Blanchet, J. and Kang, Y. Sample-out-of-sample Inference Based on Wasserstein Distance. To appear in Operations Research.

Summary:

This paper was actually produced slightly before “Blanchet, J., Kang, Y., Murthy, K. Robust Wasserstein Profile Inference and Applications to Machine Learning. Journal of Applied Probability, 56, (2019), pp. 830-857.”. Our motivation is also DRO (Distributionally Robust Optimization) based on the Wasserstein distance. The cool thing is that the support of the alternative measures in the uncertainty set is chosen at random, based on a sample. I think this is very interesting because this is a way to inform the uncertainty set in a data-driven way. We actually use these results in the context of semi-supervised learning. But also the asymptotic statistics of the profile function are also very interesting. In this setting, in contrast to the unconstrained case (i.e. paper cited above), the rate of convergence is dimension dependent but never worse than the root of the unconstrained case.

Bibtex:

@Article{BK_2020,

author = {J. Blanchet and Y. Kang},

title = {Sample-out-of-sample Inference Based on Wasserstein Distance.},

journal = {Operations Research},

year = {2020},

volume = {To appear},

% pages = {271-276}

}