In model-based cluster analysis, the expectation-maximization (EM) algorithm has a number of desirable properties, but in some situations, this algorithm can be slow to converge. Some variants are proposed to speed-up...
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In model-based cluster analysis, the expectation-maximization (EM) algorithm has a number of desirable properties, but in some situations, this algorithm can be slow to converge. Some variants are proposed to speed-up EM in reducing the time spent in the E-step, in the case of Gaussian mixture. The main aims of such methods is first to speed-up convergence of EM, and second to yield same results (or not so far) than EM itself. In this paper, we compare these methods from categorical data, with the latent class model, and we propose a new variant that sustains better results on synthetic and real data sets, in terms of convergence speed-up and number of misclassified objects.
A solution is given to the problem of estimating reliability indicators in a context of crude data arising in an industrial study devoted to the reliability assessment of electronic calculators used in modern airplane...
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A solution is given to the problem of estimating reliability indicators in a context of crude data arising in an industrial study devoted to the reliability assessment of electronic calculators used in modern airplanes. We introduce the concept of amalgamated data and develop an expectation-maximization algorithm to obtain a maximum likelihood estimator of the reliability function and the cumulative failure intensity associated with the lifetime of calculators.
This article addresses adaptive radar detection of N pulses coherently backscattered by a prospective target in heterogeneous disturbance. As customary K >= N range cells adjacent to the one under test are used for...
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This article addresses adaptive radar detection of N pulses coherently backscattered by a prospective target in heterogeneous disturbance. As customary K >= N range cells adjacent to the one under test are used for estimation purposes. The disturbance in each range cell is described by a non-Gaussian model based on a mixture of L < K Gaussian distributions. Gaussian components are characterized by an unknown low-rank matrix plus thermal noise with unknown power level. We first derive a detector inspired by the generalized likelihood ratio test that adaptively estimates the statistical properties of the disturbance from the observed data. To overcome the intractability of the involved maximum-likelihood estimation problem, a suitable approximate strategy based on the expectation-maximization algorithm is developed. This also allows us to classify the cell under test by selecting the "maximum a posteriori Gaussian distribution" for the disturbance (under both hypotheses). Accordingly, a likelihood ratio test is also proposed. An extensive performance analysis, conducted on synthetic data as well as on two different experimental datasets (PhaseOne and IPIX for land and sea radar returns, respectively), shows that the proposed approaches outperform state-of-the-art competitors in terms of both detection capabilities and false alarms control.
An efficient initialization of the expectation-maximization algorithm to estimate mixture models via maximum likelihood is proposed. A fully unsupervised network-based initial-ization technique is provided by mapping ...
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An efficient initialization of the expectation-maximization algorithm to estimate mixture models via maximum likelihood is proposed. A fully unsupervised network-based initial-ization technique is provided by mapping time series to complex networks using as adja-cency matrix the Markov Transition Field associated to the time series. In this way, the optimal number of mixture model components and the vector of initial parameters can be directly obtained. An experiment conducted on financial times series with very different characteristics shows that our approach produces significantly better results if compared to conventional methods of initialization, such as K-means and Random, thus demonstrat-ing the effectiveness of the proposed method.(c) 2022 Elsevier Inc. All rights reserved.
The controlled branching process is a generalization of the classical Bienayme-Galton-Watson branching process. It is a useful model for describing the evolution of populations in which the population size at each gen...
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The controlled branching process is a generalization of the classical Bienayme-Galton-Watson branching process. It is a useful model for describing the evolution of populations in which the population size at each generation needs to be controlled. The maximum likelihood estimation of the parameters of interest for this process is addressed under various sample schemes. Firstly, assuming that the entire family tree can be observed, the corresponding estimators are obtained and their asymptotic properties investigated. Secondly, since in practice it is not usual to observe such a sample, the maximum likelihood estimation is initially considered using the sample given by the total number of individuals and progenitors of each generation, and then using the sample given by only the generation sizes. expectation-maximization algorithms are developed to address these problems as incomplete data estimation problems. The accuracy of the procedures is illustrated by means of a simulated example. (C) 2015 Elsevier B.V. All rights reserved.
