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A Study of EM algorithm as an Imputation Method: A Model-Based Simulation Study with Application to a Synthetic Compositional Data

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Open Journal of Modelling and Simulation 2024年第2期12卷 33-42页

作者： Yisa Adeniyi Abolade Yichuan Zhao Department of Mathematics and Statistics Georgia State University Atlanta Georgia USA

Compositional data, such as relative information, is a crucial aspect of machine learning and other related fields. It is typically recorded as closed data or sums to a constant, like 100%. The statistical linear model is the most used technique for identifying hidden relationships between underlying random variables of interest. However, data quality is a significant challenge in machine learning, especially when missing data is present. The linear regression model is a commonly used statistical modeling technique used in various applications to find relationships between variables of interest. When estimating linear regression parameters which are useful for things like future prediction and partial effects analysis of independent variables, maximum likelihood estimation (MLE) is the method of choice. However, many datasets contain missing observations, which can lead to costly and time-consuming data recovery. To address this issue, the expectation-maximization (EM) algorithm has been suggested as a solution for situations including missing data. The EM algorithm repeatedly finds the best estimates of parameters in statistical models that depend on variables or data that have not been observed. This is called maximum likelihood or maximum a posteriori (MAP). Using the present estimate as input, the expectation (E) step constructs a log-likelihood function. Finding the parameters that maximize the anticipated log-likelihood, as determined in the E step, is the job of the maximization (M) phase. This study looked at how well the EM algorithm worked on a made-up compositional dataset with missing observations. It used both the robust least square version and ordinary least square regression techniques. The efficacy of the EM algorithm was compared with two alternative imputation techniques, k-Nearest Neighbor (k-NN) and mean imputation (), in terms of Aitchison distances and covariance.

关键词： Compositional Data Linear Regression Model Least Square Method Robust Least Square Method Synthetic Data Aitchison Distance Maximum Likelihood Estimation expectation-maximization algorithm k-Nearest Neighbor and Mean imputation

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Unsupervised Learning in RSS-Based DFLT Using an EM algorithm

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SENSORS 2021年第16期21卷 5549-5549页

作者： Kaltiokallio, Ossi Hostettler, Roland Yigitler, Huseyin Valkama, Mikko Tampere Univ Unit Elect Engn Tampere 33720 Finland Uppsala Univ Dept Elect Engn S-75237 Uppsala Sweden Aalto Univ Dept Commun & Networking Espoo 02150 Finland

Received signal strength (RSS) changes of static wireless nodes can be used for device-free localization and tracking (DFLT). Most RSS-based DFLT systems require access to calibration data, either RSS measurements from a time period when the area was not occupied by people, or measurements while a person stands in known locations. Such calibration periods can be very expensive in terms of time and effort, making system deployment and maintenance challenging. This paper develops an expectation-maximization (EM) algorithm based on Gaussian smoothing for estimating the unknown RSS model parameters, liberating the system from supervised training and calibration periods. To fully use the EM algorithm's potential, a novel localization-and-tracking system is presented to estimate a target's arbitrary trajectory. To demonstrate the effectiveness of the proposed approach, it is shown that: (i) the system requires no calibration period;(ii) the EM algorithm improves the accuracy of existing DFLT methods;(iii) it is computationally very efficient;and (iv) the system outperforms a state-of-the-art adaptive DFLT system in terms of tracking accuracy.

关键词： received signal strength localization and tracking bayesian filtering and smoothing parameter estimation expectation-maximization algorithm

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Dynamic movement primitives based on positive and negative demonstrations

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INTERNATIONAL JOURNAL OF ADVANCED ROBOTIC SYSTEMS 2023年第1期20卷

作者： Dong, Shuai Yang, Zhihua Zhang, Weixi Zou, Kun Univ Elect Sci & Technol China Zhongshan Inst Zhongshan Peoples R China Univ Elect Sci & Technol China Zhongshan Inst Xueyuan Rd 1 Zhongshan 528400 Guangdong Peoples R China

