4,128 research outputs found
A subelliptic Bourgain-Brezis inequality
We prove an approximation lemma on (stratified) homogeneous groups that
allows one to approximate a function in the non-isotropic Sobolev space
by functions, generalizing a result of
Bourgain-Brezis \cite{MR2293957}. We then use this to obtain a
Gagliardo-Nirenberg inequality for on the Heisenberg group
.Comment: 44 page
Some higher order isoperimetric inequalities via the method of optimal transport
In this paper, we establish some sharp inequalities between the volume and
the integral of the -th mean curvature for -convex domains in the
Euclidean space. The results generalize the classical Alexandrov-Fenchel
inequalities for convex domains. Our proof utilizes the method of optimal
transportation.Comment: 21 page
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
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