In the first project, we propose to generalize the notion of depth in temporal point process observations. The new depth is defined as a weighted product of two probability terms: 1) the number of events in each process, and 2) the center-outward ranking on the event times conditioned on the number of events. In this study, we adopt the Poisson distribution for the first term and the Mahalanobis depth for the second term. We propose an efficient bootstrapping approach to estimate parameters in the defined depth. In the case of Poisson process, the observed events are order statistics where the parameters can be estimated robustly with respect to sample size. We demonstrate the use of the new depth by ranking realizations from a Poisson process. We also test the new method in classification problems using simulations as well as real neural spike train data. It is found that the new framework provides more accurate and robust classifications as compared to commonly used likelihood methods. In the second project, we demonstrate the value of semi-supervised dimension reduction in clinical area. The advantage of semi-supervised dimension reduction is very easy to understand. Semi-Supervised dimension reduction method adopts the unlabeled data information to perform dimension reduction and it can be applied to help build a more precise prediction model comparing with common supervised dimension reduction techniques. After thoroughly comparing with dimension embedding methods with label data only, we show the improvement of semi-supervised dimension reduction with unlabeled data in breast cancer chemotherapy clinical area. In our semi-supervised dimension reduction method, we not only explore adding unlabeled data to linear dimension reduction such as PCA, we also explore semi-supervised non-linear dimension reduction, such as semi-supervised LLE and semi-supervised Isomap. / A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Spring Semester 2018. / March 21, 2018. / depth, point process, semi-supervised learning / Includes bibliographical references. / Wei Wu, Professor Directing Dissertation; Xiaoqiang Wang, University Representative; Jinfeng Zhang, Committee Member; Qing Mai, Committee Member.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_653460 |
| Contributors | Liu, Shuyi (author), Wu, Wei (professor directing dissertation), Wang, Xiaoqiang (university representative), Zhang, Jinfeng (committee member), Mai, Qing (committee member), Florida State University (degree granting institution), College of Arts and Sciences (degree granting college), Department of Statistics (degree granting departmentdgg) |
| Publisher | Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text, doctoral thesis |
| Format | 1 online resource (97 pages), computer, application/pdf |
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