in real applications and inappropriate assumptions will inevitably deteriorate the behavior of LRMF. On the other hand, real data are often corrupted by skew rather than symmetric noise. To tackle this problem, this paper presents a novel LRMF model called AQ-LRMF by modeling noise with a mixture of asymmetric Laplace distributions. An efficient algorithm based on the expectation-maximization (EM) algorithm is also offered to estimate the parameters involved in AQ-LRMF. The AQ-LRMF model possesses the advantage that it can approximate noise well no matter whether the real noise is symmetric or skew. The core idea of AQ-LRMF lies in solving a weighted L-1 problem with weights being learned from data. The experiments conducted on synthetic and real data sets show that AQ-LRMF outperforms several state-of-the-art techniques. Furthermore, AQ-LRMF also has the superiority over the other algorithms in terms of capturing local structural information contained in real images. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Low-rank matrix factorization Mixture of asymmetric Laplace distributions expectation maximization algorithm Skew noise

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Cheating Detection Method Based on Improved Cognitive Diagnosis Model 18th

Cheating Detection Method Based on Improved Cognitive Diagno...

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18th Annual International Conference on Web-Based Learning (ICWL)

作者： Li, Zhizhuang Zhu, Zhengzhou Xie, Qiongyu Peking Univ Sch Software & Microelect Beijing Peoples R China Anhui Normal Univ Wuhu Anhui Peoples R China

ISBN: (纸本)9783030357580;9783030357573

Cheating in examinations destroys the principles of fairness and justice in evaluation. Cheating detection is of great practical significance. Traditional cheating detection methods have many disadvantages, such as difficult to detect covert equipment cheating, multi-source cheating, difficult to distinguish plagiarists from plagiarists, difficult to distinguish plagiarists from victims, or plagiarism from coincidences. In this paper, the concept of knowledge point mastery Index is introduced to measure students' mastery of a certain knowledge point, and a test method of cheating based on improved cognitive diagnostic model is proposed. This method calculates the weight of each knowledge point in every examination question through linear regression and EM algorithm according to students' historical learning behavior, and then calculates students' mastering degree of knowledge point based on historical answers. Then calculate the mastering degree of knowledge point based on the examination results. Finally, we compare the mastering degree of knowledge point based on the examination results and the historical answers to detect students' cheating situation. The experiments show that the precision and recall rate of this method are significantly higher than those of the method based on the false-same rate, the method based on the false-same rate and the right-same rate and the method based on the Person-Fit index.

关键词： Weight of knowledge point Cheating detection Mastering degree of knowledge point Linear regression expectation maximization algorithm

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Track Segment Association of Maneuvering Target based on expectation maximization 11

Track Segment Association of Maneuvering Target based on Exp...

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11th International Congress on Image and Signal Processing, BioMedical Engineering and Informatics (CISP-BMEI)

作者： Sun, Jinping Wang, Naiyu Zhang, Zhiguo Beihang Univ Sch Elect & Informat Engn Beijing 100191 Peoples R China

ISBN: (纸本)9781538676042

Because of the high maneuverability of targets, track breakages are common in the tracking process. With the purpose of stitching the track segments and achieving better tracking results, we adopt an algorithm to stitch the track segments based on expectation maximization (EM). The EM algorithm can be used to estimate and identify the maneuvering targets' state and angular velocities simultaneously. It consists of two steps. The expectation (E) step is implemented by an extended Kalman filter (EKF) and extended Rauch-Tung-Striebel smoother (ERTSS). The maximization (M) step is implemented by genetic algorithm, which can achieve the Maximum likelihood sequence estimation for unknown parameters. Experiments show that this algorithm can achieve better tracking results. Moreover, it also exhibits good capability when estimating the unknown parameter.

关键词： expectation maximization algorithm target tracking track segment association parameter estimation

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Finding the Key Influences on the House Price by Finite Mixture Model Based on the Real Estate Data in Changchun 24th

Finding the Key Influences on the House Price by Finite Mixt...

