On Optimization and Regularization for Grouped Dirichlet-multinomial Regression

dc.contributor.advisorAli, R. Ayesha
dc.contributor.authorCrea, Catherine
dc.date.accessioned2018-05-07T12:57:24Z
dc.date.available2018-05-07T12:57:24Z
dc.date.copyright2018-05
dc.date.created2018-02-27
dc.date.issued2018-05-07
dc.degree.departmentDepartment of Mathematics and Statisticsen_US
dc.degree.grantorUniversity of Guelphen_US
dc.degree.nameDoctor of Philosophyen_US
dc.degree.programmeMathematics and Statisticsen_US
dc.description.abstractThis thesis focuses on developing the grouped Dirichlet-multinomial (DM) regression model for ecological applications with particular attention to optimization (for parameter estimation) and regularization (for variable selection). We adapt the grouped DM regression model for discrete choice behaviour to the analysis of mutualistic interactions between plant and pollinator species within a given ecosystem. The DM model provides a flexible approach to modelling over-dispersed grouped data and is fully parametric, but has not been well studied. The first part of this thesis focuses on establishing the DM model as a viable approach for analyzing pollination networks that can provide insights into the mechanisms driving ecological processes. Next, we study the behaviour of various parameterizations of the DM likelihood and identify non-convex regions that are either flat or non-smooth. Correspondingly, we evaluate the performance of three optimization methods (derivative and derivative-free) and assess their robustness to misspecification of dispersion structure. The last part of this thesis implements regularized regression for most parameterizations of the grouped Dirichlet-multinomial model using standard and adaptive lasso methods. Tuning parameters are selected using an information criterion while optimization is achieved via the fast iterative shrinkage-thresholding algorithm. All the proposed methods are evaluated via simulated and empirical data sets and all implementations of the standard and regularized grouped DM regression model are publicly available as routines in R.en_US
dc.description.sponsorshipNatural Sciences and Engineering Research Council of Canada - Discovery Grant
dc.description.sponsorshipNatural Sciences and Engineering Research Council of Canada - Strategic Network Grant
dc.identifier.urihttp://hdl.handle.net/10214/12975
dc.language.isoenen_US
dc.publisherUniversity of Guelphen_US
dc.rightsAttribution 2.5 Canada*
dc.rights.urihttp://creativecommons.org/licenses/by/2.5/ca/*
dc.subjectoverdispersionen_US
dc.subjectquasi-Newton methodsen_US
dc.subjectDirichlet-multinomial regressionen_US
dc.subjectadaptive lassoen_US
dc.subjectvariable selectionen_US
dc.subjectinformation criteriaen_US
dc.subjectproximal gradient methodsen_US
dc.subjectplant-pollinator networksen_US
dc.subjectlinkage rulesen_US
dc.subjectnetwork structureen_US
dc.subjectlog-likelihood sliceen_US
dc.titleOn Optimization and Regularization for Grouped Dirichlet-multinomial Regressionen_US
dc.typeThesisen_US

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