We address the problem of computing the largest fraction of missing information for the em algorithm and the worst linear function for data augmentation. These are the largest eigenvalue and its associated eigenvector...
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We address the problem of computing the largest fraction of missing information for the em algorithm and the worst linear function for data augmentation. These are the largest eigenvalue and its associated eigenvector for the Jacobian of the em operator at a maximum likelihood estimate, which are important for assessing convergence in iterative simulation. An estimate of the largest fraction of missing information is available from the em iterates;this is often adequate since only a few figures of accuracy are needed. In some instances the em iteration also gives an estimate of the worst linear function. We show that improved estimates can be essential for proper inference. In order to obtain improved estimates efficiently, we use the power method for eigencomputation. Unlike eigenvalue decomposition, the power method computes only the largest eigenvalue and eigenvector of a matrix, it can take advantage of a good eigenvector estimate as an initial value and it can be terminated after only a few figures of accuracy are achieved. Moreover, the matrix products needed in the power method can be computed by extrapolation, obviating the need to form the Jacobian of the em operator. We give results of simulation studies on multivariate normal data showing that this approach becomes more efficient as the data dimension increases than methods that use a finite-difference approximation to the Jacobian, which is the only general-purpose alternative available. (C) 1999 Elsevier Science B.V. All rights reserved.
Gaussian process (GP) regression is a fully probabilistic method for performing non-linear regression. In a Bayesian framework, regression models can be made robust by using heavy-tailed distributions instead of using...
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Gaussian process (GP) regression is a fully probabilistic method for performing non-linear regression. In a Bayesian framework, regression models can be made robust by using heavy-tailed distributions instead of using normal distribution for modeling noise. This work focuses on estimation of parameters for robust GP regression. In literature, these are learned by maximizing the approximate marginal likelihood of data. However, gradient-based optimization algorithms which are used for this purpose can be unstable or may require tuning. In this work, an em algorithm based approach is derived and implemented to infer the parameters. The pros and cons of the two approaches are analyzed. The advantage of em algorithm lies in its ease of implementation and theoretical guarantees of numerical stability and convergence while its prediction performance is still comparable to gradient-based approaches. In some cases em algorithm may be slow to converge. To circumvent this issue a faster em based approach known as Expectation Conjugate Gradient (ECG) is implemented on robust GP regression. Finally, the proposed em approach to robust GP regression is validated using an industrial data set. (C) 2016 Elsevier Ltd. All rights reserved.
Since histograms of many real network traces show strong evidence of mixture, this paper uses mixture distributions to model Internet traffic and applies the em algorithm to fit the models. Making use of the fact that...
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Since histograms of many real network traces show strong evidence of mixture, this paper uses mixture distributions to model Internet traffic and applies the em algorithm to fit the models. Making use of the fact that at each iteration of the em algorithm the parameter increment has a positive projection on the gradient of the likelihood function, this paper proposes an online em algorithm to fit the models and the Bayesian Information Criterion is applied to select the best model. Experimental results on real traces are provided to illustrate the efficiency of the proposed algorithm. (c) 2004 Elsevier B.V. All rights reserved.
This paper describes a new approach to matching geometric structure in 2D point-sets. The novel feature is to unify the tasks of estimating transformation geometry and identifying point-correspondence matches. Unifica...
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This paper describes a new approach to matching geometric structure in 2D point-sets. The novel feature is to unify the tasks of estimating transformation geometry and identifying point-correspondence matches. Unification is realized by constructing a mixture model over the bipartite graph representing the correspondence match and by affecting optimization using the em algorithm. According to our em framework, the probabilities of structural correspondence gate contributions to the expected likelihood function used to estimate maximum likelihood transformation parameters. These gating probabilities measure the consistency of the matched neighborhoods in the graphs. The recovery of transformational geometry and hard correspondence matches are interleaved and are realized by applying coupled update operations to the expected log-likelihood function. In this way, the two processes bootstrap one another. This provides a means of rejecting structural outliers. We evaluate the technique on two real-world problems. The first involves the matching of different perspective views of 3.5-inch floppy discs. The second example is furnished by the matching of a digital map against aerial images that are subject to severe barrel distortion due to a line-scan sampling process. We complement these experiments with a sensitivity study based on synthetic data.
Orthogonal Frequency Division Multiplexing (OFDM) systems are very sensitive to the frequency offset of the local oscillator at the receiver while the symbol timing offset can be absorbed in the guard interval. For th...
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Orthogonal Frequency Division Multiplexing (OFDM) systems are very sensitive to the frequency offset of the local oscillator at the receiver while the symbol timing offset can be absorbed in the guard interval. For the same reason, estimation of the frequency characteristics, needed for OFDM to be adapted to the frequency selective fading, can only be carried out conventionally after the frequency offset has been compensated. And accurate estimation of large frequency offset certainly requires high precision estimate of the frequency characteristics. In this paper, we propose a new joint estimation method of the frequency offset and the channel frequency response using an Expectation-Maximization (em) algorithm for,OFDM systems. The proposed algorithm overcomes the limitation of the thus far proposed algorithm. By computer simulations, we show the proposed algorithm provides estimation accuracy close to its lower bound in a wide range of the frequency offset.
