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Marginal pseudolikehood in labelled graphical models

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dc.date.accessioned 2015-05-28T06:14:48Z und
dc.date.accessioned 2017-10-24T12:21:45Z
dc.date.available 2015-05-28T06:14:48Z und
dc.date.available 2017-10-24T12:21:45Z
dc.date.issued 2015-05-28T06:14:48Z
dc.identifier.uri http://radr.hulib.helsinki.fi/handle/10138.1/4750 und
dc.identifier.uri http://hdl.handle.net/10138.1/4750
dc.title Marginal pseudolikehood in labelled graphical models en
ethesis.discipline Applied Mathematics en
ethesis.discipline Soveltava matematiikka fi
ethesis.discipline Tillämpad matematik sv
ethesis.discipline.URI http://data.hulib.helsinki.fi/id/2646f59d-c072-44e7-b1c1-4e4b8b798323
ethesis.department.URI http://data.hulib.helsinki.fi/id/61364eb4-647a-40e2-8539-11c5c0af8dc2
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 http://data.hulib.helsinki.fi/id/8d59209f-6614-4edd-9744-1ebdaf1d13ca
ethesis.university.URI http://data.hulib.helsinki.fi/id/50ae46d8-7ba9-4821-877c-c994c78b0d97
ethesis.university Helsingfors universitet sv
ethesis.university University of Helsinki en
ethesis.university Helsingin yliopisto fi
dct.creator Pusa, Taneli
dct.issued 2015
dct.language.ISO639-2 eng
dct.abstract The objective of this work is to generalize the pseudolikelihood-based inference method from ordinary Markov networks to an extension of the model containing context-specific independencies: the labelled graphical model. Probabilistic graphical models like the Markov and Bayes networks are used to represent the dependence structure of multivariate probability distributions. Machine learning methodology can then be used to learn these dependence structures from sample data. The Markov network is a model, which assigns no directionality to interactions between variables: the probability distribution is represented by an undirected graph, where nodes correspond to variables and edges to direct interactions. A labelled graphical model extends this idea by assigning labels to edges to represent contexts, i.e outcomes of other variables in the distribution, in which the associated variables are independent. Bayesian inference can be used to learn the dependence structure of a set of variables using data. The standard procedure is to consider the posterior probability of a model given the data and aim to maximize this score. This involves explicitly calculating the marginal likelihood of the model. In the case of Markov networks and consequently labelled models, this can not be done analytically and approximation methods must be used. Pseudolikelihood is one such method, which allows for both the analytical calculation of the so-called marginal pseudolikehood replacing the actual marginal likelihood of a model and the computationally very advantageous property of a node-wise factorizable score-function. This thesis presents the general theory behind the labelled graphical models and the basics of Bayesian inference. The pseudolikelihood approximation is introduced and applied to labelled models and the consistency of the score is proved. Lastly a greedy hill climb -algorithm is used to demonstrate the inference in practice by a synthetic and a real data example. en
dct.language en
ethesis.language.URI http://data.hulib.helsinki.fi/id/languages/eng
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
ethesis.thesistype.URI http://data.hulib.helsinki.fi/id/thesistypes/mastersthesis
dct.identifier.urn URN:NBN:fi-fe2017112252413
dc.type.dcmitype Text

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