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A GAMP-Based Low Complexity Sparse Bayesian Learning Algorithm

IEEE TRANSACTIONS ON SIGNAL PROCESSING 2018年第2期66卷 294-308页

作者： Al-Shoukairi, Maher Schniter, Philip Rao, Bhaskar D. Univ Calif San Diego Dept Elect & Comp Engn San Diego CA 92093 USA Ohio State Univ Dept Elect & Comp Engn Columbus OH 43210 USA

In this paper, we present an algorithm for the sparse signal recovery problem that incorporates damped Gaussian generalized approximate message passing (GGAMP) into expectation-maximization-based sparse Bayesian learning (SBL). In particular, GGAMP is used to implement the E-step in SBL in place of matrix inversion, leveraging the fact that GGAMP is guaranteed to converge with appropriate damping. The resulting GGAMP-SBL algorithm is much more robust to arbitrary measurement matrix A than the standard damped GAMP algorithm while being much lower complexity than the standard SBL algorithm. We then extend the approach from the single measurement vector case to the temporally correlated multiple measurement vector case, leading to the GGAMP-TSBL algorithm. We verify the robustness and computational advantages of the proposed algorithms through numerical experiments.

关键词： Compressed sensing approximate message passing (AMP) sparse Bayesian learning (SBL) expectation-maximization algorithms Gaussian scale mixture multiple measurement vectors (MMV)

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A note on the exponential Poisson distribution: A nested EM algorithm

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2009年第4期53卷 894-899页

作者： Karlis, Dimitris Athens Univ Econ & Business Dept Stat Athens 10434 Greece

An EM type algorithm for estimating the parameters of the exponential Poisson distribution has recently been proposed. This algorithm uses a Newton Raphson approach at the M-step. An alternative approach, where the Newton Raphson step is replaced by another EM algorithm is described. This approach has simple closed form expressions, making use of a nested EM scheme where the M-step itself is solved with an EM algorithm. An advantage of this algorithm is that it provides estimates in the admissible range when the initial values are in the admissible range, and avoids overflow problems that may occur during Newton-Raphson iterations and, in certain cases, it can be faster. Some simulation evidence on the speed of the new approach compared to the one that uses Newton-Raphson is provided. (C) 2008 Elsevier B.V. All rights reserved.

关键词： POISSON distribution EXPONENTIAL functions expectation-maximization algorithms PARAMETER estimation NEWTON-Raphson method SIMULATION methods & models

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Image Denoising Based on Dilated Singularity Prior

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MATHEMATICAL PROBLEMS IN ENGINEERING 2012年第1期2012卷 1-15页

作者： Hu, Shaoxiang Liao, Zhiwu Chen, Wufan Univ Elect Sci & Technol China Sch Automat Engn Chengdu 610054 Peoples R China Sichuan Normal Univ Visual Comp & Virtual Real Key Lab Sichuan Prov Chengdu 610066 Peoples R China

In order to preserve singularities in denoising, we propose a new scheme by adding dilated singularity prior to noisy images. The singularities are detected by canny operator firstly and then dilated using mathematical morphology for finding pixels "near" singularities instead of "on" singularities. The denoising results for pixels near singularities are obtained by nonlocal means in spatial domain to preserve singularities while the denoising results for pixels in smooth regions are obtained by EM algorithm constrained by a mask formed by downsampled spatial image with dilated singularity prior to suiting the sizes of the subbands of wavelets. The final denoised results are got by combining the above two results. Experimental results show that the scheme can preserve singularity well with relatively high PSNR and good visual quality.

关键词： IMAGE processing SINGULARITIES (Mathematics) PIXELS expectation-maximization algorithms IMAGE quality analysis

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New global optimization algorithms for model-based clustering

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2009年第12期53卷 3999-4017页

作者： Heath, Jeffrey W. Fu, Michael C. Jank, Wolfgang Univ Maryland Robert H Smith Sch Business College Pk MD 20742 USA Ctr Coll Danville Dept Math Danville KY 40422 USA

The expectation-maximization (EM) algorithm is a very popular optimization tool for mixture problems and in particular for model-based clustering problems. However, while the algorithm is convenient to implement and numerically very stable, it only produces local solutions. Thus, it may not achieve the globally optimal solution in problems that have a large number of local optima. This paper introduces several new algorithms designed to produce global solutions in model-based clustering. The building blocks for these algorithms are methods from the operations research literature, namely the Cross-Entropy (CE) method and Model Reference Adaptive Search (MRAS). One problem with applying these methods directly is the efficient simulation of positive definite covariance matrices. We propose several new solutions to this problem. One solution is to apply the principles of expectation-maximization updating, which leads to two new algorithms, CE-EM and MRAS-EM. We also propose two additional algorithms, CE-CD and MRAS-CD, which rely on the Cholesky decomposition. We conduct numerical experiments of varying complexity to evaluate the effectiveness of the proposed algorithms in comparison to classical EM. We find that although a single run of the new algorithms is slower than a single run of EM, all have the potential for producing significantly better solutions. We also find that although repeat application of EM may achieve similar results, our algorithms provide automated, data-driven decision rules which may significantly reduce the burden of searching for the global optimum. (C) 2009 Elsevier B.V. All rights reserved.

