Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Large-scale optimal transport map estimation using projection pursuit   This paper studies the estimation of large-scale optimal transport maps
(OTM), which is a well-known challenging problem owing to the curse of
dimensionality. Existing literature approximates the large-scale OTM by a
series of one-dimensional OTM problems through iterative random projection.
Such methods, however, suffer from slow or none convergence in practice due to
the nature of randomly selected projection directions. Instead, we propose an
estimation method of large-scale OTM by combining the idea of projection
pursuit regression and sufficient dimension reduction. The proposed method,
named projection pursuit Monge map (PPMM), adaptively selects the most
``informative'' projection direction in each iteration. We theoretically show
the proposed dimension reduction method can consistently estimate the most
``informative'' projection direction in each iteration. Furthermore, the PPMM
algorithm weakly convergences to the target large-scale OTM in a reasonable
number of steps. Empirically, PPMM is computationally easy and converges fast.
We assess its finite sample performance through the applications of Wasserstein
distance estimation and generative models.

22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