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On Optimization and Regularization for Grouped Dirichlet-multinomial Regression

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dc.contributor.advisor Ali, R. Ayesha
dc.contributor.author Crea, Catherine
dc.date.accessioned 2018-05-07T12:57:24Z
dc.date.available 2018-05-07T12:57:24Z
dc.date.copyright 2018-05
dc.date.created 2018-02-27
dc.date.issued 2018-05-07
dc.identifier.uri http://hdl.handle.net/10214/12975
dc.description.abstract This 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.sponsorship NSERC Discovery Grant and NSERC Strategic Network Grant en_US
dc.language.iso en en_US
dc.rights Attribution 2.5 Canada *
dc.rights.uri http://creativecommons.org/licenses/by/2.5/ca/ *
dc.subject overdispersion en_US
dc.subject quasi-Newton methods en_US
dc.subject Dirichlet-multinomial regression en_US
dc.subject adaptive lasso en_US
dc.subject variable selection en_US
dc.subject information criteria en_US
dc.subject proximal gradient methods en_US
dc.subject plant-pollinator networks en_US
dc.subject linkage rules en_US
dc.subject network structure en_US
dc.subject log-likelihood slice en_US
dc.title On Optimization and Regularization for Grouped Dirichlet-multinomial Regression en_US
dc.type Thesis en_US
dc.degree.programme Mathematics and Statistics en_US
dc.degree.name Doctor of Philosophy en_US
dc.degree.department Department of Mathematics and Statistics en_US
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Attribution 2.5 Canada Except where otherwise noted, this item's license is described as Attribution 2.5 Canada