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Pseudo-Likelihood Learning of Gaussian Graphical Models

Show simple item record 2014-10-28T07:57:13Z und 2017-10-24T12:21:35Z 2014-10-28T07:57:13Z und 2017-10-24T12:21:35Z 2014-10-28T07:57:13Z
dc.identifier.uri und
dc.title Pseudo-Likelihood Learning of Gaussian Graphical Models en
ethesis.discipline Applied Mathematics en
ethesis.discipline Soveltava matematiikka fi
ethesis.discipline Tillämpad matematik sv
ethesis.department Institutionen för matematik och statistik sv
ethesis.department Department of Mathematics and Statistics en
ethesis.department Matematiikan ja tilastotieteen laitos fi
ethesis.faculty Matematisk-naturvetenskapliga fakulteten sv
ethesis.faculty Matemaattis-luonnontieteellinen tiedekunta fi
ethesis.faculty Faculty of Science en
ethesis.faculty.URI Helsingfors universitet sv University of Helsinki en Helsingin yliopisto fi
dct.creator Leppä-aho, Janne Lauri Antero
dct.issued 2014
dct.language.ISO639-2 eng
dct.abstract Multivariate Gaussian distribution is an often encountered continuous distribution in applied mathematics and statistics due to its well known properties and wide applicability. In the graphical models framework, we make use of graphs to compactly represent the conditional independences between a set of random variables. Combining these two together leads to the class of Gaussian graphical models. This thesis discusses learning of Gaussian graphical models from multivariate data. Given the data, our goal is to identify the graphical structure that specifies the conditional independence statements between the variables under consideration. Following the footsteps of Pensar et al [10], we adopt a Bayesian, score-based approach for learning graphical models. Using pseudo-likelihood to approximate the true likelihood allows us to apply results of Consonni et al [4] to compute marginal likelihood integrals in closed form. This results in a method that can be used to make objective comparisons among Gaussian graphical models. We test the method numerically and show that it can be readily applied in high-dimensional settings. According to our tests, the method presented here outperforms the widely used graphical LASSO method in accuracy. The structure of this thesis is as follows. The chapters 2-4 discuss graphical models, multivariate Normal distribution and Bayesian model comparison in general. The fifth chapter goes through the results derived by Consonni, which are utilised in the next chapter to develop a scoring function and a learning algorithm for Gaussian graphical model selection. In the sixth chapter, we test the method in practice and present the obtained numerical results. The last appendix chapter is dedicated to the consistency proof, which gives the theoretical justification for the presented method. en
dct.language en
ethesis.language English en
ethesis.language englanti fi
ethesis.language engelska sv
ethesis.thesistype pro gradu-avhandlingar sv
ethesis.thesistype pro gradu -tutkielmat fi
ethesis.thesistype master's thesis en
dct.identifier.urn URN:NBN:fi-fe2017112251636
dc.type.dcmitype Text

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