1,328 research outputs found
Fast Optimal Transport Averaging of Neuroimaging Data
Knowing how the Human brain is anatomically and functionally organized at the
level of a group of healthy individuals or patients is the primary goal of
neuroimaging research. Yet computing an average of brain imaging data defined
over a voxel grid or a triangulation remains a challenge. Data are large, the
geometry of the brain is complex and the between subjects variability leads to
spatially or temporally non-overlapping effects of interest. To address the
problem of variability, data are commonly smoothed before group linear
averaging. In this work we build on ideas originally introduced by Kantorovich
to propose a new algorithm that can average efficiently non-normalized data
defined over arbitrary discrete domains using transportation metrics. We show
how Kantorovich means can be linked to Wasserstein barycenters in order to take
advantage of an entropic smoothing approach. It leads to a smooth convex
optimization problem and an algorithm with strong convergence guarantees. We
illustrate the versatility of this tool and its empirical behavior on
functional neuroimaging data, functional MRI and magnetoencephalography (MEG)
source estimates, defined on voxel grids and triangulations of the folded
cortical surface.Comment: Information Processing in Medical Imaging (IPMI), Jun 2015, Isle of
Skye, United Kingdom. Springer, 201
Optimal Transport Filtering with Particle Reweighing in Finance
We show the application of an optimal transportation approach to estimate
stochastic volatility process by using the flow that optimally transports the
set of particles from the prior to a posterior distribution. We also show how
to direct the flow to a rarely visited areas of the state space by using a
particle method (a mutation and a reweighing mechanism). We demonstrate the
efficiency of our approach on a simple example of the European option price
under the Stein-Stein stochastic volatility model for which a closed form
formula is available. Both homotopy and reweighted homotopy methods show a
lower variance, root-mean squared errors and a bias compared to other filtering
schemes recently developed in the signal-processing literature, including
particle filter techniques
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