Dynamic motion primitive has been the most prevalent model-based imitation learning method in the last few decades. Gaussian mixed regression dynamic motion primitive, which draws upon the strengths of both the motion model and the probability model to cope with multiple demonstrations, is a very practical and conspicuous branch in the dynamic motion primitive family. As Gaussian mixed regression dynamic motion primitive only learns from expert demonstrations and requires full environmental information, it is incapable of handling tasks with unmodeled obstacles. Aiming at this problem, we proposed the positive and negative demonstrations-based dynamic motion primitive, for which the introduction of negative demonstrations can bring additional flexibility. Positive and negative demonstrations-based dynamic motion primitive extends Gaussian mixed regression dynamic motion primitive in three aspects. The first aspect is a new maximum log-likelihood function that balances the probabilities on positive and negative demonstrations. The second one is the positive and negative demonstrations-based expectation-maximum, which involves iteratively calculating the lower bound of a new Q-function. And the last is the application framework of data set aggregation for positive and negative demonstrations-based dynamic motion primitive to handle unmodeled obstacles. Experiments on several typical robot manipulating tasks, which include letter writing, obstacle avoidance, and grasping in a grid box, are conducted to validate the performance of positive and negative demonstrations-based dynamic motion primitive.

关键词： expectation-maximization algorithm Gaussian mixed regression negative demonstrations skill transfer learning data set aggregation

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One-shot device test data analysis using non-parametric and semi-parametric inferential methods and applications

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RELIABILITY ENGINEERING & SYSTEM SAFETY 2022年第0期221卷 108319-108319页

作者： Zhu, Xiaojun Balakrishnan, N. Xian Jiaotong Liverpool Univ Dept Financial & Actuarial Math Suzhou 215123 Peoples R China McMaster Univ Dept Math & Stat Hamilton ON L8S 4K1 Canada

A one-shot device, such as an automobile airbag, electro-explosive unit or munition, is a product that can be used only once. Its actual lifetime is unobservable, rendering the corresponding reliability analysis quite challenging. In this paper, two non-parametric methodologies-maximum likelihood estimation via EM-algorithm and Nelson-Aalen based estimation are developed for identical testing environment on one-shot devices. The EM-algorithm is usually used for unobserved failure times under some specific parametric models. But, here the EM-algorithm is adopted for the number of failures in each time interval in a nonparametric manner. Next, a semi-parametric approach, based on proportional hazards assumption, is developed for nonidentical testing environments, such as under an accelerated life-test. A Monte Carlo simulation study is then carried out for evaluating the performance of the inferential methods developed here. Finally, two data sets are analyzed for illustrative purpose.

关键词： Accelerated life-test expectation-maximization algorithm Kaplan-Meier estimator Nelson-Aalen estimator Non-parametric inference One-shot device test Proportional hazards model Semi-parametric inference

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Improved Gaussian mixture modeling for accurate Wi-Fi based indoor localization systems

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PHYSICAL COMMUNICATION 2020年 43卷 101218-101218页

作者： Alfakih, Marwan Keche, Mokhtar Benoudnine, Hadjira Meche, Abdelkrim Univ Sci & Technol Oran Mohamed Boudiaf Elect Dept Signals & Images Lab USTO MB BP 1505 El Mnaouer 31000 Oran Algeria Univ Abdelhamid Ibn Badis Fac Sci & Technol Dept Elect & Elect Engn BP 227 Route Belhacel Mostaganem Algeria

This paper deals with the problem of device's location using Wi-Fi signal strength in an indoor environment. In order to improve the location accuracy a new fingerprinting-probabilistic algorithm is proposed. In this algorithm, the probability distribution of the Received Signal Strength (RSS) by a Mobile User (MU) from several Access Points (AP) is approximated using the Gaussian Mixture Model (GMM) approach. This probability distribution is then exploited to improve the location estimation of the mobile user. To tackle the initialization problem of the expectation maximization (EM) algorithm, which is used to estimate the Gaussian mixture parameters, a deterministic initialization method is proposed. This method named Manual initialization (MI) initializes manually the mixture parameters directly from the data. To cope with the MI shortcomings, an Adaptive Initialization (AI) technique is proposed. The performance of the resulting method, named the Improved GMM (IGMM) is evaluated experimentally and compared to that of other robust methods. The obtained results illustrate the efficiency of the IGMM method. Compared to the standard initialization technique, the MI and AI initialization techniques improve the location accuracy by 14.4% and 18.4%, respectively. Compared to other location methods, the improvement brought about by the IGMM method, varies from 5.1% to 17.7%, when the MI technique is used, and from 10% to 21.5%, when the AI technique is used. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Indoor positioning Wi-Fi fingerprinting Received signal strength Gaussian mixture model expectation-maximization algorithm

