6,721 research outputs found
Cross-validation in nonparametric regression with outliers
A popular data-driven method for choosing the bandwidth in standard kernel
regression is cross-validation. Even when there are outliers in the data,
robust kernel regression can be used to estimate the unknown regression curve
[Robust and Nonlinear Time Series Analysis. Lecture Notes in Statist. (1984) 26
163--184]. However, under these circumstances standard cross-validation is no
longer a satisfactory bandwidth selector because it is unduly influenced by
extreme prediction errors caused by the existence of these outliers. A more
robust method proposed here is a cross-validation method that discounts the
extreme prediction errors. In large samples the robust method chooses
consistent bandwidths, and the consistency of the method is practically
independent of the form in which extreme prediction errors are discounted.
Additionally, evaluation of the method's finite sample behavior in a simulation
demonstrates that the proposed method performs favorably. This method can also
be applied to other problems, for example, model selection, that require
cross-validation.Comment: Published at http://dx.doi.org/10.1214/009053605000000499 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Expressive Completeness of Existential Rule Languages for Ontology-based Query Answering
Existential rules, also known as data dependencies in Databases, have been
recently rediscovered as a promising family of languages for Ontology-based
Query Answering. In this paper, we prove that disjunctive embedded dependencies
exactly capture the class of recursively enumerable ontologies in
Ontology-based Conjunctive Query Answering (OCQA). Our expressive completeness
result does not rely on any built-in linear order on the database. To establish
the expressive completeness, we introduce a novel semantic definition for OCQA
ontologies. We also show that neither the class of disjunctive tuple-generating
dependencies nor the class of embedded dependencies is expressively complete
for recursively enumerable OCQA ontologies.Comment: 10 pages; the full version of a paper to appear in IJCAI 2016.
Changes (regarding to v1): a new reference has been added, and some typos
have been correcte
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