159,090 research outputs found
Diffeomorphic density registration
In this book chapter we study the Riemannian Geometry of the density
registration problem: Given two densities (not necessarily probability
densities) defined on a smooth finite dimensional manifold find a
diffeomorphism which transforms one to the other. This problem is motivated by
the medical imaging application of tracking organ motion due to respiration in
Thoracic CT imaging where the fundamental physical property of conservation of
mass naturally leads to modeling CT attenuation as a density. We will study the
intimate link between the Riemannian metrics on the space of diffeomorphisms
and those on the space of densities. We finally develop novel computationally
efficient algorithms and demonstrate there applicability for registering RCCT
thoracic imaging.Comment: 23 pages, 6 Figures, Chapter for a Book on Medical Image Analysi
Semi-supervised Learning based on Distributionally Robust Optimization
We propose a novel method for semi-supervised learning (SSL) based on
data-driven distributionally robust optimization (DRO) using optimal transport
metrics. Our proposed method enhances generalization error by using the
unlabeled data to restrict the support of the worst case distribution in our
DRO formulation. We enable the implementation of our DRO formulation by
proposing a stochastic gradient descent algorithm which allows to easily
implement the training procedure. We demonstrate that our Semi-supervised DRO
method is able to improve the generalization error over natural supervised
procedures and state-of-the-art SSL estimators. Finally, we include a
discussion on the large sample behavior of the optimal uncertainty region in
the DRO formulation. Our discussion exposes important aspects such as the role
of dimension reduction in SSL
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