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Optimization at Work, April 14, Moscow, 2018
Statistical inference with optimal transport
Vladimir Spokoiny (WIAS, Berlin)
Optimal transportation (OT) theory provides a powerful toolbox
for data analysis in nonlinear spaces, where nonlinearity appears as an inevitable consequence of
complexity of objects of interest (e.g. medical images or meta-genomes).
OT opens a new direction in creating complete package of statistical instruments
which takes into account the underlying geometry of an observed data set.
In this talk we introduce basics on statistical inference based on OT and present recent results.
Implementable tensor methods in unconstrained convex optimization
Yirii Nesterov (CORE UCL, Belgium)
In this paper we develop new tensor methods for unconstrained convex optimization, which solve at each iteration an auxiliary problem of minimizing convex multivariate polynomial. We analyze the simplest scheme, based on minimization of a regularized local model of the objective function, and its accelerated version obtained in the framework of estimating sequences. Their rates of convergence are compared with the worst-case lower complexity bounds for corresponding problem classes. Finally, for the third-order methods, we suggest an efficient technique for solving the auxiliary problem, which is based on the recently developed relative smoothness condition. With this elaboration, the third-order methods become implementable and very fast.
Метод неравномерных покрытий для задачи оптимизации и аппроксимации
Евтушенко Ю.Г. (ВЦ РАН, МГУ), Посыпкин М.А. (ВЦ РАН)
Новый взгляд на теорему Куна-Такера
Третьяков А.А. (ВЦ РАН), Евтушенко (ВЦ РАН, МГУ)
Randomized distributed computation of Wasserstein barycenter with mini-batch
Двинских Дарина (МФТИ)
An Accelerated Directional Derivative Method for Smooth Stochastic Convex Optimization
Горбунов Эдуард (МФТИ)