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Linear Transport methods assumes that the left and right distributions are multivariate normal distributions. In practice their parameters such as mean and covariance are estimated from the data. So they do not provide a transport plan between samples but a continuous affine mapping that is the Monge mapping. You can interpret the transport by looking at the displacement of the samples but there is not OT plan giving you correspondences for those methods (a coarse approximation would be to do a closets sample assignment after mapping but this will not be a transport plan). |
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Hi @ttsesm, thanks for the interesting questions! PS I cannot speak for everyone, but for safety reasons I would never open a stranger's zip file ;) |
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Hi,
I am trying to use the
ot.da.LinearGWTransport()
function as described in the POT documentation as follows:where
Cs
,Ms
andct
,mt
are my 3D and 2D gaussians respectively (i.e. covariance and mean values).However, I am not sure how to retrieve back the transport plan and the projection matrix from the fitted distribution. From what I've noticed I can get back the
A
andB
matrices but I am not sure how these are related to the transport plan and projection matrix.I would appreciated if someone has an idea and/or provide some feedback.
Thanks.
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