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Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
Data Analysis Methods Using Persistence Diagrams, Andrew Marchese
Data Analysis Methods Using Persistence Diagrams, Andrew Marchese
Doctoral Dissertations
In recent years, persistent homology techniques have been used to study data and dynamical systems. Using these techniques, information about the shape and geometry of the data and systems leads to important information regarding the periodicity, bistability, and chaos of the underlying systems. In this thesis, we study all aspects of the application of persistent homology to data analysis. In particular, we introduce a new distance on the space of persistence diagrams, and show that it is useful in detecting changes in geometry and topology, which is essential for the supervised learning problem. Moreover, we introduce a clustering framework directly …
Information Metrics For Predictive Modeling And Machine Learning, Kostantinos Gourgoulias
Information Metrics For Predictive Modeling And Machine Learning, Kostantinos Gourgoulias
Doctoral Dissertations
The ever-increasing complexity of the models used in predictive modeling and data science and their use for prediction and inference has made the development of tools for uncertainty quantification and model selection especially important. In this work, we seek to understand the various trade-offs associated with the simulation of stochastic systems. Some trade-offs are computational, e.g., execution time of an algorithm versus accuracy of simulation. Others are analytical: whether or not we are able to find tractable substitutes for quantities of interest, e.g., distributions, ergodic averages, etc. The first two chapters of this thesis deal with the study of the …
Statistical Methods For High Dimensional Data Arising From Large Epidemiological Studies, Hui Xu
Statistical Methods For High Dimensional Data Arising From Large Epidemiological Studies, Hui Xu
Doctoral Dissertations
In this thesis, we propose statistical models for addressing commonly encountered data types and study designs in large epidemiologic investigations aimed at understanding the molecular basis of complex disorders. The motivating applications come from diverse disease areas in Women's Health, including the study of type II diabetes in the Women's Health Initiative (WHI), invasive breast cancer in the Nurses' Health Study and the study of the metabolomic underpinnings of cardiovascular disease in the WHI. We have also put significant effort into making the implementation of the proposed methods accessible through freely available, user-friendly software packages in R. The first chapter …
Inference In Networking Systems With Designed Measurements, Chang Liu
Inference In Networking Systems With Designed Measurements, Chang Liu
Doctoral Dissertations
Networking systems consist of network infrastructures and the end-hosts have been essential in supporting our daily communication, delivering huge amount of content and large number of services, and providing large scale distributed computing. To monitor and optimize the performance of such networking systems, or to provide flexible functionalities for the applications running on top of them, it is important to know the internal metrics of the networking systems such as link loss rates or path delays. The internal metrics are often not directly available due to the scale and complexity of the networking systems. This motivates the techniques of inference …
Inference From Network Data In Hard-To-Reach Populations, Isabelle Beaudry
Inference From Network Data In Hard-To-Reach Populations, Isabelle Beaudry
Doctoral Dissertations
The objective of this thesis is to develop methods to make inference about the prevalence of an outcome of interest in hard-to-reach populations. The proposed methods address issues specific to the survey strategies employed to access those populations. One of the common sampling methodology used in this context is respondent-driven sampling (RDS). Under RDS, the network connecting members of the target population is used to uncover the hidden members. Specialized techniques are then used to make inference from the data collected in this fashion. Our first objective is to correct traditional RDS prevalence estimators and their associated uncertainty estimators for …