Mathematics
Permanent URI for this communityhttp://hdl.handle.net/1903/2261
Browse
4 results
Search Results
Item Analysis of Data Security Vulnerabilities in Deep Learning(2022) Fowl, Liam; Czaja, Wojciech; Goldstein, Thomas; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)As deep learning systems become more integrated into important application areas, the security of such systems becomes a paramount concern. Specifically, as modern networks require an increasing amount of data on which to train, the security of data that is collected for these models cannot be guaranteed. In this work, we investigate several security vulnerabilities and security applications of the data pipeline for deep learning systems. We systematically evaluate the risks and mechanisms of data security from multiple perspectives, ranging from users to large companies and third parties, and reveal several security mechanisms and vulnerabilities that are of interest to machine learning practitioners.Item Application of Mathematical and Computational Models to Mitigate the Overutilization of Healthcare Systems(2017) Hu, Xia; Golden, Bruce; Barnes, Sean; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The overutilization of the healthcare system has been a significant issue financially and politically, placing burdens on the government, patients, providers and individual payers. In this dissertation, we study how mathematical models and computational models can be utilized to support healthcare decision-making and generate effective interventions for healthcare overcrowding. We focus on applying operations research and data mining methods to mitigate the overutilization of emergency department and inpatient services in four scenarios. Firstly, we systematically review research articles that apply analytical queueing models to the study of the emergency department, with an additional focus on comparing simulation models with queueing models when applied to similar research questions. Secondly, we present an agent-based simulation model of epidemic and bioterrorism transmission, and develop a prediction scheme to differentiate the simulated transmission patterns during the initial stage of the event. Thirdly, we develop a machine learning framework for effectively selecting enrollees for case management based on Medicaid claims data, and demonstrate the importance of enrolling current infrequent users whose utilization of emergency visits might increase significantly in the future. Lastly, we study the role of temporal features in predicting future health outcomes for diabetes patients, and identify the levels to which the aggregation can be most informative.Item Spectral Frame Analysis and Learning through Graph Structure(2016) Clark, Chae Almon; Okoudjou, Kasso A; Czaja, Wojciech K; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This dissertation investigates the connection between spectral analysis and frame theory. When considering the spectral properties of a frame, we present a few novel results relating to the spectral decomposition. We first show that scalable frames have the property that the inner product of the scaling coefficients and the eigenvectors must equal the inverse eigenvalues. From this, we prove a similar result when an approximate scaling is obtained. We then focus on the optimization problems inherent to the scalable frames by first showing that there is an equivalence between scaling a frame and optimization problems with a non-restrictive objective function. Various objective functions are considered, and an analysis of the solution type is presented. For linear objectives, we can encourage sparse scalings, and with barrier objective functions, we force dense solutions. We further consider frames in high dimensions, and derive various solution techniques. From here, we restrict ourselves to various frame classes, to add more specificity to the results. Using frames generated from distributions allows for the placement of probabilistic bounds on scalability. For discrete distributions (Bernoulli and Rademacher), we bound the probability of encountering an ONB, and for continuous symmetric distributions (Uniform and Gaussian), we show that symmetry is retained in the transformed domain. We also prove several hyperplane-separation results. With the theory developed, we discuss graph applications of the scalability framework. We make a connection with graph conditioning, and show the in-feasibility of the problem in the general case. After a modification, we show that any complete graph can be conditioned. We then present a modification of standard PCA (robust PCA) developed by Cand\`es, and give some background into Electron Energy-Loss Spectroscopy (EELS). We design a novel scheme for the processing of EELS through robust PCA and least-squares regression, and test this scheme on biological samples. Finally, we take the idea of robust PCA and apply the technique of kernel PCA to perform robust manifold learning. We derive the problem and present an algorithm for its solution. There is also discussion of the differences with RPCA that make theoretical guarantees difficult.Item Using Domain-Specific Information in Image Processing(2014) Cash, Brianna Rose; O'Leary, Dianne P; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)With the increasing availability of high resolution imaging tools, even in our pockets (i.e. smartphones), everyday users can do far more than simply digitally capturing a family moment. The ease of new applications available in these portable forms, linked with users who have expert knowledge about the images and tasks, opens the door to new possibilities. With this in mind we propose two new approaches that utilize the user's knowledge for improved results. We apply these approaches to real life problems in medical and scientific image applications. In the first approach, we introduce a class of linear and nonlinear methods which we call Domain-Specific Grayscale (DSGS) methods. A DSGS method transforms a color image into an image analogous to a grayscale image, where user-specified information is used to optimize a specified image processing task and reduce the computational complexity. We introduce new methods based on projection into the space of single-coordinate images, and we adapt support vector machines by using their scores to create a DSGS image. We apply these methods to applications in dermatology, analyzing images of skin tests and skin lesions, and demonstrate their usefulness. In the second approach, we introduce a tool for improved image deblurring that safeguards against bias that can easily be introduced by a user favoring a particular result. This is particularly important in scientific and medical applications used for discovery or diagnosis. We provide real-time results of choices of regularization methods and parameter selection, and we check the statistical plausibility of the results, using three statistical diagnostics, allowing a user to see the results of the choices. Our work demonstrates the utility of domain-specific information, supplied by the user, in improving the results of image processing algorithms.