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Domain problem-solving expert identification in community question answering

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EXPERT SYSTEMS 2020年第5期37卷 e12582-e12582页

作者： Tang, Weizhao Lu, Tun Gu, Hansu Zhang, Peng Gu, Ning Fudan Univ Sch Comp Sci Shanghai 200433 Peoples R China Shanghai Key Lab Data Sci Shanghai Peoples R China Shanghai Inst Intelligent Elect & Syst Shanghai Peoples R China Microsoft Inc Seattle WA 98052 USA

Question-Answering (Q&A) services provide internet users with platforms to exchange knowledge and ideas. The development of Q&A sites, or Community Question Answering (CQA), mainly depends on the high-quality content continuously contributed by users with high-level expertise, who can be recognized as experts. Expert finding is an important task for the authorities of Q&A communities to encourage commitment. In a highly competitive market environment, CQA managers have to take measures to retain and nurture users, especially superior contributors. However, current expertise scoring techniques adopted in CQA often give much credit to very active users and fail to identify real experts. This study aims to develop a robust and practical expert identification framework for Q&A communities, by combining well-designed expertise scoring technique and probabilistic clustering model. With regard to expert identification, a numerical metric of users' expertise is developed as the optimal expert finding strategy, and a clustering algorithm based on Gaussian-Gamma mixture model (GGMM) is proposed to efficiently distinguish experts from nonexperts. In the experiments, the proposed method is applied to real-world datasets collected from subcommunities of Stack Exchange Q&A networks. Results obtained from comparative experiments show that our method achieves better performance than the state-of-the-art methods and demonstrate the effectiveness of the proposed framework. The analysis shows that the framework which combines the proposed expertise scoring technique and Gaussian-Gamma mixture clustering model is capable of detecting excellent domain problem-solving experts who exhibit both domain interest and expertise.

关键词： expectation-maximization algorithm expert finding mixture model Q&A community

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Discrete Latent Variable Models

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Statistics and Its Application 1000年第1期9卷 425-452页

作者： Francesco Bartolucci Silvia Pandolfi Fulvia Pennoni 1Department of Economics University of Perugia Perugia 06123 Italy email: francesco.bartolucci@unipg.itsilvia.pandolfi@unipg.it 2Department of Statistics and Quantitative Methods University of Milano-Bicocca Milan 20126 Italy email: fulvia.pennoni@unimib.it

We review the discrete latent variable approach, which is very popular in statistics and related fields. It allows us to formulate interpretable and flexible models that can be used to analyze complex datasets in the presence of articulated dependence structures among variables. Specific models including discrete latent variables are illustrated, such as finite mixture, latent class, hidden Markov, and stochastic block models. algorithms for maximum likelihood and Bayesian estimation of these models are reviewed, focusing, in particular, on the expectation–maximization algorithm and the Markov chain Monte Carlo method with data augmentation. Model selection, particularly concerning the number of support points of the latent distribution, is discussed. The approach is illustrated by summarizing applications available in the literature; a brief review of the main software packages to handle discrete latent variable models is also provided. Finally, some possible developments in this literature are suggested.

关键词： data augmentation expectation-maximization algorithm finite mixture model hidden Markov model latent class model model selection stochastic block model

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Stochastic model for enhanced PET image reconstruction

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BIOMEDICAL SIGNAL PROCESSING AND CONTROL 2024年 94卷

作者： Matulic, Tomislav Sersic, Damir Univ Zagreb Fac Elect Engn & Comp Dept Elect Syst & Informat Proc Unska 3 Zagreb 10000 Croatia

