The energy distance for ensemble and scenario reduction
This work addresses scenario reduction for stochastic programs in domains like energy systems, offering an incremental improvement over existing methods.
The authors tackled the problem of ensemble and scenario reduction by proposing a new method based on the energy distance, showing that it yields reduced scenario sets with better statistical properties compared to the widely used Wasserstein distance, as demonstrated in examples including electricity demand and price data.
Scenario reduction techniques are widely applied for solving sophisticated dynamic and stochastic programs, especially in energy and power systems, but also used in probabilistic forecasting, clustering and estimating generative adversarial networks (GANs). We propose a new method for ensemble and scenario reduction based on the energy distance which is a special case of the maximum mean discrepancy (MMD). We discuss the choice of energy distance in detail, especially in comparison to the popular Wasserstein distance which is dominating the scenario reduction literature. The energy distance is a metric between probability measures that allows for powerful tests for equality of arbitrary multivariate distributions or independence. Thanks to the latter, it is a suitable candidate for ensemble and scenario reduction problems. The theoretical properties and considered examples indicate clearly that the reduced scenario sets tend to exhibit better statistical properties for the energy distance than a corresponding reduction with respect to the Wasserstein distance. We show applications to a Bernoulli random walk and two real data based examples for electricity demand profiles and day-ahead electricity prices.