Variable Selection Bias in Classification Trees Based on Imprecise Probabilities

Classification trees based on imprecise probabilities provide an advancement of classical classification trees. The Gini Index is the default splitting criterion in classical classification trees, while in classification trees based on imprecise probabilities, an extension of the Shannon entropy has been introduced as the splitting criterion. However, the use of these empirical entropy measures as split selection criteria can lead to a bias in variable selection, such that variables are preferred for features other than their information content. This bias is not eliminated by the imprecise probability approach. The source of variable selection bias for the estimated Shannon entropy, as well as possible corrections, are outlined. The variable selection performance of the biased and corrected estimators are evaluated in a simulation study. Additional results from research on variable selection bias in classical classification trees are incorporated, implying further investigation of alternative split selection criteria in classification trees based on imprecise probabilities

Statistical Sources of Variable Selection Bias in Classification Tree Algorithms Based on the Gini Index

Evidence for variable selection bias in classification tree algorithms based on the Gini Index is reviewed from the literature and embedded into a broader explanatory scheme: Variable selection bias in classification tree algorithms based on the Gini Index can be caused not only by the statistical effect of multiple comparisons, but also by an increasing estimation bias and variance of the splitting criterion when plug-in estimates of entropy measures like the Gini Index are employed. The relevance of these sources of variable selection bias in the different simulation study designs is examined. Variable selection bias due to the explored sources applies to all classification tree algorithms based on empirical entropy measures like the Gini Index, Deviance and Information Gain, and to both binary and multiway splitting algorithms

Lie Algebroid Yang Mills with Matter Fields

Lie algebroid Yang-Mills theories are a generalization of Yang-Mills gauge theories, replacing the structural Lie algebra by a Lie algebroid E. In this note we relax the conditions on the fiber metric of E for gauge invariance of the action functional. Coupling to scalar fields requires possibly nonlinear representations of Lie algebroids. In all cases, gauge invariance is seen to lead to a condition of covariant constancy on the respective fiber metric in question with respect to an appropriate Lie algebroid connection. The presentation is kept in part explicit so as to be accessible also to a less mathematically oriented audience.Comment: 24 pages, accepted for publication in J. Geom. Phy

The Economic Growth Impact of Hurricanes: Evidence from US Coastal counties

We estimate for the first time the impact of hurricane strikes on local economic growth rates and how this is reflected in more aggregate growth patterns. To this end we assemble a panel data set of US coastal counties' growth rates and construct a novel hurricane destruction index that is based on a monetary loss equation, local wind speed estimates derived from a physical wind field model, and local exposure characteristics. Our econometric results suggest that in response to a hurricane strike a county's annual economic growth rate will initially fall by 0.8, but then partially recover by 0.2 percentage points. While the pattern is qualitatively similar at the state level, the net effect over the long term is negligible. Hurricane strikes do not appear to be economically important enough to be reflected in national economic growth rates.hurricanes, economic growth, US coastal counties

Dirac Sigma Models from Gauging

The G/G WZW model results from the WZW-model by a standard procedure of gauging. G/G WZW models are members of Dirac sigma models, which also contain twisted Poisson sigma models as other examples. We show how the general class of Dirac sigma models can be obtained from a gauging procedure adapted to Lie algebroids in the form of an equivariantly closed extension. The rigid gauge groups are generically infinite dimensional and a standard gauging procedure would give a likewise infinite number of 1-form gauge fields; the proposed construction yields the requested finite number of them. Although physics terminology is used, the presentation is kept accessible also for a mathematical audience.Comment: 20 pages, 3 figure