In this paper, we present a detailed stochastic model of crystal -to -crystal response for PET scanners, which is crucial for addressing their physical constraints. We present both a closed -form solution and several accurate approximations to manage the complexity of the exact mathematical expressions. Through experimental and analytical validation, we demonstrate that the disparities between the best approximations and actual crystalto -crystal response are negligible. These responses are utilized to develop a compensation model termed a white image. This model is expressed in a single closed -form equation, simplifying its integration into established reconstruction methods. We modify the maximum likelihood expectation maximization (MLEM) algorithm and integrate our white image model into it. Unlike the conventional approach that relies on the system matrix, the modified MLEM algorithm operates on ray -driven projections and back -projections. The system matrix, being large and requiring complex methods and simulations for evaluation, contrasts with the white image, which is smaller and enables efficient computation. Our compensation model provides comprehensive information about the PET system. We validate our approach with both synthetic and real data. For real -world data acquisition, we utilize the Raytest ClearPET camera for small animals and the NEMA NU 4-2008 phantom. The proposed modification outperforms competing uncompensated reconstruction methods, delivering superior Peak Signal -to -Noise Ratio (PSNR) and reduced execution time. This research deepens our understanding of real PET measurement systems, providing improved input for subsequent reconstruction algorithms and ultimately producing high -quality images.

关键词： Exact crystal response model Maximum-likelihood expectation-maximization algorithm Positron Emission Tomography White image model

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Improving geometric P-norm-based glioma segmentation through deep convolutional autoencoder encapsulation

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BIOMEDICAL SIGNAL PROCESSING AND CONTROL 2022年第PartB期71卷 103232-103232页

作者： Takrouni, Wiem Douik, Ali Univ Sousse Noccs ISITCom Sousse 4011 Tunisia Univ Sousse NOCCS ENISO Sousse 4054 Tunisia

Gliomas are the most common types of brain tumors. Their shapes are irregular and their boundaries are ambiguous, producing a tumor that is hard to detect. To improve the segmentation performance, we propose a PNorm-Based Glioma Segmentation by encapsulating it within a Deep Convolutional Autoencoder (DCA). In this paper, we first develop a new robust Deep P-norm Generative Model (DPGM) that can extract and classify the feature by the encoder section and segment this latter by the decoder section. After that, we utilise a Deep Discriminative Model (DDM) which applies the conditional random fields to refine the segmentation result. Effectiveness is gained by gradient descent training on the set of pre-P-norm filtering and thresolding convolutional operations using a novel geometric P-norm-based loss function. This latter will be optimized by the RANSAC layer, which is geared toward optimizing the strength of the correct model relative to the most convincing false model. We evaluate the accuracy and robustness of our method within MRI sequences (T1, T2, T2c & FLAIR) from the Multimodal Brain Tumor Image Segmentation Challenge (BRATS 2013 Leaderboard, BRATS 2013 Challenge, BRATS 2015 and BRATS 2017). The experiments demonstrate a high-quality segmentation results of our DPGM-DDM architecture and the average Dice is as high as 97.2%, 97.6%, and 98.4% respectively for complete, core, and enhancing tumor regions. Overall, our deep proposed architecture is effective in segmenting gliomas in multimodal images or fair images, and has the potential in routine examinations of gliomas in daily clinical practice.

关键词： Generative-discriminative model Deep convolutional autoencoder Geometric P-norm model Glioma segmentation expectation-maximization algorithm

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An EM-based likelihood inference for degradation data analysis using gamma process

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APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY 2024年第0期41卷

作者： Palayangoda, Lochana Balakrishnan, N. Univ Nebraska Omaha Dept Math & Stat Sci Omaha NE 68182 USA McMaster Univ Dept Math & Stat Hamilton ON Canada

The gamma process is widely used for the lifetime estimation of highly reliable products that degrade over time. Typically, incomplete likelihood is used to estimate the model parameters and the reliability estimates for the first passage time distribution of the gamma process;however, it (i.e., pseudo method) does not consider interval censoring and right censoring information of the degradation data. In this work, the expectation-maximization algorithm-based method (EM method) is developed for the estimation of the gamma process model parameters and the reliability estimates incorporating interval censoring and right censoring. The asymptotic variance-covariance matrix and the asymptotic confidence intervals for the parameters are constructed, and then a comparison between the pseudo method and the EM method is made. Monte Carlo simulation studies and real-life data applications are conducted in order to illustrate the performance of the proposed EM method over the pseudo method.

关键词： asymptotic variance-covariance matrix coverage probability expectation-maximization algorithm first-passage time distribution gamma process interval censoring Monte Carlo simulation pseudo likelihood right censoring

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