Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distributionally Robust Learning   This monograph develops a comprehensive statistical learning framework that
is robust to (distributional) perturbations in the data using Distributionally
Robust Optimization (DRO) under the Wasserstein metric. Beginning with
fundamental properties of the Wasserstein metric and the DRO formulation, we
explore duality to arrive at tractable formulations and develop finite-sample,
as well as asymptotic, performance guarantees. We consider a series of learning
problems, including (i) distributionally robust linear regression; (ii)
distributionally robust regression with group structure in the predictors;
(iii) distributionally robust multi-output regression and multiclass
classification, (iv) optimal decision making that combines distributionally
robust regression with nearest-neighbor estimation; (v) distributionally robust
semi-supervised learning, and (vi) distributionally robust reinforcement
learning. A tractable DRO relaxation for each problem is being derived,
establishing a connection between robustness and regularization, and obtaining
bounds on the prediction and estimation errors of the solution. Beyond theory,
we include numerical experiments and case studies using synthetic and real
data. The real data experiments are all associated with various health
informatics problems, an application area which provided the initial impetus
for this work.

37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol