Statistical inference for Bures-Wasserstein barycenters

01/02/2019
by   Alexey Kroshnin, et al.
0

In this work we introduce the concept of Bures-Wasserstein barycenter Q_*, that is essentially a Fréchet mean of some distribution supported on a subspace of positive semi-definite Hermitian operators _̋+(d). We allow a barycenter to be restricted to some affine subspace of _̋+(d) and provide conditions ensuring its existence and uniqueness. We also investigate convergence and concentration properties of an empirical counterpart of Q_* in both Frobenious norm and Bures-Wasserstein distance, and explain, how obtained results are connected to optimal transportation theory and can be applied to statistical inference in quantum mechanics.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset