Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kernel Two-Sample and Independence Tests for Non-Stationary Random
  Processes   Two-sample and independence tests with the kernel-based MMD and HSIC have
shown remarkable results on i.i.d. data and stationary random processes.
However, these statistics are not directly applicable to non-stationary random
processes, a prevalent form of data in many scientific disciplines. In this
work, we extend the application of MMD and HSIC to non-stationary settings by
assuming access to independent realisations of the underlying random process.
These realisations - in the form of non-stationary time-series measured on the
same temporal grid - can then be viewed as i.i.d. samples from a multivariate
probability distribution, to which MMD and HSIC can be applied. We further show
how to choose suitable kernels over these high-dimensional spaces by maximising
the estimated test power with respect to the kernel hyper-parameters. In
experiments on synthetic data, we demonstrate superior performance of our
proposed approaches in terms of test power when compared to current
state-of-the-art functional or multivariate two-sample and independence tests.
Finally, we employ our methods on a real socio-economic dataset as an example
application.

17
The categories of this paper are: q-fin
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
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con