Function approximation is an important problem. This work presents applications of interpolants to modeling random variables. Specifically, this work studies the prediction of distributions of random variables applied to computer system throughput variability. Existing approximation methods including multivariate adaptive regression splines, support vector regressors, multilayer perceptrons, Shepard variants, and the Delaunay mesh are investigated in the context of computer variability modeling. New methods of approximation using Box splines, Voronoi cells, and Delaunay for interpolating distributions of data with moderately high dimension are presented and compared with existing approaches. Novel theoretical error bounds are constructed for piecewise linear interpolants over functions with a Lipschitz continuous gradient. Finally, a mathematical software that constructs monotone quintic spline interpolants for distribution approximation from data samples is proposed. / Doctor of Philosophy / It is common for scientists to collect data on something they are studying. Often scientists want to create a (predictive) model of that phenomenon based on the data, but the choice of how to model the data is a difficult one to answer. This work proposes methods for modeling data that operate under very few assumptions that are broadly applicable across science. Finally, a software package is proposed that would allow scientists to better understand the true distribution of their data given relatively few observations.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/100059 |
| Date | 23 September 2020 |
| Creators | Lux, Thomas Christian Hansen |
| Contributors | Computer Science, Watson, Layne T., Hong, Yili, Wang, Gang Alan, Cameron, Kirk W., Huang, Bert, Cao, Young |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Dissertation |
| Format | ETD, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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