关键词： expectation-maximization algorithms NUMERICAL analysis CROSS-entropy method ANALYSIS of covariance DECOMPOSITION (Mathematics) COMPARATIVE studies

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Fast estimation of spatially dependent temporal vegetation trends using Gaussian Markov random fields

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2009年第8期53卷 2885-2896页

作者： Bolin, David Lindstroem, Johan Eklundh, Lars Lindgren, Finn Lund Univ Ctr Math Sci SE-22100 Lund Sweden Lund Univ Dept Phys Geog & Ecosyst Anal GeoBiosphere Sci Ctr SE-22100 Lund Sweden

There is a need for efficient methods for estimating trends in spatio-temporal Earth Observation data. A suitable model for such data is a space-varying regression model, where the regression coefficients for the spatial locations are dependent. A second order intrinsic Gaussian Markov Random Field prior is used to specify the spatial covariance structure. Model parameters are estimated using the expectation Maximisation (EM) algorithm, which allows for feasible computation times for relatively large data sets. Results are illustrated with simulated data sets and real vegetation data from the Sahel area in northern Africa. The results indicate a substantial gain in accuracy compared with methods based on independent ordinary least squares regressions for the individual pixels in the data set. Use of the EM algorithm also gives a substantial performance gain over Markov Chain Monte Carlo-based estimation approaches. (c) 2008 Elsevier B.V. All rights reserved.

关键词： ESTIMATION theory VEGETATION dynamics SPATIAL analysis (Statistics) GAUSSIAN Markov random fields REGRESSION analysis ANALYSIS of covariance expectation-maximization algorithms MONTE Carlo method

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Maximum likelihood estimation in vector long memory processes via EM algorithm

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2009年第12期53卷 4133-4142页

作者： Pai, Jeffrey Ravishanker, Nalini Univ Connecticut Dept Stat Storrs CT 06269 USA Univ Manitoba Warren Ctr Actuarial Studies & Res Winnipeg MB R3T 5V4 Canada

We present an approach for exact maximum likelihood estimation of parameters from univariate and multivariate autoregressive fractionally integrated moving average models with Gaussian errors using the expectation maximization (EM) algorithm. The method takes advantage of the relation between the VARFIMA(0, d, 0) process and the corresponding VARFIMA(p, d, q) process in the computation of the likelihood. (C) 2009 Elsevier B.V. All rights reserved.

关键词： MAXIMUM likelihood statistics ESTIMATION theory expectation-maximization algorithms MULTIVARIATE analysis AUTOREGRESSION (Statistics) GAUSSIAN processes

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Estimation of propagation channel parameters using multi-dimensional hybrid-space SAGE algorithm

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IET MICROWAVES ANTENNAS & PROPAGATION 2007年第6期1卷 1212-1222页

作者： Tan, C. M. Beach, M. A. BT Grp Plc Chief Architect Off Kuala Lumpur 50470 Malaysia Univ Bristol Ctr Commun Res Bristol BS8 1UB Avon England

To-date, most multipath propagation parameters are estimated in the element-space domain due to implementation simplicity. Although estimation in the beam-space domain can reduce both the dimensionality of the data size and numerical complexity, it is only beneficial if applied to arrays with a large number of uniformly spaced elements. A new implementation of the space-alternating generalised expectation-maximisation (SAGE) algorithm is presented in joint element-space and beam-space, namely the 'hybrid-space' (HS), such that the underlying features of these dual domains can be simultaneously exploited. The resultant algorithm, namely HS-SAGE algorithm, retains the advantages of the individual domains as the user can specify which parameter should be evaluated in each domain, thus optimising the overall performance. Here, the efficient execution flow of the HS-SAGE algorithm is presented, where the estimation quality is demonstrated through results obtained from both synthetic and real-measurement environments employing circular arrays. It is shown that the proposed algorithm can achieve significant timesaving when compared with the classical implementation approach, whilst maintaining accuracy.

