  Selecting the most relevant features and samples out of a large set of
candidates is a task that occurs very often in the context of automated data
analysis, where it can be used to improve the computational performance, and
also often the transferability, of a model. Here we focus on two popular
sub-selection schemes which have been applied to this end: CUR decomposition,
that is based on a low-rank approximation of the feature matrix and Farthest
Point Sampling, that relies on the iterative identification of the most diverse
samples and discriminating features. We modify these unsupervised approaches,
incorporating a supervised component following the same spirit as the Principal
Covariates Regression (PCovR) method. We show that incorporating target
information provides selections that perform better in supervised tasks, which
we demonstrate with ridge regression, kernel ridge regression, and sparse
kernel regression. We also show that incorporating aspects of simple supervised
learning models can improve the accuracy of more complex models, such as
feed-forward neural networks. We present adjustments to minimize the impact
that any subselection may incur when performing unsupervised tasks. We
demonstrate the significant improvements associated with the use of PCov-CUR
and PCov-FPS selections for applications to chemistry and materials science,
typically reducing by a factor of two the number of features and samples which
are required to achieve a given level of regression accuracy.

Chemical Physics;Machine Learning