The estimation and detection of a weak magnetic dipole signal is a critical problem in magnetic target detection. The difficulty arises due to a latent variable in the model, which affects the estimation and detection...
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The estimation and detection of a weak magnetic dipole signal is a critical problem in magnetic target detection. The difficulty arises due to a latent variable in the model, which affects the estimation and detection performance, especially at low signal-to-noise ratios (SNRs). A non-probability-distribution expectation maximization (NPD-em) algorithm is proposed to estimate the magnetic dipole signal with the latent variable at low SNRs. A reasonable value of an intermediate variable instead of the optimal one is determined without any probability information in the iteration of the NPD-em algorithm, which overcomes an unknown probability distribution appearing in the traditional expectation maximization (em) algorithm and reduces the calculated amount by 3 orders of magnitude compared with the traditional em algorithm. A statistic based on the NPD-em algorithm representing an unbiased estimator of the target signal energy is constructed to detect the magnetic dipole signal at low SNRs, and an innovative compensation in the detector is introduced so as to reduce the noise influence on the statistic. The experiment results show that, the constructed detector is comparable to the ideal matching filter due to the attractive performance of the NPD-em algorithm and the outstanding statistic.
We study properties and parameter estimation of a finite-state, homogeneous, continuous-time, bivariate Markov chain. Only one of the two processes of the bivariate Markov chain is assumed observable. The general form...
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We study properties and parameter estimation of a finite-state, homogeneous, continuous-time, bivariate Markov chain. Only one of the two processes of the bivariate Markov chain is assumed observable. The general form of the bivariate Markov chain studied here makes no assumptions on the structure of the generator of the chain. Consequently, simultaneous jumps of the observable and underlying processes are possible, neither process is necessarily Markov, and the time between jumps of each of the two processes has a phase-type distribution. Examples of bivariate Markov chains include the Markov modulated Poisson process and the batch Markovian arrival process when appropriate modulo counts are used in each case. We develop an expectation-maximization (em) procedure for estimating the generator of a bivariate Markov chain, and we demonstrate its performance. The procedure does not rely on any numerical integration or sampling scheme of the continuous-time bivariate Markov chain. The proposed em algorithm is equally applicable to multivariate Markov chains. (C) 2012 Elsevier B.V. All rights reserved.
In this paper, a distributed expectation maximization (Dem) algorithm is first introduced in a general form for estimating the parameters of a finite mixture of components. This algorithm is used for density estimatio...
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In this paper, a distributed expectation maximization (Dem) algorithm is first introduced in a general form for estimating the parameters of a finite mixture of components. This algorithm is used for density estimation and clustering of data distributed over nodes of a network. Then, a distributed incremental em algorithm (DIem) with a higher convergence rate is proposed. After a full derivation of distributed em algorithms, convergence of these algorithms is analyzed based on the negative free energy concept used in statistical physics. An analytical approach is also developed for evaluating the convergence rate of both incremental and distributed incremental em algorithms. It is analytically shown that the convergence rate of DIem is much faster than that of the Dem algorithm. Finally, simulation results approve that DIem remarkably outperforms Dem for both synthetic and real data sets.
Application of the em (Expectation-Maximization) algorithm to sequence estimation in an unknown channel can in principle produce MLSE (maximum likelihood sequence estimates) that are not dependent on a particular chan...
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Application of the em (Expectation-Maximization) algorithm to sequence estimation in an unknown channel can in principle produce MLSE (maximum likelihood sequence estimates) that are not dependent on a particular channel estimate. The Expectation step of this algorithm cannot be directly performed for continuous phase modulated (CPM) signals transmitted in a time varying multipath channel. We therefore derive a simplification of the em algorithm for CPM signals in this channel. Simulations applied to the Global System for Mobile Communications (GSM) show that the simplified em algorithm significantly decreases the amount of training data needed for the channel model considered, and removes the majority of the bit errors that are due to imperfect knowledge of the channel.
This paper presents a deterministic annealing em (DAem) algorithm for maximum likelihood estimation problems to overcome a local maxima problem associated with the conventional em algorithm. In our approach, a new pos...
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This paper presents a deterministic annealing em (DAem) algorithm for maximum likelihood estimation problems to overcome a local maxima problem associated with the conventional em algorithm. In our approach, a new posterior parameterized by 'temperature' is derived by using the principle of maximum entropy and is used for controlling the annealing process. In the DAem algorithm, the em process is reformulated as the problem of minimizing the thermodynamic free energy by using a statistical mechanics analogy. Since this minimization is deterministically performed at each temperature, the total search is executed far more efficiently than in the simulated annealing. Moreover, the derived DAem algorithm, unlike the conventional em algorithm, can obtain better estimates free of the initial parameter values. We also apply the DAem algorithm to the training of probabilistic neural networks using mixture models to estimate the probability density and demonstrate the performance of the DAem algorithm. (C) 1998 Elsevier Science Ltd. All rights reserved.
