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IEEE International Conference on Evolutionary Computation

作者： D.E. Waagen M.D. Parsons J.R. McDonnell F.L. Datz TRW Systems Integration Group Ogden UT USA RDT&E Div NCCOSC San Diego CA USA University of Utah Health Sciences Center Salt Lake UT USA

This work investigates the application of stochastic optimization in the development of a new paradigm, polydistributional mixtures, for automated data modeling. This new paradigm increases the generality of mixture methods by allowing for the automated simultaneous optimization of the number of components, the distributional form of each component, the proportionality associated with each component, as well as the parameters of each component. A general evolutionary approach, based on the mutation and selection from a population of potential solutions, is used as the optimization procedure. The approach is applied to modeling texture features extracted from digitized mammograms of cancerous and noncancerous regions. The resulting polydistributional mixtures are compared to optimal (in terms of model fitness) normal mixtures optimized via the expectation-maximization algorithm.

关键词： Stochastic processes Probability distribution Cost function Cities and towns Stochastic systems Optimization methods Genetic mutations Feature extraction expectation-maximization algorithms Probability density function

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Language modeling by variable length sequences: theoretical formulation and evaluation of multigrams

Language modeling by variable length sequences: theoretical ...

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International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： S. Deligne F. Bimbot Department Signal Télécom Paris ENST Paris France

The multigram model assumes that language can be described as the output of a memoryless source that emits variable-length sequences of words. The estimation of the model parameters can be formulated as a maximum likelihood estimation problem from incomplete data. We show that estimates of the model parameters can be computed through an iterative expectation-maximization algorithm and we describe a forward-backward procedure for its implementation. We report the results of a systematical evaluation of multigrams for language modeling on the ATIS database. The objective performance measure is the test set perplexity. Our results show that multigrams outperform conventional n-grams for this task.

关键词： Maximum likelihood estimation Telecommunications Electronic mail expectation-maximization algorithms Databases Testing Probability Parameter estimation Dictionaries Vocabulary

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Hierarchical mixture of experts and Max-Min propagation neural networks

Hierarchical mixture of experts and Max-Min propagation neur...

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International Conference on Neural Networks

作者： P.A. Estevez R. Nakano Department of Electrical Engineering University of Chile Santiago Chile Communication Science Laboratories NTT Kyoto Japan

The max-min propagation neural network model is considered as a hierarchical mixture of experts by replacing the max (min) units with softmax functions. The resulting mixture is different from the model of Jordan and Jacobs, but we exploit the similarities between both models to derive a probability model. Learning is treated as a maximum-likelihood problem, in particular we present a gradient ascent algorithm and an expectation-maximization algorithm. Simulation results on the parity problem and the majority problem are reported.

关键词： Neural networks Jacobian matrices expectation-maximization algorithms

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SPACE-ALTERNATING GENERALIZED expectation-maximization ALGORITHM

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 1994年第10期42卷 2664-2677页

作者： FESSLER, JA HERO, AO UNIV MICHIGAN DEPT ELECT ENGN & COMP SCI ANN ARBOR MI 48109 USA

The expectation-maximization (EM) method can facilitate maximizing likelihood functions that arise in statistical estimation problems. In the classical EM paradigm, one iteratively maximizes the conditional log-likelihood of a single unobservable complete data space, rather than maximizing the intractable likelihood function for the measured or incomplete data. EM algorithms update all parameters simultaneously, which has two drawbacks: 1) slow convergence, and 2) difficult maximization steps due to coupling when smoothness penalties are used. This paper describes the space-alternating generalized EM (SAGE) method, which updates the parameters sequentially by alternating between several small hidden-data spaces defined by the algorithm designer. We prove that the sequence of estimates monotonically increases the penalized-likelihood objective, we derive asymptotic convergence rates, and we provide sufficient conditions for monotone convergence in norm. Two signal processing applications illustrate the method: estimation of superimposed signals in Gaussian noise, and image reconstruction from Poisson measurements. In both applications, our SAGE algorithms easily accommodate smoothness penalties and converge faster than the EM algorithms.

