Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Statistical Analysis of Wasserstein Distributionally Robust Estimators   We consider statistical methods which invoke a min-max distributionally
robust formulation to extract good out-of-sample performance in data-driven
optimization and learning problems. Acknowledging the distributional
uncertainty in learning from limited samples, the min-max formulations
introduce an adversarial inner player to explore unseen covariate data. The
resulting Distributionally Robust Optimization (DRO) formulations, which
include Wasserstein DRO formulations (our main focus), are specified using
optimal transportation phenomena. Upon describing how these
infinite-dimensional min-max problems can be approached via a
finite-dimensional dual reformulation, the tutorial moves into its main
component, namely, explaining a generic recipe for optimally selecting the size
of the adversary's budget. This is achieved by studying the limit behavior of
an optimal transport projection formulation arising from an inquiry on the
smallest confidence region that includes the unknown population risk minimizer.
Incidentally, this systematic prescription coincides with those in specific
examples in high-dimensional statistics and results in error bounds that are
free from the curse of dimensions. Equipped with this prescription, we present
a central limit theorem for the DRO estimator and provide a recipe for
constructing compatible confidence regions that are useful for uncertainty
quantification. The rest of the tutorial is devoted to insights into the nature
of the optimizers selected by the min-max formulations and additional
applications of optimal transport projections.

36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th