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Full-Text Articles in Physical Sciences and Mathematics
Convergence Rates For Empirical Estimation Of Binary Classification Bounds, Salimeh Yasaei Sekeh, Morteza Noshad, Kevin R. Moon, Alfred O. Hero
Convergence Rates For Empirical Estimation Of Binary Classification Bounds, Salimeh Yasaei Sekeh, Morteza Noshad, Kevin R. Moon, Alfred O. Hero
Mathematics and Statistics Faculty Publications
Bounding the best achievable error probability for binary classification problems is relevant to many applications including machine learning, signal processing, and information theory. Many bounds on the Bayes binary classification error rate depend on information divergences between the pair of class distributions. Recently, the Henze–Penrose (HP) divergence has been proposed for bounding classification error probability. We consider the problem of empirically estimating the HP-divergence from random samples. We derive a bound on the convergence rate for the Friedman–Rafsky (FR) estimator of the HP-divergence, which is related to a multivariate runs statistic for testing between two distributions. The FR estimator is …
Classification Of Isometry Algebras Of Solutions Of Einstein's Field Equations, Eugene Hwang
Classification Of Isometry Algebras Of Solutions Of Einstein's Field Equations, Eugene Hwang
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
Since Schwarzschild found the first solution of the Einstein’s equations, more than 800 solutions were found. Solutions of Einstein’s equations are classified according to their Lie algebras of isometries and their isotropy subalgebras. Solutions were taken from the USU electronic library of solutions of Einstein’s field equations and the classification used Maple code developed at USU. This classification adds to the data contained in the library of solutions and provides additional tools for addressing the equivalence problem for solutions to the Einstein field equations. In this thesis, homogeneous spacetimes, hypersurface-homogeneous spacetimes, Robinson-Trautman solutions, and some famous black hole solutions have …