关键词： expectation-maximization algorithms Signal processing algorithms Convergence Extraterrestrial measurements Iterative algorithms Algorithm design and analysis Sufficient conditions Signal processing Gaussian noise Image reconstruction

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A NOTE ON STOPPING RULES IN EM-ML RECONSTRUCTIONS OF ECT IMAGES

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IEEE TRANSACTIONS ON MEDICAL IMAGING 1994年第3期13卷 569-571页

作者： JOHNSON, VE Institute of Statistics and Decision Sciences Duke University Durham NC USA

The use of the expectation-maximization algorithm to obtain pseudo-maximum likelihood estimates (i.e. the EM-ML algorithm) of radiopharmaceutical distributions based on data collected from emission computed tomography (ECT) systems is now a well developed area, as witnessed by a number of recent articles on that topic, including the detailed study of the relative performance of EM-ML and FBP reconstructions provided in J. Llacer et al. (ibid., vol. 12, p. 215-31, 1993). However, there remains considerable confusion in the field regarding appropriate stopping rules for EM-ML algorithms, and in this correspondence the author attempts to detail a shortcoming of one of the more recent and innovative stopping rule criteria. In particular, the author discusses the effect of total photon counts on stopping criteria based on cross-validation.< >

关键词： Image reconstruction Electrical capacitance tomography expectation-maximization algorithms Computed tomography Positron emission tomography Imaging phantoms Probability Artificial intelligence Statistics Biomedical imaging

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ONLINE ESTIMATION OF DYNAMIC SHOCK-ERROR MODELS BASED ON THE KULLBACK-LEIBLER INFORMATION MEASURE

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 1994年第5期39卷 1129-1135页

作者： KRISHNAMURTHY, V Cooperative Res. Center for Robust & Adaptive Syst. Australian Nat. Univ. Canberra ACT Australia

In this paper we develop two sequential or ''on-line'' estimation schemes in the time domain for dynamic shock-error models which are special cases of errors-in-variables models. Our approach utilizes a state-space representation of the model, Kalman filtering techniques, and on-line algorithms. The first on-line algorithm is based on the expectation-maximization algorithm and uses a recursive Gauss-Newton scheme to maximize the Kullback Leibler information measure. The second on-line algorithm we propose is a gradient-based scheme and uses stochastic approximations to maximize the log likelihood. In comparison to the off-line Maximum Likelihood estimation scheme used in [1], our on-line algorithms have significantly reduced computational costs and negligible memory requirements. Simulations illustrate the satisfactory performance of the algorithms in estimating errors-in-variables systems with parameters that vary slowly with time or undergo infrequent jump changes.

关键词： Kalman filters Filtering algorithms expectation-maximization algorithms Newton method Least squares methods Recursive estimation Stochastic processes Maximum likelihood estimation Computational efficiency Computational modeling

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APPLICATION OF expectation-maximization ALGORITHM TO THE DETECTION OF A DIRECT-SEQUENCE SIGNAL IN PULSED NOISE JAMMING

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IEEE TRANSACTIONS ON COMMUNICATIONS 1993年第8期41卷 1151-1154页

作者： ANSARI, A VISWANATHAN, R Department of Electrical Engineering Southem Illinois University Carbondale IL USA

We consider the detection of a direct-sequence spread-spectrum signal received in a pulsed noise jamming environment. The expectation-maximization algorithm is used to estimate the unknown jammer parameters and hence obtain a decision on the binary signal based on the estimated likelihood functions. The probability of error performance of the algorithm is simulated for a repeat code and a (7,4) block code. Simulation results show that at low signal-to-thermal noise ratio and high jammer power, the EM detector performs significantly better than the hard limiter and somewhat better than the soft limiter. Also, at low SNR, there is little degradation as compared to the maximum-likelihood detector with true jammer parameters. At high SNR, the soft limiter outperforms the EM detector.

