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dc.contributor.authorGoeva, Aleksandrinaen_US
dc.date.accessioned2018-02-16T18:19:16Z
dc.date.available2018-02-16T18:19:16Z
dc.date.issued2017
dc.identifier.urihttps://hdl.handle.net/2144/27072
dc.description.abstractA fundamental goal of statisticians is to make inferences from the sample about characteristics of the underlying population. This is an inverse problem, since we are trying to recover a feature of the input with the availability of observations on an output. Towards this end, we consider complexity penalized methods, because they balance goodness of fit and generalizability of the solution. The data from the underlying population may come in diverse formats - structured or unstructured - such as probability distributions, text tokens, or graph characteristics. Depending on the defining features of the problem we can chose the appropriate complexity penalized approach, and assess the quality of the estimate produced by it. Favorable characteristics are strong theoretical guarantees of closeness to the true value and interpretability. Our work fits within this framework and spans the areas of simulation optimization, text mining and network inference. The first problem we consider is model calibration under the assumption that given a hypothesized input model, we can use stochastic simulation to obtain its corresponding output observations. We formulate it as a stochastic program by maximizing the entropy of the input distribution subject to moment matching. We then propose an iterative scheme via simulation to approximately solve it. We prove convergence of the proposed algorithm under appropriate conditions and demonstrate the performance via numerical studies. The second problem we consider is summarizing text documents through an inferred set of topics. We propose a frequentist reformulation of a Bayesian regularization scheme. Through our complexity-penalized perspective we lend further insight into the nature of the loss function and the regularization achieved through the priors in the Bayesian formulation. The third problem is concerned with the impact of sampling on the degree distribution of a network. Under many sampling designs, we have a linear inverse problem characterized by an ill-conditioned matrix. We investigate the theoretical properties of an approximate solution for the degree distribution found by regularizing the solution of the ill-conditioned least squares objective. Particularly, we study the rate at which the penalized solution tends to the true value as a function of network size and sampling rate.en_US
dc.language.isoen_US
dc.rightsAttribution 4.0 Internationalen_US
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subjectStatisticsen_US
dc.subjectComplexity penalizeden_US
dc.subjectEntropyen_US
dc.subjectInverse problemen_US
dc.subjectNetwork inferenceen_US
dc.subjectStochastic simulationen_US
dc.subjectText miningen_US
dc.titleComplexity penalized methods for structured and unstructured dataen_US
dc.typeThesis/Dissertationen_US
dc.date.updated2017-11-08T20:16:46Z
etd.degree.nameDoctor of Philosophyen_US
etd.degree.leveldoctoralen_US
etd.degree.disciplineMathematics & Statisticsen_US
etd.degree.grantorBoston Universityen_US


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Attribution 4.0 International
Except where otherwise noted, this item's license is described as Attribution 4.0 International