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Mixtures of equispaced normal distributions and their use for testing symmetry with univariate data

COMPUTATIONAL STATISTICS & DATA ANALYSIS 2014年 71卷 262-272页

作者： Bacci, Silvia Bartolucci, Francesco Univ Perugia IT Dept Econ Finance & Stat Perugia Italy

Given a random sample of observations, mixtures of normal densities are often used to estimate the unknown continuous distribution from which the data come. The use of this semi-parametric framework is proposed for testing symmetry about an unknown value. More precisely, it is shown how the null hypothesis of symmetry may be formulated in terms of a normal mixture model, with weights about the center of symmetry constrained to be equal one another. The resulting model is nested in a more general unconstrained one, with the same number of mixture components and free weights. Therefore, after having maximized the constrained and unconstrained log-likelihoods, by means of the expectation-maximization algorithm, symmetry is tested against skewness through a likelihood ratio statistic with p-value computed by using a parametric bootstrap method. The behavior of this mixture-based test is studied through a Monte Carlo simulation, where the proposed test is compared with the traditional one, based on the third standardized moment, and with the non-parametric triples test. An illustrative example is also given which is based on real data. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Bootstrap method Density estimation expectation-maximization algorithm Skewness

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A numerical method for resolving finite mixtures of three-dimensional inter-site distance distributions measured by single-molecule localization microscopy

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MICROSCOPY 2023年第1期72卷 43-48页

作者： Tu, Zhiwen Song, Congwei Qin, Xianan Zhejiang Sci Tech Univ Natl Engn Lab Textile Fiber Mat & Proc Technol Hangzhou 310018 Peoples R China Yanqi Lake Beijing Inst Math Sci & Applicat BIMSA Beijing 101408 Peoples R China Zhejiang Sci Tech Univ Sch Mat Sci & Engn Hangzhou 310018 Peoples R China Zhejiang Prov Innovat Ctr Adv Text Technol Shaoxing 312000 Peoples R China

The three-dimensional (3D) inter-site distance can be measured by single-molecule localization microscopy. Existing theories and analysis tools for 3D inter-site distance measurement only consider the simplest case where all measured distances are from an identical 3D Rician distribution. There are many problems where the 3D inter-site distance measurement result is made up of multiple components, for example, the measurement of intramolecular distances of deoxyribonucleic acid with multiple possible conformations. In these cases, the overall distance distributions become finite mixtures of 3D Rician distributions (or 3D Rician mixtures). Here, we provide a numerical method using the 3D Rician mixture model to resolve the finite 3D inter-site distance mixtures, which is based on the expectation-maximization algorithm. The proposed method has been tested on simulation data of finite 3D inter-site distance mixtures. The result using the Gaussian mixture model in the developed method is also discussed for comparison.

关键词： distance measurement inter-site distance finite mixture model expectation-maximization algorithm single-molecule localization microscopy

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Optimal Multi-Objective Burn-In Policy Based on Time-Transformed Wiener Degradation Process

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IEEE ACCESS 2019年 7卷 73529-73539页

作者： Lyu, Yi Zhang, Yun Chen, Kairui Chen, Ci Zeng, Xianxian Guangdong Univ Technol Sch Automat Guangzhou 510006 Guangdong Peoples R China Univ Elect Sci & Technol China Sch Comp Zhongshan Inst Zhongshan 528400 Peoples R China Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore

Burn-in is an effective and widely used means to improve product reliability by eliminating weak units before they are distributed in the market. Traditional burn-in that distinguishes weak units by failure during testing is inefficient and incompetent for degradation-failed products in which weak units degrade faster than normal individuals. Hence, the manufacturers have to turn to the degradation-based method. The mean lifetime to failure (MTTF) of a burnt-in population is diminished because of this type of burn-in increases the degradation level of all tested units. Ignoring the impact of burn-in leads to inferior test decisions. This study develops a multi-objective burn-in method that can simultaneously minimize the burn-in cost and maximize the burnt-in population's MTTF. We employ the time-transformed Wiener process with random effects to model the nonlinear degradation path of products and develop a burn-in scheme with two decision variables, namely, test duration and screening cutoff level. Cost expression and lifetime-based optimal objective are analytically developed. The optimal test policy is determined using the multi-objective evolutionary algorithm based on decomposition. A simulation study is conducted to demonstrate the usage and effectiveness of the multi-objective burn-in method.

