Recent theoretical results on adversarial multi-class classification showed a similarity to the multi-marginal formulation of Wasserstein-barycenter in optimal transport. Unfortunately, both problems suffer from the curse of dimension, making it hard to exploit the nice linear program structure of the problems for numerical calculations. We investigate how ideas from Genetic Column Generation for multi-marginal optimal transport can be used to overcome the curse of dimension in computing the minimal adversarial risk in multi-class classification.
This introduction addresses some key issues and questions in the study of negation and polarity. Focussing on negative polarity and negative indefinites, it summarizes research trends and results. Special attention is paid to the issues of synchronic variation and diachronic change in the realm of negative polarity items, which figure prominently in the articles and commentaries contained in this special issue.
Negative indefinites, i.e. expressions like English nobody and no boy, give rise to split scope readings where another operator takes scope in between the negative and the indefinite meaning component. Split readings are puzzling under the standard analysis of negative indefinites as negative quantifiers. This article surveys recent approaches to split scope.
The assumption that negative indefinites are semantically non-negative elements associating with sentential negation has proven fruitful to account for the behaviour of negative indefinites in languages exhibiting negative concord. Under this view, negative indefinites carry a negative feature that has to be licensed by a semantic negation. This paper critically discusses and evaluates different ways in which the notion of negative features can be spelled out. Particular attention is paid to approaches that build on the indefinite nature of negative indefinites and postulate that negative indefinites have to be bound by a negation operator (e.g. Ladusaw, 1992;Kratzer, 2005). It is shown that such analyses are problematic in light of the fact that another semantic operator can take scope in between the negation and the negative indefinite. Parallel data have been discussed for negative indefinites in German and Dutch under the label split scope (e.g. Jacobs, 1980;de Swart, 2000;Abels and Mart铆, 2010).
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