Matching Items (53)
Description
In this work, the author analyzes quantitative and structural aspects of Bayesian inference using Markov kernels, Wasserstein metrics, and Kantorovich monads. In particular, the author shows the following main results: first, that Markov kernels can be viewed as Borel measurable maps with values in a Wasserstein space; second, that the Disintegration Theorem can be interpreted as a literal equality of integrals using an original theory of integration for Markov kernels; third, that the Kantorovich monad can be defined for Wasserstein metrics of any order; and finally, that, under certain assumptions, a generalized Bayes’s Law for Markov kernels provably leads to convergence of the expected posterior distribution in the Wasserstein metric. These contributions provide a basis for studying further convergence, approximation, and stability properties of Bayesian inverse maps and inference processes using a unified theoretical framework that bridges between statistical inference, machine learning, and probabilistic programming semantics.
ContributorsEikenberry, Keenan (Author) / Cochran, Douglas (Thesis advisor) / Lan, Shiwei (Thesis advisor) / Dasarathy, Gautam (Committee member) / Kotschwar, Brett (Committee member) / Shahbaba, Babak (Committee member) / Arizona State University (Publisher)
Created2023
Description
Deforestation in the Amazon rainforest has the potential to have devastating effects
on ecosystems on both a local and global scale, making it one of the most environmentally
threatening phenomena occurring today. In order to minimize deforestation in the Ama-
zon and its consequences, it is helpful to analyze its occurrence using machine learning
architectures such as the U-Net. The U-Net is a type of Fully Convolutional Network that
has shown significant capability in performing semantic segmentation. It is built upon
a symmetric series of downsampling and upsampling layers that propagate feature infor-
mation into higher spatial resolutions, allowing for the precise identification of features
on the pixel scale. Such an architecture is well-suited for identifying features in satellite
imagery. In this thesis, we construct and train a U-Net to identify deforested areas in
satellite imagery of the Amazon through semantic segmentation.
ContributorsDouglas, Liam (Author) / Giel, Joshua (Co-author) / Espanol, Malena (Thesis director) / Cochran, Douglas (Committee member) / Barrett, The Honors College (Contributor) / Computer Science and Engineering Program (Contributor)
Created2024-05
Description
Deforestation in the Amazon rainforest has the potential to have devastating effects on ecosystems on both a local and global scale, making it one of the most environmentally threatening phenomena occurring today. In order to minimize deforestation in the Amazon and its consequences, it is helpful to analyze its occurrence using machine learning architectures such as the U-Net. The U-Net is a type of Fully Convolutional Network that has shown significant capability in performing semantic segmentation. It is built upon a symmetric series of downsampling and upsampling layers that propagate feature information into higher spatial resolutions, allowing for the precise identification of features on the pixel scale. Such an architecture is well-suited for identifying features in satellite imagery. In this thesis, we construct and train a U-Net to identify deforested areas in satellite imagery of the Amazon through semantic segmentation.
ContributorsGiel, Joshua (Author) / Douglas, Liam (Co-author) / Espanol, Malena (Thesis director) / Cochran, Douglas (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of Sustainability (Contributor)
Created2024-05