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24th Int Conference on Database Systems for Advanced Applications / 6th Int Workshop on Big Data Management and Service / 4th Int Workshop on Big Data Quality Management / 3rd Int Workshop on Graph Data Management and Analysis

作者： Xu, Xin Huang, Zeyu Wu, Jingyi Fu, Yanjie Luo, Na Chen, Weitong Wang, Jianan Yin, Minghao Northeast Normal Univ Changchun Jilin Peoples R China Missouri Univ Sci & Technol Rolla MO 65409 USA Univ Queensland Brisbane Qld Australia

ISBN: (纸本)9783030185909;9783030185893

Nowadays it's difficult for us to analyze the development law of real estate. What's more, predictable house price and understandable key influences can also build a healthier real estate market. Therefore, we propose a model which can predict the house price, while it can find key influences which are important influences on the house price. Our method is inspired by the finite mixture model (FMM) and information gain ratio (IGO). Specifically, we collect data that includes detail information about houses and communities from Anjuke Inc. which is an online platform for house sales. Then, according to the data, we find the scope of latent groups number by cluster methods to avoid blind searching the number of latent groups. Next, we use IGO to rank the features and weight them and we build a regression model based on the finite mixture model. Finally, the experimental results demonstrate our method performance on predicting house price, and we find key influences on house price.

关键词： Real estate Finite mixture model Information gain ratio expectation maximization algorithm

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An Improved Initialization Method using Firefly Movement and Light Intensity for Better Clustering Performance 2019

An Improved Initialization Method using Firefly Movement and...

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2nd International Conference on Software Engineering and Information Management (ICSIM) / 2nd International Conference on Big Data and Smart Computing (ICBDSC)

作者： Masangcap, Maria Lolita G. Sison, Ariel M. Medina, Ruji P. Technol Inst Philippines Quezon City Philippines Emilio Aguinaldo Coll Manila Philippines

ISBN: (纸本)9781450366427

K-Means and EM algorithms are the most well-known clustering algorithms because they are simple, easy to understand and implement. However, both algorithms are sensitive to initial seeds which are randomly selected leading to slow convergence and less reliable clustering results. In this paper, an improved initialization method adopted the concept of light intensity and firefly movement to search for better initial seeds. Numerical experiments were conducted to evaluate the performance of the Enhanced K-Means and EM using faculty performance evaluation ratings as the dataset. The experiments showed that the implementation of the improved initialization method before the clustering process resulted in a higher intra-cluster and lower inter-cluster similarity. Also, there are fifty-nine percent (59%) and sixty-three percent (63%) decrease in the runtime execution while there are forty-four percent (44%) and twenty-seven percent (27%) fewer number of iterations recorded in the implementation of the enhanced KMeans and EM algorithms respectively.

关键词： Clustering K-Means algorithm expectation maximization algorithm Light Intensity Firefly Movement

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Robust CSI Estimation under Complex Communication Environment

Robust CSI Estimation under Complex Communication Environmen...

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IEEE International Conference on Communications (IEEE ICC)

作者： Zhang, Haipei Xue, Jiang Meng, Deyu Zhao, Qian Xu, Zongben Shijiazhuang Campus Army Engineering University Shijiazhuang China

ISBN: (纸本)9781538680889

Channel estimation is the critical and fundamental problem in wireless communication techniques, however, the complexity environment, including interference and noise, post a fundamental limit on the accuracy of channel estimation on practical applications. Most existing channel estimation techniques are based on the simple assumption of Gaussian white noise, which makes the performance poorly within real communication environment. To address this problem, we propose a new channel estimation method by assuming the environment as Mixture of Gaussian (MoG) distributions and penalized MoG (PMoG) model by combining the penalized likelihood method with MoG distributions. This model is proposed by the first time in the research of wireless communication, and the superiority of this method lies on its approximation capability to wide range of scenarios of complex communication environments adaptively and analyzing the environment by learning the proper number of statistical components. Moreover, we design an expectation maximization (EM) algorithm to estimate the parameters of the PMoG model. The advantage of our method is demonstrated by simulation experiments.

