6 papers
Robust -means Clustering for Distributions with Two Moments
Yegor Klochkov, Alexey Kroshnin, Nikita Zhivotovskiy
We consider the robust algorithms for the -means clustering problem where a quantizer is constructed based on independent observations. Our main results are median of means…
Gradient Methods for Problems with Inexact Model of the Objective
Fedor Stonyakin, Darina Dvinskikh, Pavel Dvurechensky +8
We consider optimization methods for convex minimization problems under inexact information on the objective function. We introduce inexact model of the objective, which as a parti…
Statistical inference for Bures-Wasserstein barycenters
Alexey Kroshnin, Vladimir Spokoiny, Alexandra Suvorikova
In this work we introduce the concept of Bures-Wasserstein barycenter , that is essentially a Fréchet mean of some distribution supported on a subspace of positiv…
On the Complexity of Approximating Wasserstein Barycenter
Alexey Kroshnin, Darina Dvinskikh, Pavel Dvurechensky +3
We study the complexity of approximating Wassertein barycenter of discrete measures, or histograms of size by contrasting two alternative approaches, both using entropic re…
Image Registration and Predictive Modeling: Learning the Metric on the Space of Diffeomorphisms
Ayagoz Mussabayeva, Alexey Kroshnin, Anvar Kurmukov +5
We present a method for metric optimization in the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework, by treating the induced Riemannian metric on the space of diffe…
Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn's Algorithm
Pavel Dvurechensky, Alexander Gasnikov, Alexey Kroshnin
We analyze two algorithms for approximating the general optimal transport (OT) distance between two discrete distributions of size , up to accuracy . For the first…