2019/01/02 by Kroshnin, Alexey, Spokoiny, Vladimir, Suvorikova, Alexandra · 4 citations
#Applications (stat.AP) #FOS: Computer and information sciences #FOS: Mathematics #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.1901.00226
In this work we introduce the concept of Bures-Wasserstein barycenter Q_*, that is essentially a Fréchet mean of some distribution ℙ supported on a subspace of positive semi-definite Hermitian operators ℍ+(d). We allow a barycenter to be restricted to some affine subspace of ℍ+(d) and provide conditions ensuring its existence and uniqueness. We also investigate convergence and concentration properties of an empirical counterpart of Q_* in both Frobenius 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.