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Energy forecasting has attracted enormous attention over the last fewdecades, with novel proposals related to the use of heterogeneous data sources,probabilistic forecasting, online learn-ing, etc. A key aspect that emerged isthat learning and forecasting may highly benefit from distributed data, thoughnot only in the geographical sense. That is, various agents collect and owndata that may be useful to others. In contrast to recent proposals that lookinto distributed and privacy-preserving learning (incentive-free), we explorehere a framework called regression markets. There, agents aiming to improvetheir forecasts post a regression task, for which other agents may contributeby sharing their data for their features and get monetarily rewarded for it.Themarket design is for regression models that are linear in their parameters, andpossibly sep-arable, with estimation performed based on either batch or onlinelearning. Both in-sample and out-of-sample aspects are considered, with marketsfor fitting models in-sample, and then for improving genuine forecastsout-of-sample. Such regression markets rely on recent concepts withininterpretability of machine learning approaches and cooperative game theory,with Shapley additive explanations. Besides introducing the market design andproving its desirable properties, application results are shown based onsimulation studies (to highlight the salient features of the proposal) and withreal-world case studies.

Regression markets and application to energy forecasting