论文标题

回声状态网络交叉验证的有效实现

Efficient implementations of echo state network cross-validation

论文作者

Lukoševičius, Mantas, Uselis, Arnas

论文摘要

背景/简介:交叉验证(CV)在时间序列建模中仍然很少见。 Echo状态网络(ESN)是储层计算(RC)模型的一个主要示例,以其快速而精确的一声学习而闻名,通常从良好的超参数调整中受益。这使他们理想地改变了现状。 方法:我们讨论了用于预测感兴趣的具体时间间隔的时间序列的简历,提出了几种用于交叉验证ESN的方案,并引入了一种有效的算法以实现它们。该算法作为执行$ k $ fold cv的两个优化级别。训练RC模型通常由两个阶段组成:(i)使用数据运行储层和(ii)计算最佳读数。我们优化的第一级介绍了计算上最昂贵的部分(i),并且无论$ k $如何,它都保持不变。它大大减少了任何类型的RC系统中的储层计算,如果$ K $很小,则足够了。第二级的优化也使(ii)部分保持恒定,无论大型$ k $,只要输出的尺寸较低即可。我们讨论了ESN提出的验证方案何时可能是有益的,这是生产最终模型并在六个不同的现实世界数据集上进行经验研究的三个选择,以及经验计算时间实验。我们在在线存储库中提供代码。 结果:提出的简历方案在所有六个不同的现实世界数据集(三种任务类型)中提供了更好,更稳定的测试性能。经验运行时间证实了我们的复杂性分析。 结论:在大多数情况下,$ k $ - 折叠的ESN和许多其他RC模型几乎可以与简单的单分解验证相同的时间和空间复杂性完成。这使CV成为RC的标准实践。

Background/introduction: Cross-Validation (CV) is still uncommon in time series modeling. Echo State Networks (ESNs), as a prime example of Reservoir Computing (RC) models, are known for their fast and precise one-shot learning, that often benefit from good hyper-parameter tuning. This makes them ideal to change the status quo. Methods: We discuss CV of time series for predicting a concrete time interval of interest, suggest several schemes for cross-validating ESNs and introduce an efficient algorithm for implementing them. This algorithm is presented as two levels of optimizations of doing $k$-fold CV. Training an RC model typically consists of two stages: (i) running the reservoir with the data and (ii) computing the optimal readouts. The first level of our optimization addresses the most computationally expensive part (i) and makes it remain constant irrespective of $k$. It dramatically reduces reservoir computations in any type of RC system and is enough if $k$ is small. The second level of optimization also makes the (ii) part remain constant irrespective of large $k$, as long as the dimension of the output is low. We discuss when the proposed validation schemes for ESNs could be beneficial, three options for producing the final model and empirically investigate them on six different real-world datasets, as well as do empirical computation time experiments. We provide the code in an online repository. Results: Proposed CV schemes give better and more stable test performance in all the six different real-world datasets, three task types. Empirical run times confirm our complexity analysis. Conclusions: In most situations $k$-fold CV of ESNs and many other RC models can be done for virtually the same time and space complexity as a simple single-split validation. This enables CV to become a standard practice in RC.

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