Theses and Dissertations
This collection includes both ASU Theses and Dissertations, submitted by graduate students, and the Barrett, Honors College theses submitted by undergraduate students.
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- Creators: Turaga, Pavan
Recursive Bayesian Estimation on Projective Spaces: Theoretical Foundations and Practical Algorithms
Description
This thesis develops geometrically and statistically rigorous foundations for multivariate analysis and bayesian inference posed on grassmannian manifolds. Requisite to the development of key elements of statistical theory in a geometric realm are closed-form, analytic expressions for many differential geometric objects, e.g., tangent vectors, metrics, geodesics, volume forms. The first part of this thesis is devoted to a mathematical exposition of these. In particular, it leverages the classical work of Alan James to derive the exterior calculus of differential forms on special grassmannians for invariant measures with respect to which integration is permissible. Motivated by various multi-sensor remote sensing applications, the second part of this thesis describes the problem of recursively estimating the state of a dynamical system propagating on the Grassmann manifold. Fundamental to the bayesian treatment of this problem is the choice of a suitable probability distribution to a priori model the state. Using the Method of Maximum Entropy, a derivation of maximum-entropy probability distributions on the state space that uses the developed geometric theory is characterized. Statistical analyses of these distributions, including parameter estimation, are also presented. These probability distributions and the statistical analysis thereof are original contributions. Using the bayesian framework, two recursive estimation algorithms, both of which rely on noisy measurements on (special cases of) the Grassmann manifold, are the devised and implemented numerically. The first is applied to an idealized scenario, the second to a more practically motivated scenario. The novelty of both of these algorithms lies in the use of thederived maximumentropy probability measures as models for the priors. Numerical simulations demonstrate that, under mild assumptions, both estimation algorithms produce accurate and statistically meaningful outputs. This thesis aims to chart the interface between differential geometry and statistical signal processing. It is my deepest hope that the geometric-statistical approach underlying this work facilitates and encourages the development of new theories and new computational methods in geometry. Application of these, in turn, will bring new insights and bettersolutions to a number of extant and emerging problems in signal processing.
ContributorsCrider, Lauren N (Author) / Cochran, Douglas (Thesis advisor) / Kotschwar, Brett (Committee member) / Scharf, Louis (Committee member) / Taylor, Thomas (Committee member) / Turaga, Pavan (Committee member) / Arizona State University (Publisher)
Created2021
Description
This thesis presents robust and novel solutions using knowledge distillation with geometric approaches and multimodal data that can address the current challenges in deep learning, providing a comprehensive understanding of the learning process involved in knowledge distillation. Deep learning has attained significant success in various applications, such as health and wellness promotion, smart homes, and intelligent surveillance. In general, stacking more layers or increasing the number of trainable parameters causes deep networks to exhibit improved performance. However, this causes the model to become large, resulting in an additional need for computing and power resources for training, storage, and deployment. These are the core challenges in incorporating such models into small devices with limited power and computational resources. In this thesis, robust solutions aimed at addressing the aforementioned challenges are presented. These proposed methodologies and algorithmic contributions enhance the performance and efficiency of deep learning models. The thesis encompasses a comprehensive exploration of knowledge distillation, an approach that holds promise for creating compact models from high-capacity ones, while preserving their performance. This exploration covers diverse datasets, including both time series and image data, shedding light on the pivotal role of augmentation methods in knowledge distillation. The effects of these methods are rigorously examined through empirical experiments. Furthermore, the study within this thesis delves into the efficient utilization of features derived from two different teacher models, each trained on dissimilar data representations, including time-series and image data. Through these investigations, I present novel approaches to knowledge distillation, leveraging geometric techniques for the analysis of multimodal data. These solutions not only address real-world challenges but also offer valuable insights and recommendations for modeling in new applications.
ContributorsJeon, Eunsom (Author) / Turaga, Pavan (Thesis advisor) / Li, Baoxin (Committee member) / Lee, Hyunglae (Committee member) / Jayasuriya, Suren (Committee member) / Arizona State University (Publisher)
Created2023