Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: LQD-RKHS-based distribution-to-distribution regression methodology for
  restoring the probability distributions of missing SHM data   Data loss is a critical problem in structural health monitoring (SHM).
Probability distributions play a highly important role in many applications.
Improving the quality of distribution estimations made using incomplete samples
is highly important. Missing samples can be compensated for by applying
conventional missing data restoration methods; however, ensuring that restored
samples roughly follow underlying distributions of true missing data remains a
challenge. Another strategy involves directly restoring the probability density
function (PDF) for a sensor when samples are missing by leveraging distribution
information from another sensor with complete data using distribution
regression techniques; existing methods include the conventional
distribution-to-distribution regression (DDR) and distribution-to-warping
function regression (DWR) methods. Due to constraints on PDFs and warping
functions, the regression functions of both methods are estimated from the
Nadaraya-Watson kernel estimator with relatively low degrees of precision. This
article proposes a new indirect distribution-to-distribution regression method
in the context of functional data analysis for restoring distributions of
missing SHM data. PDFs are transformed to ordinary functions residing in a
Hilbert space via the newly proposed log-quantile-density (LQD) transformation;
the regression for distributions is realized in the transformed space via a
functional regression model constructed based on the theory of Reproducing
Kernel Hilbert Space (RKHS), corresponding result is subsequently mapped back
to the density space through the inverse LQD transformation. Test results using
field monitoring data indicate that the new method significantly outperforms
conventional methods in general cases; however, in extrapolation cases, the new
method is inferior to the distribution-to-warping function regression method.

23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
2
The categories of this paper are: math
11
The categories of this paper are: hep-lat