关键词： Degradation Wiener process burn-in expectation-maximization algorithm multi-objective optimization

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Adaptive sparseness for supervised learning

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2003年第9期25卷 1150-1159页

作者： Figueiredo, MAT Univ Tecn Lisboa Inst Telecommun Inst Super Tecn P-1049001 Lisbon Portugal Univ Tecn Lisboa Dept Elect & Comp Engn Inst Super Tecn P-1049001 Lisbon Portugal

The goal of supervised teaming is to infer a functional mapping based on a set of training examples. To achieve good generalization, it is necessary to control the "complexity" of the learned function. In Bayesian approaches, this is done by adapting a prior for the parameters of the function being teamed. We propose a Bayesian approach to supervised teaming, which leads to sparse solutions;that is, in which irrelevant parameters are automatically set exactly to zero. Other ways to obtain sparse classifiers (such as Laplacian priors, support vector machines) involve (hyper)parameters which control the degree of sparseness of the resulting classifiers;these parameters have to be somehow adjusted/estimated from the training data. In contrast, our approach does not involve any (hyper)parameters to be adjusted or estimated. This is achieved by a hierarchical-Bayes interpretation of the Laplacian prior, which is then modified by the adoption of a Jeffreys' noninformative hyperprior. Implementation is carried out by an expectation-maximization (EM) algorithm. Experiments with several benchmark data sets show that the proposed approach yields state-of-the-art performance. In particular, our method outperforms SVMs and performs competitively with the best alternative techniques, although it involves no tuning or adjustment of sparseness-controlling hyperparameters.

关键词： supervised learning classification regression sparseness feature selection kernel methods expectation-maximization algorithm

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Linear parameter-varying systems identification with slowly sampled outputs subjected to unknown time-delays and outliers

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART I-JOURNAL OF SYSTEMS AND CONTROL ENGINEERING 2019年第1期233卷 5-17页

作者： Liu, Xin Yang, Xianqiang Guo, Feng Harbin Inst Technol Res Inst Intelligent Control & Syst Harbin 150080 Heilongjiang Peoples R China NanTong Inst Technol Nantong Peoples R China

This article proposes a robust global identification approach for nonlinear systems with slowly sampled outputs subjected to unknown time-delays. The inputs of the system are fast-rate sampled while the informative outputs are uniformly sampled at a slow rate. In practical industries, the outlier and output time-delays are commonly encountered and they are both considered in this work. To eliminate the impact brought by the outliers, the robust linear parameter-varying finite impulse response observation model based on the Laplace distribution is established. The unknown time-delay is treated as a random integer at each sampling moment which follows the uniform distribution with the boundary known a priori. The proposed robust approach is derived in the expectation-maximization algorithm scheme and the formulas to iteratively update the model parameters, the scale parameter and the random output time-delays are derived, respectively. The unmeasurable noise-free fast-rate sampled outputs are estimated by simulating the identified model. A numerical example, the mass-spring-damper system and the two-link robotic manipulator are utilized to verify the effectiveness of the proposed approach.

关键词： Robust global approach linear parameter-varying model identification random output time-delays Laplace distribution expectation-maximization algorithm

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Handling multi-mapped reads in RNA-seq

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COMPUTATIONAL AND STRUCTURAL BIOTECHNOLOGY JOURNAL 2020年 18卷 1569-1576页

作者： Deschamps-Francoeur, Gabrielle Simoneau, Joel Scott, Michelle S. Univ Sherbrooke Fac Med & Sci Sante Dept Biochim & Genom Fonct Sherbrooke PQ J1E 4K8 Canada

Many eukaryotic genomes harbour large numbers of duplicated sequences, of diverse biotypes, resulting from several mechanisms including recombination, whole genome duplication and retro-transposition. Such repeated sequences complicate gene/transcript quantification during RNA-seq analysis due to reads mapping to more than one locus, sometimes involving genes embedded in other genes. Genes of different biotypes have dissimilar levels of sequence duplication, with long-noncoding RNAs and messenger RNAs sharing less sequence similarity to other genes than biotypes encoding shorter RNAs. Many strategies have been elaborated to handle these multi-mapped reads, resulting in increased accuracy in gene/transcript quantification, although separate tools are typically used to estimate the abundance of short and long genes due to their dissimilar characteristics. This review discusses the mechanisms leading to sequence duplication, the biotypes affected, the computational strategies employed to deal with multi-mapped reads and the challenges that still remain to be overcome. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Research Network of Computational and Structural Biotechnology.

关键词： RNA-seq Multi-mapped reads Duplicated genes Noncoding RNAs Gene isoforms expectation-maximization algorithm

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Real-Valued Sparse DOA Estimation for MIMO Array System Under Unknown Nonuniform Noise

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IEEE ACCESS 2018年 6卷 52218-52226页

作者： Dong, Fang Shen, Chong Zhang, Kun Wang, Huafei Hainan Univ State Key Lab Marine Resource Utilizat South Chin Haikou 570228 Hainan Peoples R China Hainan Univ Coll Informat Sci & Technol Haikou 570228 Hainan Peoples R China

In this paper, the problem of the direction of arrival (DOA) estimation for the multiple input multiple output (MIMO) array system is considered as a real-valued sparse signal recover procedure under the condition of unknown nonuniform noise. Then, a real-valued covariance vector-based sparse Bayesian learning framework is proposed, in which the reduced dimensional (RD) transformation is utilized to remove the redundant elements of MIMO array system, and a linear transformation is applied to eliminate the influence of unknown non-uniform noise. Then by supposing that the source powers follow an independent prior Gaussian distribution with zero-mean, a real-valued covariance vector-based sparse Bayesian model is formulated. And considering its unknown variance as hyperparameters, they can be estimated by adopting the expectation-maximization algorithm. Finally, the DOA can be achieved according to the spatial spectrum of hyperparameters. Simulation results have demonstrated that our proposed method not only achieves more superior performance but also provides robustness against nonuniform noise, compared with other recently reported sparse signal representation based methods.

