This article gives details of a technique for machine learning based on piecewise linear functions having the structure of a tree composed of linear functions at the leaves and minimum and maximum operations at internal nodes. These are called ALNs. By virtue of this structure, the functions are always continuous. The technique is being used successfully for short-term forecasting of wind power supply, electrical power demand and for planning natural gas distribution. The simple architecture allows constraints to be imposed on linear pieces that carry over to global functions, for example monotonicity constraints or, more generally, constraints on partial derivatives of approximants. We show how constraints can be used to improve accuracy and reduce the risk of unexpected values when training data is in short supply.
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