Bayesian Inference in Estimation of Distribution Algorithms

Metaheuristics such as Estimation of Distribution Algorithms and the Cross-Entropy method use probabilistic modelling and inference to generate candidate solutions in optimization problems. The model fitting task in this class of algorithms has largely been carried out to date based on maximum likelihood. An alternative approach that is prevalent in statistics and machine learning is to use Bayesian inference. In this paper, we provide a framework for the application of Bayesian inference techniques in probabilistic model-based optimization. Based on this framework, a simple continuous Bayesian Estimation of Distribution Algorithm is described. We evaluate and compare this algorithm experimentally with its maximum likelihood equivalent, UMDAG c

Extended Object Tracking: Introduction, Overview and Applications

This article provides an elaborate overview of current research in extended object tracking. We provide a clear definition of the extended object tracking problem and discuss its delimitation to other types of object tracking. Next, different aspects of extended object modelling are extensively discussed. Subsequently, we give a tutorial introduction to two basic and well used extended object tracking approaches - the random matrix approach and the Kalman filter-based approach for star-convex shapes. The next part treats the tracking of multiple extended objects and elaborates how the large number of feasible association hypotheses can be tackled using both Random Finite Set (RFS) and Non-RFS multi-object trackers. The article concludes with a summary of current applications, where four example applications involving camera, X-band radar, light detection and ranging (lidar), red-green-blue-depth (RGB-D) sensors are highlighted.Comment: 30 pages, 19 figure

Soft clustering analysis of galaxy morphologies: A worked example with SDSS

Context: The huge and still rapidly growing amount of galaxies in modern sky surveys raises the need of an automated and objective classification method. Unsupervised learning algorithms are of particular interest, since they discover classes automatically. Aims: We briefly discuss the pitfalls of oversimplified classification methods and outline an alternative approach called "clustering analysis". Methods: We categorise different classification methods according to their capabilities. Based on this categorisation, we present a probabilistic classification algorithm that automatically detects the optimal classes preferred by the data. We explore the reliability of this algorithm in systematic tests. Using a small sample of bright galaxies from the SDSS, we demonstrate the performance of this algorithm in practice. We are able to disentangle the problems of classification and parametrisation of galaxy morphologies in this case. Results: We give physical arguments that a probabilistic classification scheme is necessary. The algorithm we present produces reasonable morphological classes and object-to-class assignments without any prior assumptions. Conclusions: There are sophisticated automated classification algorithms that meet all necessary requirements, but a lot of work is still needed on the interpretation of the results.Comment: 18 pages, 19 figures, 2 tables, submitted to A

The EM Algorithm and the Rise of Computational Biology

In the past decade computational biology has grown from a cottage industry with a handful of researchers to an attractive interdisciplinary field, catching the attention and imagination of many quantitatively-minded scientists. Of interest to us is the key role played by the EM algorithm during this transformation. We survey the use of the EM algorithm in a few important computational biology problems surrounding the "central dogma"; of molecular biology: from DNA to RNA and then to proteins. Topics of this article include sequence motif discovery, protein sequence alignment, population genetics, evolutionary models and mRNA expression microarray data analysis.Comment: Published in at http://dx.doi.org/10.1214/09-STS312 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org