The authors address the problem of estimating an inter-event distribution on the basis of count data. They derive a nonparametric maximum likelihood estimate of the inter-event distribution utilizing the EM algorithm ...
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The authors address the problem of estimating an inter-event distribution on the basis of count data. They derive a nonparametric maximum likelihood estimate of the inter-event distribution utilizing the EM algorithm both in the case of an ordinal renewal process and in the case of an equilibrium renewal process. In the latter case, the iterative estimation procedure follows the basic scheme proposed by Vardi for estimating the inter-event distribution on the basis of time-interval data; it combines the outputs of the E-step corresponding to the inter-event distribution and to the length-biased distribution. The authors also investigate a penalized likelihood approach to provide the proposed estimation procedures with regularization capabilities. They evaluate the practical estimation procedure using simulated count data and apply it to real count data representing the elongation of coffee-tree leafy axes.
In this paper, we present a statistical method to extract images of passenger cars from highway traffic scenes. The expectation-maximization (EM) algorithm is used to classify the vehicles in the images as either bein...
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In this paper, we present a statistical method to extract images of passenger cars from highway traffic scenes. The expectation-maximization (EM) algorithm is used to classify the vehicles in the images as either being passenger cars or some other bigger vehicles, cars versus non-cars. The vehicle classification algorithm uses training sets of 100-frame video sequences. The car group is comprised of passenger cars and light trucks. The non-car group is comprised of heavy single trucks as well as 3-axle and more combination trucks. We use the properties of their dimensional distribution and the probability of their appearance to identify the vehicle group. We present a validation of our algorithm using real-world traffic scenes.
Bayesian algorithms have lately been used in a large variety of applications. This paper proposes a new methodology for hyperparameter initialization in the Variational Bayes (VB) algorithm. We employ a dual expectati...
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Bayesian algorithms have lately been used in a large variety of applications. This paper proposes a new methodology for hyperparameter initialization in the Variational Bayes (VB) algorithm. We employ a dual expectation-maximization (EM) algorithm as the initialization stage in the VB-based learning. In the first stage, the EM algorithm is used on the given data set while the second EM algorithm is applied on distributions of parameters resulted from several runs of the first stage EM. The graphical model case study considered in this paper consists of a mixture of Gaussians. Appropriate conjugate prior distributions are considered for modelling the parameters. The proposed methodology is applied on blind source separation of modulated signals.
Adaptability is an important attribute for any robotic system operating in an unstructured environment. The paper describes the first steps towards an adaptable robotic platform, capable of learning behaviours. This i...
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Adaptability is an important attribute for any robotic system operating in an unstructured environment. The paper describes the first steps towards an adaptable robotic platform, capable of learning behaviours. This involves learning a new low-level behaviour 'on the fly' and integrating it into the existing set of behaviours. The first task selected for the robot to learn is obstacle avoidance. The paper will introduce an innovative and structured method of building knowledge acquired during robotic explorations. The aim is to make direct use of sensory information to construct abstractions of 'perceptions' and build strategies based on constructed knowledge to solve simple navigation tasks.
The expectation-maximization (EM) algorithm with split-and-merge operations (SMEM algorithm) proposed by Ueda, Nakano, Ghahramani, and Hinton (2000) is a nonlocal searching method, applicable to mixture models, for re...
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The expectation-maximization (EM) algorithm with split-and-merge operations (SMEM algorithm) proposed by Ueda, Nakano, Ghahramani, and Hinton (2000) is a nonlocal searching method, applicable to mixture models, for relaxing the local optimum property of the EM algorithm. In this article, we point out that the SMEM algorithm uses the acceptance-rejection evaluation method, which may pick up a distribution with smaller likelihood, and demonstrate that an increase in likelihood can then be guaranteed only by comparing log likelihoods.
Density optimization of a plantation is a classical task with important practical consequences. In this article, we present an adaptation of criss-cross design and an alternative analysis. If a tree is missing, the sp...
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Density optimization of a plantation is a classical task with important practical consequences. In this article, we present an adaptation of criss-cross design and an alternative analysis. If a tree is missing, the spacing of neighbouring trees is altered and considerable information is lost. We derive the estimate of the missing value that minimizes the residual sum of squares and obtain the analytical solution of the EM algorithm. The relationships between the two techniques are clarified. The method is applied to data from a plantation of Eucalyptus in the Congo.
The significance of task-induced cerebral blood flow responses, assessed using statistical parametric mapping, depends, among other things, on the signal-to-noise ratio (SNR) of these responses. Generally, positron em...
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The significance of task-induced cerebral blood flow responses, assessed using statistical parametric mapping, depends, among other things, on the signal-to-noise ratio (SNR) of these responses. Generally, positron emission tomography sinograms of (H2O)-O-15 activation studies are reconstructed using filtered backprojection (FBP). Alternatively, the acquired data can be reconstructed using an iterative reconstruction procedure. It has been demonstrated that the application of iterative reconstruction methods improves image SNR as compared with FBP. The aim of this study was to compare FBP with iterative reconstruction, to assess the statistical power of (H2O)-O-15-PET activation studies using statistical parametric mapping. For this case study, PET data originating from a bimanual motor task were reconstructed using both FBP and maximum likelihood expectationmaximization (ML-EM), an iterative algorithm. Both resulting data sets were statistically analyzed using statistical parametric mapping. It was found, with this dataset, that the statistical analysis of the iteratively reconstructed data confirm the a priori expected physiological response. In addition, increased Z scores were obtained in the iteratively reconstructed data. In particular, for the expected task-related response, activation of the posterior border of the left angular gyrus, the Z score increased from 3.00 to 3.96. Furthermore, the number of statistically significant clusters doubled while their volume increased by more than 50%. In conclusion, iterative reconstruction has the potential to increase the statistical power in (H2O)-O-15-PET activation studies as compared with FBP reconstruction. (C) 2002 Elsevier Science.
An algorithm for joint depth estimation and segmentation from multi-view images is presented. The distribution of the luminance of each image pixel is modeled as a random variable, which is approximated by a "mix...
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An algorithm for joint depth estimation and segmentation from multi-view images is presented. The distribution of the luminance of each image pixel is modeled as a random variable, which is approximated by a "mixture of Gaussians model". After recovering 3D motion, a reference image is segmented into a fixed number of regions, each characterized by a distinct affine depth model with three parameters. The estimated depth parameters and segmentation masks are iteratively estimated using an expectation-maximization algorithm, similar to that proposed in Sawhney et al. (1996). In addition, the proposed algorithm is extended for cases where more than two images are available.
We consider the problem of outliers in incomplete multivariate data when the aim is to estimate a measure of mean and covariance, as is the case, for example, in factor analysis. The ER algorithm of Little and Smith w...
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We consider the problem of outliers in incomplete multivariate data when the aim is to estimate a measure of mean and covariance, as is the case, for example, in factor analysis. The ER algorithm of Little and Smith which combines the EM algorithm for missing data and a robust estimation step based on an M-estimator could be used in such a situation. However, the ER algorithm as originally proposed can fail to be robust in some cases, especially in high dimensions. We propose here two alternatives to avoid the problem. One is to combine a small modification of the ER algorithm with a so-called high-breakdown estimator as the starting point for the iterative procedure, and the other is to base the estimation step of the ER algorithm on a high-breakdown estimator. Among the high-breakdown estimators which are actually built to keep their robustness properties even if the number of variables is relatively large, we consider here the minimum covariance determinant estimator and the t-biweight S-estimator. Simulated and real data are used to compare and illustrate the different procedures.
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