关键词： expectation-maximization algorithms Jamming Detectors Gaussian noise Spread spectrum communication Block codes Signal to noise ratio Working environment noise Degradation Maximum likelihood detection

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REDUCING NEGATIVITY ARTIFACTS IN EMISSION TOMOGRAPHY - POST-PROCESSING FILTERED BACKPROJECTION SOLUTIONS

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IEEE TRANSACTIONS ON MEDICAL IMAGING 1993年第4期12卷 653-663页

作者： OSULLIVAN, F PAWITAN, Y HAYNOR, D UNIV WASHINGTON DEPT BIOSTATSEATTLEWA 98195 UNIV COLL DUBLIN DEPT STATBELFIELD 4DUBLINIRELAND UNIV WASHINGTON DEPT RADIOLSEATTLEWA 98195

The problem of negative artifacts in emission tomography reconstructions computed by filtered backprojection (FBP) is of practical concern particularly in low count studies. Statistical reconstruction methods based on maximum likelihood (ML) are automatically constrained to be non-negative but their excessive computational overhead (orders of magnitude greater than FBP) has limited their use in operational settings. Motivated by the statistical character of the negativity artifact, we develop a simple post-processing technique that iteratively adjusts negative values by cancellation with positive values in a surrounding local neighborhood. The compute time of this approach is roughly equivalent to two applications of FBP. The approach was evaluated by numerical simulation in one- and two-dimensional settings. In two dimensions, the source distributions included the Hoffman, the Shepp and Vardi, and a digitized version of the Jaszczak cold spheres phantoms. Our studies compared smoothed versions of FBP, the post-processed FBP, and ML implemented by the expectation-maximization algorithm. The root mean square (RMS) error between the true and estimated source distribution was used to evaluate performance;in two dimensions, additional region-of-interest-based measures of reconstruction accuracy were also employed. In making comparisons between the different methods, the amount of smoothing applied to each reconstruction method was adapted to minimize the RMS error-this was found to be critical. After adjusting for this effect, the average RMS error for FBP was typically between 13% and 20% higher than ML;the modified FPB method was between 2% and 5% greater than ML. Similar results were found for the region-of-interest error. These experiments suggest that it may be possible to achieve much of the gain associated with ML reconstruction in emission tomography by simpler computational means.

关键词： Tomography Reconstruction algorithms Image reconstruction Statistics Bayesian methods Maximum likelihood estimation Numerical simulation Imaging phantoms expectation-maximization algorithms Root mean square

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AN ITERATIVE METHOD FOR EXACT MAXIMUM-LIKELIHOOD-ESTIMATION OF THE PARAMETERS OF A HARMONIC SERIES

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 1993年第2期38卷 367-370页

作者： WHITE, LB Electronics Research Laboratory Defence Science and Technology Organization Salisbury UK

This correspondence describes a procedure for determining the exact maximum likelihood (ML) estimates of the parameters of a harmonic series (i.e., the fundamental frequency, and the amplitude and phase of each harmonic). Existing ML methods are only approximate in the sense that terms present due to mixing between the harmonics are ignored;these terms asymptotically reduce to zero as the sample size increases to infinity. The note argues that these terms can be significant for short signal lengths. The application of the expectation-maximization algorithm results in an iterative procedure that converges to a stationary point on the true parameter likelihood surface. If global convergence results, this point yields the exact ML estimates. Simulation studies illustrate the advantages of the method when short data lengths are used.

关键词： Iterative methods Maximum likelihood estimation Frequency estimation Amplitude estimation Parameter estimation Phase estimation H infinity control expectation-maximization algorithms Convergence Yield estimation

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Covariance estimation for multidimensional data using the EM algorithm

Covariance estimation for multidimensional data using the EM...

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Asilomar Conference on Signals, Systems & Computers

作者： T.A. Barton D.R. Fuhrmann Department of Electrical Engineering Washington University Saint Louis MO USA

Under a complex-Gaussian data model, a maximum likelihood method based on the iterative expectation-maximization algorithm is given to estimate structured covariance matrices for multidimensional data organized into column-vector form. The covariance structures of interest involve a hierarchy of subblocks within the covariance matrix, and include block-circulant and block Toeplitz matrices and their generalizations. These covariance matrices are elements of certain covariance constraint sets such that each element may be described as a matrix multiplication of a known matrix of Kronecker products and a nonnegative-definite, block-diagonal matrix. Several convergence properties of the estimation procedure are discussed, and an example of algorithm behavior is provided.< >

关键词： Multidimensional systems Covariance matrix Data models Maximum likelihood estimation Iterative methods expectation-maximization algorithms Convergence

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