An expectation maximization (em) algorithm is presented for ARX modeling with uncertain communication channels. The considered model consists of two parts: a dynamic model which is expressed by an ARX model, and an ou...
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An expectation maximization (em) algorithm is presented for ARX modeling with uncertain communication channels. The considered model consists of two parts: a dynamic model which is expressed by an ARX model, and an output model, both subject to white Gaussian noises. Since the true outputs of the ARX model are assumed to be unknown, a modified Kalman filter is derived to estimate the output, and then the parameters are estimated by the em algorithm using the estimated outputs. The Kullback-Leibler divergence and the submartingale are used to prove that the parameter estimates can converge to the true values with the em algorithm. Furthermore, a simulation example is presented to verify the theoretical results. (C) 2020 Elsevier B.V. All rights reserved.
The Mixture of Gaussian Processes (MGP) is a powerful statistical model for characterizing multimodal data, but its conventional Expectation-Maximization (em) algorithm (Dempster et al., 1977) is computationally intra...
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The Mixture of Gaussian Processes (MGP) is a powerful statistical model for characterizing multimodal data, but its conventional Expectation-Maximization (em) algorithm (Dempster et al., 1977) is computationally intractable because of its time complexity. To solve this problem, some approximation techniques have been proposed in the conventional em algorithm. However, these approximate em algorithms are ineffective or limited in some situations. To implement the em algorithm more effectively, we approximate the em algorithm with simulated samples of latent variable via the Monte Carlo Markov Chain (MCMC) sampling, and design an MCMC em algorithm. Experiments on both synthetic and real-world data sets demonstrate that our MCMC em algorithm is more effective than the state-of-the-art em algorithms on classification and prediction problems. (C) 2018 Elsevier B.V. All rights reserved.
Constructing confidence interval (CI) for functions of cell probabilities (e.g., rate difference, rate ratio and odds ratio) is a standard procedure for categorical data analysis in clinical trials and medical studies...
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Constructing confidence interval (CI) for functions of cell probabilities (e.g., rate difference, rate ratio and odds ratio) is a standard procedure for categorical data analysis in clinical trials and medical studies. In the presence of incomplete data, existing methods could be problematic. For example, the inverse of the observed information matrix may not exist and the asymptotic CIs based on delta methods are hence not available. Even though the inverse of the observed information matrix exists, the large-sample delta methods are generally not reliable in small-sample studies. In addition, existing expectation-maximization (em) algorithm via the conventional data augmentation (DA) may suffer from slow convergence due to the introduction of too many latent variables. In this article, for r x c tables with incomplete data, we propose a novel DA scheme that requires fewer latent variables and this will consequently lead to a more efficient em algorithm. We present two bootstrap-type CIs for parameters of interest via the new em algorithm with and without the normality assumption. For r x c tables with only one incomplete/supplementary margin, the improved em algorithm converges in only one step and the associated maximum likelihood estimates can hence be obtained in closed form. Theoretical and simulation results showed that the proposed em algorithm outperforms the existing em algorithm. Three real data from a neurological study, a rheumatoid arthritis study and a wheeze study are used to illustrate the methodologies. (c) 2006 Elsevier B.V. All rights reserved.
Most of the researchers in the application areas usually use the em algorithm to find estimators of the normal mixture distribution with unknown component specific variances without knowing much about the properties o...
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Most of the researchers in the application areas usually use the em algorithm to find estimators of the normal mixture distribution with unknown component specific variances without knowing much about the properties of the estimators. It is unclear for which situations the em algorithm provides "good" estimators, good in the sense of statistical properties like consistency, bias, or mean square error. A simulation study is designed to investigate this problem. The scope of this study is set for the mixture model of normal distributions with component specific variance, while the number of components is fixed. The asymptotic properties of the em algorithm estimate is investigated in each situation. The results show that the em algorithm estimate does provide good asymptotic properties except for some situations in which the population means are quite close to each other and larger differences in the variances of the component distributions occur. (C) 2002 Elsevier Science B.V. All rights reserved.
We consider the problem of change-point in a classical framework while assuming a probability distribution for the change-point. An em algorithm is proposed to estimate the distribution of the change-point. A change-p...
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We consider the problem of change-point in a classical framework while assuming a probability distribution for the change-point. An em algorithm is proposed to estimate the distribution of the change-point. A change-point model for multiple profiles is also proposed, and em algorithm is presented to estimate the model. Two examples of Illinois traffic data and Dow Jones Industrial Averages are used to demonstrate the proposed methods.
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