  Supervised learning of time series data has been extensively studied for the
case of a categorical target variable. In some application domains, e.g.,
energy, environment and health monitoring, it occurs that the target variable
is numerical and the problem is known as time series extrinsic regression
(TSER). In the literature, some well-known time series classifiers have been
extended for TSER problems. As first benchmarking studies have focused on
predictive performance, very little attention has been given to
interpretability. To fill this gap, in this paper, we suggest an extension of a
Bayesian method for robust and interpretable feature construction and selection
in the context of TSER. Our approach exploits a relational way to tackle with
TSER: (i), we build various and simple representations of the time series which
are stored in a relational data scheme, then, (ii), a propositionalisation
technique (based on classical aggregation / selection functions from the
relational data field) is applied to build interpretable features from
secondary tables to "flatten" the data; and (iii), the constructed features are
filtered out through a Bayesian Maximum A Posteriori approach. The resulting
transformed data can be processed with various existing regressors.
Experimental validation on various benchmark data sets demonstrates the
benefits of the suggested approach.
