You signed in with another tab or window. Reload to refresh your session.You signed out in another tab or window. Reload to refresh your session.You switched accounts on another tab or window. Reload to refresh your session.Dismiss alert
Moving earth & Soldiers Monge problem: what is the most efficient way to bring earth from one place to another
How to move the sand to fill the hole most efficiently?
Characterise the work involved here by the product between mass and the moving distance:
Exact solution: linear programming
Sinkhorn Algorithm for Entropy Regularized Optimal Transport
Dealing with curse of high dimensionality
Sliced Wasserstein distance:
PCA projection
k-dim (robust) projection
Applications: Average measures
k-means
You can consider W distance as a k-mean algorithm, if the dimension of X is much higher than the dimension of Y.
Wasserstein Barycenter:
Brain imaging
Mapping visual stimulus to different cortex of the brain using MEG. Different subject will have slightly different response -- to account for this spatial variation one can use Wasserstein average.
KL, MMD vs. Wasserstein
there is no geometry in KL/MMD, they're better for high dimensional data. For KL, when you have two Gaussians very close to each other, if the variance goes to zero, the divergence can go to infinity
Wasserstein vs. L2 averages
Domain adaptation
Learning with Wasserstein loss:
Sorting
On 1D, calculating the Wasserstein plan is equivalent to sorting (because the nth ranking point in X is always going to map to the nth ranking in Y)
The text was updated successfully, but these errors were encountered:
Optimal transport
Introduction
Two examples:
How to move the sand to fill the hole most efficiently? Characterise the work involved here by the product between mass and the moving distance:
Exact solution: linear programming
Sinkhorn Algorithm for Entropy Regularized Optimal Transport
Dealing with curse of high dimensionality
Sliced Wasserstein distance:
PCA projection
k-dim (robust) projection
Applications: Average measures
k-means
You can consider W distance as a k-mean algorithm, if the dimension of X is much higher than the dimension of Y.
Wasserstein Barycenter:
Brain imaging
Mapping visual stimulus to different cortex of the brain using MEG. Different subject will have slightly different response -- to account for this spatial variation one can use Wasserstein average.
KL, MMD vs. Wasserstein
there is no geometry in KL/MMD, they're better for high dimensional data. For KL, when you have two Gaussians very close to each other, if the variance goes to zero, the divergence can go to infinity
Wasserstein vs. L2 averages
Domain adaptation
Learning with Wasserstein loss:
Sorting
On 1D, calculating the Wasserstein plan is equivalent to sorting (because the nth ranking point in X is always going to map to the nth ranking in Y)
The text was updated successfully, but these errors were encountered: