论文标题
部分可观测时空混沌系统的无模型预测
Quantile absolute deviation
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
The median absolute deviation (MAD) is a popular robust measure of statistical dispersion. However, when it is applied to non-parametric distributions (especially multimodal, discrete, or heavy-tailed), lots of statistical inference issues arise. Even when it is applied to distributions with slight deviations from normality and these issues are not actual, the Gaussian efficiency of the MAD is only 37% which is not always enough. In this paper, we introduce the quantile absolute deviation (QAD) as a generalization of the MAD. This measure of dispersion provides a flexible approach to analyzing properties of non-parametric distributions. It also allows controlling the trade-off between robustness and statistical efficiency. We use the trimmed Harrell-Davis median estimator based on the highest density interval of the given width as a complimentary median estimator that gives increased finite-sample Gaussian efficiency compared to the sample median and a breakdown point matched to the QAD. As a rule of thumb, we suggest using two new measures of dispersion called the standard QAD and the optimal QAD. They give 54% and 65% of Gaussian efficiency having breakdown points of 32% and 14% respectively.
