基于分布鲁棒性优化，用半定规划求解电力价格预测的低风险估计。
Wasserstein Distributionally Robust Risk-Sensitive Estimation via Conditional Value-at-Risk
- 在瓦瑟斯坦球不确定性集下，用条件风险价值评估估计误差。
- 当中心分布有限支持时，可精确求解最优仿射估计器。
- 实证显示在电力市场数据上优于现有方法，风险更低。
我们提出一种分布鲁棒方法，用于从观测信号 y 估计未知信号 x。观测信号与未知信号建模为随机向量，其联合分布未知，但假设属于给定的二型瓦瑟斯坦球（Wasserstein ball）中的分布集合，称为不确定性集。估计器性能通过平方估计误差的条件风险价值（CVaR）衡量。在此框架下，我们研究计算使最坏情况 CVaR 最小化的仿射估计器的问题。主要结果表明：当瓦瑟斯坦球中心的名义分布为有限支撑时，该类估计器可通过一个可解的半定规划问题精确计算。我们在真实电力市场数据上对所提估计器进行评估，结果显示其在样本外的平方误差 CVaR 显著低于现有方法。
原文摘要 · Abstract (English)
We propose a distributionally robust approach to risk-sensitive estimation of an unknown signal x from an observed signal y. The observation and unknown signal are modeled as random vectors whose joint probability distribution is unknown, but assumed to belong to a given type-2 Wasserstein ball of distributions, termed the ambiguity set. The performance of an estimator is measured according to the conditional value-at-risk (CVaR) of the squared estimation error. Within this framework, we study the problem of computing affine estimators that minimize the worst-case CVaR over all distributions in the given ambiguity set. As our main result, we show that, when the nominal distribution at the center of the Wasserstein ball is finitely supported, such estimators can be exactly computed by solving a tractable semidefinite program. We evaluate the proposed estimators on a wholesale electricity price forecasting task using real market data and show that they deliver lower out-of-sample CVaR of squared error compared to existing methods.
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