Latent class model (LCM), which is a finite mixture of different categorical distributions, is one of the most widely used models in statistics and machine learning fields. Because of its noncontinuous nature and flex...
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Latent class model (LCM), which is a finite mixture of different categorical distributions, is one of the most widely used models in statistics and machine learning fields. Because of its noncontinuous nature and flexibility in shape, researchers in areas such as marketing and social sciences also frequently use LCM to gain insights from their data. One likelihood-based method, the expectation-maximization (em) algorithm, is often used to obtain the model estimators. However, the em algorithm is well-known for its notoriously slow convergence. In this research, we explore alternative likelihood-based methods that can potential remedy the slow convergence of the em algorithm. More specifically, we regard likelihood-based approach as a constrained nonlinear optimization problem, and apply quasi-Newton type methods to solve them. We examine two different constrained optimization methods to maximize the log-likelihood function. We present simulation study results to show that the proposed methods not only converge in less iterations than the em algorithm but also produce more accurate model estimators.
The advent of complete genetic linkage maps of DNA markers has made systematic studies of mapping quantitative trait loci (QTL) in experimental organisms feasible. The method of multiple-interval mapping provides an a...
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The advent of complete genetic linkage maps of DNA markers has made systematic studies of mapping quantitative trait loci (QTL) in experimental organisms feasible. The method of multiple-interval mapping provides an appropriate way for mapping QTL using genetic markers. However, efficient algorithms for the computation involved remain to be developed. In this article, a full em algorithm for the simultaneous computation of the MLEs of QTL effects and positions is developed. em-based formulas are derived for computing the observed Fisher information matrix. The full em algorithm is compared with an ECM algorithm developed by Kao and Zeng (1997, Biometrics 53, 653-665). The validity of the inverted observed Fisher information matrix as an estimate of the variance matrix of the MLEs is demonstrated by a simulation study.
This paper describes an application of the em (expectation and maximisation) algorithm to the registration of incomplete millimetric radar images. The data used in this study consists of a series of non-overlapping ra...
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This paper describes an application of the em (expectation and maximisation) algorithm to the registration of incomplete millimetric radar images. The data used in this study consists of a series of non-overlapping radar sweeps. Our registration process aims to recover transformation parameters between the radar-data and a digital map. The tokens used in the matching process are fragmented line-segments extracted from the radar images which predominantly correspond to hedge-rows in the cartographic data. The em technique models data uncertainty using Gaussian mixtures defined over the positions and orientations of the lines. The resulting weighted least-squares parameter estimation problem is solved using the Levenberg-Marquardt method. A sensitivity analysis reveals that the data-likelihood function is unimodal in the translation and scale parameters. In fact, the algorithm is only potentially sensitive to the choice of initial rotation parameter;this is attributable to local sub-optima in the log-likelihood function associated with pi/2 orientation ambiguities in the map. By adopting Levenberg-Marquardt optimisation we reduce the local convergence difficulties posed by these local rotation maxima. The method is also demonstrated to be relatively insensitive to random measurement errors on the line-segments. (C) 1997 Elsevier Science B.V.
We advocate linear regression by modeling the error term through a finite mixture of asymmetric Laplace distributions (ALDs). The model expands the flexibility of linear regression to account for heterogeneity among d...
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We advocate linear regression by modeling the error term through a finite mixture of asymmetric Laplace distributions (ALDs). The model expands the flexibility of linear regression to account for heterogeneity among data and allows us to establish the equivalence between maximum likelihood estimation of the model parameters and the composite quantile regression (CQR) estimation developed by Zou and Yuan (Ann. Stat. 36:1108-1126, 2008), providing a new likelihood-based solution to CQR. Particularly, we develop a computationally efficient estimation procedure via a two-layer em algorithm, where the first layer em algorithm incorporates missing information from the component memberships of the mixture model and nests the second layer em in its M-step to accommodate latent variables involved in the location-scale mixture representation of the ALD. An appealing feature of the proposed algorithm is that the closed form updates for parameters in each iteration are obtained explicitly, instead of resorting to numerical optimization methods as in the existing work. Computational complexity can be reduced significantly. We evaluate the performance through simulation studies and illustrate its usefulness by analyzing a gene expression dataset. (C) 2017 Elsevier B.V. All rights reserved.
The platoon arrival process (PAP), a special case of Markovian arrival process (MAP), occurs in several practical queueing systems. Developing procedures for estimating its parameters is essential in order to successf...
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The platoon arrival process (PAP), a special case of Markovian arrival process (MAP), occurs in several practical queueing systems. Developing procedures for estimating its parameters is essential in order to successfully use it for representing arrival processes in real systems. We present an em-based procedure for estimating the parameters of a PAR (c) 2004 Elsevier B.V. All rights reserved.
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