GNSS (Global Navigation Satellite Systems) tropospheric delay, specifically zenith wet delay (ZWD), shows clear spatial-temporal variations and is usually modeled as RWPN (random walk process noise). However, because ...
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GNSS (Global Navigation Satellite Systems) tropospheric delay, specifically zenith wet delay (ZWD), shows clear spatial-temporal variations and is usually modeled as RWPN (random walk process noise). However, because RWPN does not take the geographical position of GNSS stations and local weather conditions into account for precise point positioning (PPP), it may lead to biased ZWD estimates. To address the scientific problem and improve ZWD estimates, we adopt the expectation-maximization algorithm (EM algorithm) to validate the feasibility of estimating RWPN using only GNSS measurements. Numerical experiments reveal that using only GNSS observations is capable of determining the RWPN parameter, although it could take several days to reach a stable solution if the initial guess deviates far away from the truth. It is also shown that estimating RWPN can almost always effectively improve ZWD estimates by several millimeters in contrast with traditional PPP results. If the ambiguities are fixed to their integer values correctly, the accuracy of RWPN estimates for ZWD can be greatly reduced by 2mm/hour\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2\text{ mm}/\sqrt{\text{hour}}$$\end{document}.
The expectation-maximization (EM) algorithm is a popular tool in a wide variety of statistical settings, in particular in the maximum likelihood estimation of parameters when clustering using mixture models. A serious...
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The expectation-maximization (EM) algorithm is a popular tool in a wide variety of statistical settings, in particular in the maximum likelihood estimation of parameters when clustering using mixture models. A serious pitfall is that in the case of a multimodal likelihood function the algorithm may become trapped at a local maximum, resulting in an inferior clustering solution. In addition, convergence to an optimal solution can be very slow. Methods are proposed to address these issues: optimizing starting values for the algorithm and targeting maximization steps efficiently. It is demonstrated that these approaches can produce superior outcomes to initialization via random starts or hierarchical clustering and that the rate of convergence to an optimal solution can be greatly improved. (C) 2012 Elsevier B.V. All rights reserved.
We consider the problem of event-related desynchronization (ERD) estimation. In existing approaches, model parameters are usually found manually through experimentation, a tedious task that often leads to suboptimal e...
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We consider the problem of event-related desynchronization (ERD) estimation. In existing approaches, model parameters are usually found manually through experimentation, a tedious task that often leads to suboptimal estimates. We propose an expectation-maximization (EM) algorithm for model parameter estimation that is fully automatic and gives optimal estimates. Further, we apply a Kalman smoother to obtain ERD estimates. Results show that the EM algorithm significantly improves the performance of the Kalman smoother. Application of the proposed approach to the motor-imagery EEG data shows that useful ERD patterns can be obtained even without careful selection of frequency bands.
In this article, I provide an illustrative, step-by-step implementation of the expectation-maximization algorithm for the nonparametric estimation of mixed logit models. In particular, the proposed routine allows user...
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In this article, I provide an illustrative, step-by-step implementation of the expectation-maximization algorithm for the nonparametric estimation of mixed logit models. In particular, the proposed routine allows users to fit straight-forwardly latent-class logit models with an increasing number of mass points so as to approximate the unobserved structure of the mixing distribution.
Many parameter estimation problems in signal processing can be reduced to the task of minimizing a function of the unknown parameters. This task is difficult owing to the existence of possibly local minima and the sha...
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Many parameter estimation problems in signal processing can be reduced to the task of minimizing a function of the unknown parameters. This task is difficult owing to the existence of possibly local minima and the sharpness of the global minimum. In this article we review three approaches that can be used to minimize functions of the type encountered in parameter estimation problems. The first two approaches, the cyclic minimization and the majorization technique, are quite general, whereas the third one, the expectation-maximization (EM) algorithm, is tied to the use of the maximum likelihood (ML) method for parameter estimation. The article provides a quick refresher of the aforementioned approaches for a wide readership.
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