关键词： MIMO array system nonuniform noise DOA estimation real-valued sparse signal recover expectation-maximization algorithm

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Uplink Synchronization in OFDMA Spectrum-Sharing Systems

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2010年第5期58卷 2771-2782页

作者： Sanguinetti, Luca Morelli, Michele Poor, H. Vincent Univ Pisa Dept Informat Engn I-56126 Pisa Italy Princeton Univ Dept Elect Engn Princeton NJ 08544 USA

Spectrum sharing employs dynamic allocation of frequency resources for a more efficient use of the radio spectrum. Despite its appealing features, this technology inevitably complicates the synchronization task, which must be accomplished in an environment that may involve interference. This paper considers the uplink of an orthogonal frequency-division multiple-access (OFDMA)-based spectrum sharing system and provides solutions for estimating the frequency and timing errors of multiple unsynchronized users. In doing so, we exploit suitably designed training blocks and apply maximum likelihood methods after modeling the interference power on each subcarrier as a random variable with an inverse gamma distribution. The resulting frequency estimator turns out to be the extension to a multiuser scenario of a scheme that has previously been proposed for single-user spectrum-sharing systems. Timing recovery is more challenging and leads to a complete search over a multidimensional domain. To overcome such a difficulty, two alternative approaches are proposed. The first one relies on a simplifying assumption about the interference distribution in the frequency domain, while the second scheme operates in an iterative fashion according to the expectation-maximization algorithm.

关键词： expectation-maximization algorithm frequency estimation narrowband interference OFDMA spectrum sharing timing estimation

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Statistical Leakage Analysis Using Gaussian Mixture Model

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IEEE ACCESS 2018年 6卷 51939-51950页

作者： Kwon, Hyunjeong Woo, Mingyu Kim, Young Hwan Kang, Seokhyeong Pohang Univ Sci & Technol Dept Elect Engn Pohang 37673 South Korea Univ Calif San Diego Dept Comp Engn La Jolla CA 92093 USA

In the design process of advanced semiconductor devices, statistical leakage analysis has emerged as a major step due to uncertainties in the leakage current caused by the process variations. In this paper, a novel statistical leakage analysis which uses Gaussian mixture model (GMM) as the density function of leakage current is proposed. To estimate the probability density function, our proposed method clusters the rapidly converged leakage data using the GMM. The GMM can represent any distributions, so it is suitable to estimate the leakage distribution, which varies as the technology node or operating condition changes. In addition, our proposed method (SLA-GMM) defines a terminating condition that guarantees the convergence of the leakage data and prevents the underfitting or overfitting in the GMM modeling process. With sequential addition, SLA-GMM significantly reduced the error that can occur during the addition process. In studies with a goodness-of-fit test, SLA-GMM achieved up to 98% and 94% improvements in the Chi-square static and the K-S static compared with the previous method based on an analytic model.

关键词： expectation-maximization algorithm Gaussian mixture model machine learning statistical leakage analysis

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3DACN: 3D Augmented convolutional network for time series data

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INFORMATION SCIENCES 2020年 513卷 17-29页

作者： Pei, Songwen Shen, Tianma Wang, Xianrong Gu, Chunhua Ning, Zhong Ye, Xiaochun Xiong, Naixue Univ Shanghai Sci & Technol Sch Opt Elect & Comp Engn Shanghai 200093 Peoples R China Fudan Univ Sch Management Shanghai 200433 Peoples R China Chinese Acad Sci Inst Comp Technol State Key Lab Comp Architecture Beijing 100190 Peoples R China Northeastern State Univ Dept Comp Sci Tahlequah OK 74464 USA

Time series data and non-time series data are increasing in the credit system of financial market, so that an effective and intelligent data mining model plays a critical role to analyze hybrid time series data. In addition, traditional mining models sometimes fail to converge because of imbalanced data problem. Therefore, we propose a 3D Augmented Convolutional Network (3DACN) to extract time series information and solve the serious imbalanced data problem. By using the augmented algorithm on time series data, hybrid time series data are enlarged to generate more examples on the minority classes. 3DACN ensures the latent variables with an expectation-maximization(EM) algorithm to improve F1 score (F1) and Area Under Curve (AUC). Experimental results show that in the benchmark of Bank database, it can gain F1 score by 81.1% and the AUC by 88.2% respectively;while in the benchmark of Credit Risk database, the 3DACN can reach high performance on F1 score by 88.1% and the AUC by 88.4%. (C) 2019 Elsevier Inc. All rights reserved.

关键词： Time series data Gated recurrent units Convolutional neural network expectation-maximization algorithm Augmented algorithm

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