用于集合和情景缩减的能量距离
The energy distance for ensemble and scenario reduction
摘要：
情景约简技术被广泛应用于解决复杂的动态和随机规划，特别是在能源和电力系统中，但也用于概率预测，聚类和估计生成对抗网络（GANs）。我们提出了一种新的方法集成和场景减少的基础上的能量距离，这是一个特殊的情况下，最大平均差异（MMD）。我们详细讨论了能量距离的选择，特别是在比较流行的瓦瑟斯坦距离，这是占主导地位的情况下减少文学。能量距离是概率测度之间的度量，允许对任意多变量分布的相等性或独立性进行强大的测试。由于后者，它是一个合适的候选人合奏和场景减少问题。的理论性质和考虑的例子清楚地表明，减少的场景集往往表现出更好的统计特性的能量距离比相应的减少相对于瓦瑟斯坦距离。我们展示了应用程序的伯努利随机游动和两个真实的数据为基础的例子，电力需求的配置文件和日前的电价。
英文摘要：
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.
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