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 encompasses a comprehensive research effort dedicated to overcoming the critical bottlenecks that hinder the current generation of neural networks, thereby significantly advancing their reliability and performance. Deep neural networks, with their millions of parameters, suffer from over-parameterization and lack of constraints, leading to limited generalization capabilities. In other words, the complex architecture and millions of parameters present challenges in finding the right balance between capturing useful patterns and avoiding noise in the data. To address these issues, this thesis explores novel solutions based on knowledge distillation, enabling the learning of robust representations. Leveraging the capabilities of large-scale networks, effective learning strategies are developed. Moreover, the limitations of dependency on external networks in the distillation process, which often require large-scale models, are effectively overcome by proposing a self-distillation strategy. The proposed approach empowers the model to generate high-level knowledge within a single network, pushing the boundaries of knowledge distillation. The effectiveness of the proposed method is not only demonstrated across diverse applications, including image classification, object detection, and semantic segmentation but also explored in practical considerations such as handling data scarcity and assessing the transferability of the model to other learning tasks. Another major obstacle hindering the development of reliable and robust models lies in their black-box nature, impeding clear insights into the contributions toward the final predictions and yielding uninterpretable feature representations. To address this challenge, this thesis introduces techniques that incorporate simple yet powerful deep constraints rooted in Riemannian geometry. These constraints confer geometric qualities upon the latent representation, thereby fostering a more interpretable and insightful representation. In addition to its primary focus on general tasks like image classification and activity recognition, this strategy offers significant benefits in real-world applications where data scarcity is prevalent. Moreover, its robustness in feature removal showcases its potential for edge applications. By successfully tackling these challenges, this research contributes to advancing the field of machine learning and provides a foundation for building more reliable and robust systems across various application domains.
ContributorsChoi, Hongjun (Author) / Turaga, Pavan (Thesis advisor) / Jayasuriya, Suren (Committee member) / Li, Wenwen (Committee member) / Fazli, Pooyan (Committee member) / Arizona State University (Publisher)
Created2023
Description
Generative models are deep neural network-based models trained to learn the underlying distribution of a dataset. Once trained, these models can be used to sample novel data points from this distribution. Their impressive capabilities have been manifested in various generative tasks, encompassing areas like image-to-image translation, style transfer, image editing, and more. One notable application of generative models is data augmentation, aimed at expanding and diversifying the training dataset to augment the performance of deep learning models for a downstream task. Generative models can be used to create new samples similar to the original data but with different variations and properties that are difficult to capture with traditional data augmentation techniques. However, the quality, diversity, and controllability of the shape and structure of the generated samples from these models are often directly proportional to the size and diversity of the training dataset. A more extensive and diverse training dataset allows the generative model to capture overall structures present in the data and generate more diverse and realistic-looking samples.
In this dissertation, I present innovative methods designed to enhance the robustness and controllability of generative models, drawing upon physics-based, probabilistic, and geometric techniques. These methods help improve the generalization and controllability of the generative model without necessarily relying on large training datasets. I enhance the robustness of generative models by integrating classical geometric moments for shape awareness and minimizing trainable parameters. Additionally, I employ non-parametric priors for the generative model's latent space through basic probability and optimization methods to improve the fidelity of interpolated images. I adopt a hybrid approach to address domain-specific challenges with limited data and controllability, combining physics-based rendering with generative models for more realistic results.
These approaches are particularly relevant in industrial settings, where the training datasets are small and class imbalance is common. Through extensive experiments on various datasets, I demonstrate the effectiveness of the proposed methods over conventional approaches.
ContributorsSingh, Rajhans (Author) / Turaga, Pavan (Thesis advisor) / Jayasuriya, Suren (Committee member) / Berisha, Visar (Committee member) / Fazli, Pooyan (Committee member) / Arizona State University (Publisher)
Created2023