关键词： RADIO wave propagation expectation-maximization algorithms MULTIDIMENSIONAL databases ESTIMATION theory ESTIMATION bias CONSTANTS of integration RADIO waves algorithms COMPUTATIONAL complexity

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EM-Based Iterative Receivers for OFDM and BICM/OFDM Systems in Doubly Selective Channels

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2011年第5期10卷 1405-1415页

作者： Ku, Meng-Lin Chen, Wen-Chuan Huang, Chia-Chi Natl Cent Univ Dept Commun Engn Tao Yuan 320 Taiwan Inst Informat Ind Taipei 106 Taiwan Natl Chiao Tung Univ Dept Elect Engn Hsinchu 300 Taiwan

In this paper, we resort to the expectation-maximization (EM) algorithm to tackle the inter-carrier interference (ICI) problem, caused by time-variant multipath channels, for both orthogonal frequency division multiplexing (OFDM) systems and bit-interleaved coded modulation (BICM)/OFDM systems. We first analyze the ICI in frequency domain with a reduced set of parameters, and following this analysis, we derive an EM algorithm for maximum likelihood (ML) data detection. An ML-EM receiver for OFDM systems and a TURBO-EM receiver for BICM/OFDM systems are then developed to reduce computational complexity of the EM algorithm and to exploit temporal diversity, the main idea of which is to integrate the proposed EM algorithm with a groupwise ICI cancellation method. Compared with the ML-EM receiver, the TURBO-EM receiver further employs a soft-output Viterbi algorithm (SOVA) decoder to exchange information with a maximum a posteriori (MAP) EM detector through the turbo principle. Computer simulation demonstrates that the two proposed receivers clearly outperform the conventional one-tap equalizer, and the performance of the TURBO-EM receiver is close to the matched-filter bound even at a normalized maximum Doppler frequency (MDF) up to 0.2.

关键词： Orthogonal frequency division multiplexing bit-interleaved coded modulation inter-carrier interference expectation-maximization algorithms turbo receivers

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Mixture Semisupervised Bayesian Principal Component Regression for Soft Sensor Modeling

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IEEE ACCESS 2018年 6卷 40909-40919页

作者： Zhu, Pengbo Liu, Xin Wang, Yanbo Yang, Xianqiang Harbin Inst Technol Res Inst Intelligent Control & Syst Harbin 150080 Heilongjiang Peoples R China

In this paper, a mixture semisupervised Bayesian principal component regression-based soft sensor modeling method for nonlinear industrial process with multiple operating modes is presented. In many chemistry processes, part of output data samples may be unavailable due to the difficulties in measurement or recording. The semisupervised method is introduced to efficiently deal with the unlabeled data set. Moreover, the Bayesian regularization method is proposed to determine the unknown dimensionality of latent variables space in each submode by introducing three different formulations of two hyperparameters to construct the Gaussian prior distributions over the loading and regression matrices. The formulation of this method is derived in expectation maximization algorithm scheme, and the formulas to update unknown parameters are derived. The effectiveness of the proposed method is verified through a numerical example, the Tennessee Eastman benchmark process, and the comparisons with the existing method.

关键词： Principal component analysis semisupervised learning mixture models expectation-maximization algorithms Bayesian regularization

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The Path Inference Filter: Model-Based Low-Latency Map Matching of Probe Vehicle Data

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IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 2014年第2期15卷 507-529页

作者： Hunter, Timothy Abbeel, Pieter Bayen, Alexandre Univ Calif Berkeley Coll Engn Dept Elect Engn & Comp Sci Berkeley CA 94720 USA

We consider the problem of reconstructing vehicle trajectories from sparse sequences of GPS points, for which the sampling interval is between 1 s and 2 min. We introduce a new class of algorithms, which are altogether called the path inference filter (PIF), that maps GPS data in real time, for a variety of tradeoffs and scenarios and with a high throughput. Numerous prior approaches in map matching can be shown to be special cases of the PIF presented in this paper. We present an efficient procedure for automatically training the filter on new data, with or without ground-truth observations. The framework is evaluated on a large San Francisco taxi data set and is shown to improve upon the current state of the art. This filter also provides insights about driving patterns of drivers. The PIF has been deployed at an industrial scale inside the Mobile Millennium traffic information system, and is used to map fleets of data in San Francisco and Sacramento, CA, USA;Stockholm, Sweden;and Porto, Portugal.

关键词： expectation-maximization algorithms filtering GPS data Markov random fields maximum likelihood estimation network-free data path observation generation probabilistic map matching route choice modeling

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