关键词： Channel estimation Machine learning MIMO Mixture of Gaussian distributions expectation maximization algorithm

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Convergence and Consistency Results in Spectral Clustering and Gaussian Mixture Models

Convergence and Consistency Results in Spectral Clustering a...

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作者： Zhao, Ruofei University of Michigan

学位级别：博士

Clustering analysis is a popular technique in statistics and machine learning. Despite its wide use, certain theoretical properties of clustering algorithms are not well-understood. In this dissertation, we investigate two problems concerning the convergence and consistency of clustering algorithms. The first problem is on the uniform consistency of spectral embeddings in spectral clustering and in, more generally, spectral methods. The second problem is on the statistical convergence of the expectation maximization (EM) algorithm on Gaussian mixture models. Specifically, in the first problem, we study the convergence of the spectral embeddings obtained from the leading eigenvectors of certain similarity matrices to their population counterparts. We opt to study this convergence in a uniform (instead of average) sense and highlight the benefits of this choice. Using the Newton-Kantorovich Theorem and other tools from functional analysis, we first establish a general perturbation result for orthonormal bases of invariant subspaces. We then apply this general result to normalized spectral clustering. By tapping into the rich literature of Sobolev spaces and exploiting some concentration results in Hilbert spaces, we are able to prove a finite sample error bound on the uniform consistency error of the spectral embeddings in normalized spectral clustering. In the second problem, we study the convergence behavior of the EM algorithm on Gaussian mixture models with an arbitrary number of mixture components and mixing weights. We show that as long as the means of the components are separated by an amount proportional to the square root of the smaller of the number of components and the dimension, the EM algorithm converges locally to the global optimum of the log-likelihood. Further, we show that the convergence rate is linear and characterize the size of the basin of attraction to the global optimum.

关键词： Gaussian mixture models Spectral embedding Spectral clustering expectation maximization algorithm Thesis

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Identification of ARX System Based on Shifted Asymmetric Laplace Distribution 38

Identification of ARX System Based on Shifted Asymmetric Lap...

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38th Chinese Control Conference (CCC)

作者： Yu, Miao Zhang, Tianyi Yang, Xianqiang Harbin Inst Technol Res Inst Intelligent Control & Syst Harbin Peoples R China

ISBN: (纸本)9789881563972

The identification of AutoRegressive eXogenous (ARX) model by outliers is addressed in this paper. Shifted(non-centralized) asymmetric Laplace (SAL) distribution and expectation maximization (EM) algorithm are employed to estimate the unknown model parameters. Outliers are common in the signal acquisition process and have a serious impact on data-driven modeling method. In this paper, the probability method is used to solve the problem of outliers. When the noise parameter is regarded as a prior exponential distribution, the model output obeys the SAL distribution which is robust to outliers. The known statistical properties of SAL distribution are applied to calculate the M-step in the EM algorithm and get the iterative parametric formula. The accuracy of the proposed algorithm is verified by a numerical simulation example.

关键词： shifted asymmetric Laplace distribution expectation maximization algorithm autoRegressive eXogenous model

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The Spectral Approach to Linear Rational expectations Models

arXiv

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arXiv 2020年

作者： Al-Sadoon, Majid M. Durham University Business School United Kingdom

This paper considers linear rational expectations models in the frequency domain. The paper characterizes existence and uniqueness of solutions to particular as well as generic systems. The set of all solutions to a given system is shown to be a finite dimensional affine space in the frequency domain. It is demonstrated that solutions can be discontinuous with respect to the parameters of the models in the context of non-uniqueness, invalidating mainstream frequentist and Bayesian methods. The ill-posedness of the problem motivates regularized solutions with theoretically guaranteed uniqueness, continuity, and even differentiability *** Codes 91B84 Copyright © 2020, The Authors. All rights reserved.

关键词： expectation maximization algorithm

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