Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Density Estimation on Manifolds with Boundary   Density estimation is a crucial component of many machine learning methods,
and manifold learning in particular, where geometry is to be constructed from
data alone. A significant practical limitation of the current density
estimation literature is that methods have not been developed for manifolds
with boundary, except in simple cases of linear manifolds where the location of
the boundary is assumed to be known. We overcome this limitation by developing
a density estimation method for manifolds with boundary that does not require
any prior knowledge of the location of the boundary. To accomplish this we
introduce statistics that provably estimate the distance and direction of the
boundary, which allows us to apply a cut-and-normalize boundary correction. By
combining multiple cut-and-normalize estimators we introduce a consistent
kernel density estimator that has uniform bias, at interior and boundary
points, on manifolds with boundary.

25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an