  Energy forecasting has attracted enormous attention over the last few
decades, with novel proposals related to the use of heterogeneous data sources,
probabilistic forecasting, online learn-ing, etc. A key aspect that emerged is
that learning and forecasting may highly benefit from distributed data, though
not only in the geographical sense. That is, various agents collect and own
data that may be useful to others. In contrast to recent proposals that look
into distributed and privacy-preserving learning (incentive-free), we explore
here a framework called regression markets. There, agents aiming to improve
their forecasts post a regression task, for which other agents may contribute
by sharing their data for their features and get monetarily rewarded for it.The
market design is for regression models that are linear in their parameters, and
possibly sep-arable, with estimation performed based on either batch or online
learning. Both in-sample and out-of-sample aspects are considered, with markets
for fitting models in-sample, and then for improving genuine forecasts
out-of-sample. Such regression markets rely on recent concepts within
interpretability of machine learning approaches and cooperative game theory,
with Shapley additive explanations. Besides introducing the market design and
proving its desirable properties, application results are shown based on
simulation studies (to highlight the salient features of the proposal) and with
real-world case studies.
