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Exploration Using Without-Replacement Sampling Of Actions Is Sometimes Inferior, Stephen W. Carden, S. Dalton Walker
Exploration Using Without-Replacement Sampling Of Actions Is Sometimes Inferior, Stephen W. Carden, S. Dalton Walker
Department of Mathematical Sciences Faculty Publications
In many statistical and machine learning applications, without-replacement sampling is considered superior to with-replacement sampling. In some cases, this has been proven, and in others the heuristic is so intuitively attractive that it is taken for granted. In reinforcement learning, many count-based exploration strategies are justified by reliance on the aforementioned heuristic. This paper will detail the non-intuitive discovery that when measuring the goodness of an exploration strategy by the stochastic shortest path to a goal state, there is a class of processes for which an action selection strategy based on without-replacement sampling of actions can be worse than with-replacement …
Conceptualizing And Interpreting Mean And Median With Future Teachers, Eryn Stehr Maher, Ha Nguyen, Gregory Chamblee, Sharon Taylor
Conceptualizing And Interpreting Mean And Median With Future Teachers, Eryn Stehr Maher, Ha Nguyen, Gregory Chamblee, Sharon Taylor
Department of Mathematical Sciences Faculty Publications
Mathematical Education of Teachers II (METII), echoed by the American Statistical Association publication, Statistical Education of Teachers, recommended teacher preparation programs support future teachers in developing deep understandings of mean and median, such that middle grades teachers may use them to “summarize, describe, and compare distributions” (Conference Board of Mathematical Sciences, 2012, p. 44; Franklin et al., 2015). Georgia Standards of Excellence require statistical reasoning from students beginning as early as 6-7 years old, including interpretation of measures of center and statistical reasoning about best measures of center (Georgia Department of Education, 2015). This level of understanding and interpretation of …