9,980 research outputs found
Logarithmic Jet Bundles and Applications
We generalize Demailly's construction of projective jet bundles and strictly
negatively curved pseudometrics on them to the logarithmic case. We establish
this logarithmic generalization explicitly via coordinates, just as Noguchi's
generalization of the jets used by Green-Griffiths. As a first application, we
give a metric proof for the logarithmic version of Lang's conjecture concerning
the hyperbolicity of complements of divisors in a semi-abelian variety as well
as for the corresponding big Picard theorem.Comment: 49 pages, Late
Optimal Inference in Crowdsourced Classification via Belief Propagation
Crowdsourcing systems are popular for solving large-scale labelling tasks
with low-paid workers. We study the problem of recovering the true labels from
the possibly erroneous crowdsourced labels under the popular Dawid-Skene model.
To address this inference problem, several algorithms have recently been
proposed, but the best known guarantee is still significantly larger than the
fundamental limit. We close this gap by introducing a tighter lower bound on
the fundamental limit and proving that Belief Propagation (BP) exactly matches
this lower bound. The guaranteed optimality of BP is the strongest in the sense
that it is information-theoretically impossible for any other algorithm to
correctly label a larger fraction of the tasks. Experimental results suggest
that BP is close to optimal for all regimes considered and improves upon
competing state-of-the-art algorithms.Comment: This article is partially based on preliminary results published in
the proceeding of the 33rd International Conference on Machine Learning (ICML
2016
The Super Size of America: An Economic Estimation of Body Mass Index and Obesity in Adults
The increased prevalence of obesity in the US stresses the need for answers as to why this rapid rise has occurred. This paper employs micro-level data from the First, Second, and Third National Health and Nutrition xamination Surveys to determine the effects that state-level policies have on BMI and obesity. These policies, which include restaurants per capita, the gasoline tax, the cigarette tax, and clean indoor air laws, display many of the expected effects on obesity and explain a substantial amount of its trend. We control for individual-level measures of household income, years of formal schooling completed, and marital status.
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