14,855 research outputs found
Bishop-Phelps-Bolloba's theorem on bounded closed convex sets
This paper deals with the \emph{Bishop-Phelps-Bollob\'as property}
(\emph{BPBp} for short) on bounded closed convex subsets of a Banach space ,
not just on its closed unit ball . We firstly prove that the \emph{BPBp}
holds for bounded linear functionals on arbitrary bounded closed convex subsets
of a real Banach space. We show that for all finite dimensional Banach spaces
and the pair has the \emph{BPBp} on every bounded closed convex
subset of , and also that for a Banach space with property
the pair has the \emph{BPBp} on every bounded closed absolutely convex
subset of an arbitrary Banach space . For a bounded closed absorbing
convex subset of with positive modulus convexity we get that the pair
has the \emph{BPBp} on for every Banach space . We further
obtain that for an Asplund space and for a locally compact Hausdorff ,
the pair has the \emph{BPBp} on every bounded closed absolutely
convex subset of . Finally we study the stability of the \emph{BPBp} on
a bounded closed convex set for the -sum or -sum of a
family of Banach spaces
"Suicide and Life Insurance"
In this paper, we investigate the nexus between life insurance and suicide behavior using OECD cross-country data from 1980 to 2002. Through semiparametric instrumental variable regressions with fixed effects, we find that for the majority of observations, there exists a positive relationship between suicide rate and life insurance density (premium per capita). Since life insurance policies pay death benefits even in suicide cases after the suicide exemption period, the presence of adverse selection and moral hazard suggests an incentive effect that leads to this positive relationship. The novelty of our analysis lies in the use of cross-country variations in the length of the suicide exemption period in life insurance policies as the identifying instrument for life insurance density. Our results provide compelling evidence suggesting the existence of adverse selection and moral hazards in life insurance markets in OECD countries.
Knowledge Distillation with Adversarial Samples Supporting Decision Boundary
Many recent works on knowledge distillation have provided ways to transfer
the knowledge of a trained network for improving the learning process of a new
one, but finding a good technique for knowledge distillation is still an open
problem. In this paper, we provide a new perspective based on a decision
boundary, which is one of the most important component of a classifier. The
generalization performance of a classifier is closely related to the adequacy
of its decision boundary, so a good classifier bears a good decision boundary.
Therefore, transferring information closely related to the decision boundary
can be a good attempt for knowledge distillation. To realize this goal, we
utilize an adversarial attack to discover samples supporting a decision
boundary. Based on this idea, to transfer more accurate information about the
decision boundary, the proposed algorithm trains a student classifier based on
the adversarial samples supporting the decision boundary. Experiments show that
the proposed method indeed improves knowledge distillation and achieves the
state-of-the-arts performance.Comment: Accepted to AAAI 201
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