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Full-Text Articles in Probability
Nonparametric Bayesian Deep Learning For Scientific Data Analysis, Devanshu Agrawal
Nonparametric Bayesian Deep Learning For Scientific Data Analysis, Devanshu Agrawal
Doctoral Dissertations
Deep learning (DL) has emerged as the leading paradigm for predictive modeling in a variety of domains, especially those involving large volumes of high-dimensional spatio-temporal data such as images and text. With the rise of big data in scientific and engineering problems, there is now considerable interest in the research and development of DL for scientific applications. The scientific domain, however, poses unique challenges for DL, including special emphasis on interpretability and robustness. In particular, a priority of the Department of Energy (DOE) is the research and development of probabilistic ML methods that are robust to overfitting and offer reliable …
Foundations Of Inference, Kevin H. Knuth, John Skilling
Foundations Of Inference, Kevin H. Knuth, John Skilling
Physics Faculty Scholarship
We present a simple and clear foundation for finite inference that unites and significantly extends the approaches of Kolmogorov and Cox. Our approach is based on quantifying lattices of logical statements in a way that satisfies general lattice symmetries. With other applications such as measure theory in mind, our derivations assume minimal symmetries, relying on neither negation nor continuity nor differentiability. Each relevant symmetry corresponds to an axiom of quantification, and these axioms are used to derive a unique set of quantifying rules that form the familiar probability calculus. We also derive a unique quantification of divergence, entropy and information.