Several techniques have been developed in the last two decades to forecast the occurrence of Solar Proton Events (SPEs), mainly based on the statistical association between the 10 MeV proton flux and precursor parameters. The Empirical model for Solar Proton Events Real Time Alert (ESPERTA; Laurenza et al., 2009, https://doi.org/10.1029/2007sw000379) provides a quite good and timely prediction of SPEs after the occurrence of M2 soft x-ray (SXR) bursts, by using as input parameters the flare heliolongitude, the SXR and the 1 MHz radio fluence. Here, we reinterpret the ESPERTA model in the framework of machine learning and perform a cross validation, leading to a comparable performance. Moreover, we find that, by applying a cut-off on the M2 flares heliolongitude, the False Alarm Rate (FAR) is reduced. The cut-off is set to where the cumulative distribution of M2 flares associated with SPEs shows a break which reflects the poor magnetic connection between the Earth and eastern hemisphere flares. The best performance is obtained by using the SMOTE algorithm, leading to probability of detection of 0.83 and a FAR of 0.39. Nevertheless, we demonstrate that a relevant FAR on the predictions is a natural consequence of the sample base rates. From a Bayesian point of view, we find that the FAR explicitly contains the prior knowledge about the class distributions. This is a critical issue of any statistical approach, which requires to perform the model validation by preserving the class distributions within the training and test datasets.

中文翻译：

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太阳质子事件统计预测中的未决问题：机器学习视角

在过去的二十年中，已经开发了几种技术来预测太阳质子事件 (SPE) 的发生，主要基于10 MeV 质子通量和前体参数之间的统计关联。太阳质子事件实时警报的经验模型（ESPERTA；Laurenza 等人，2009 年，https://doi.org/10.1029/2007sw000379）在M2 软 X 射线发生后提供了对 SPE 的很好和及时的预测(SXR) 爆发，通过使用耀斑日经度、SXR 和1 MHz 无线电能量密度作为输入参数。在这里，我们在机器学习框架中重新解释 ESPERTA 模型并进行交叉验证，从而获得可比的性能。此外，我们发现，通过对M2 耀斑日经度，误报率 (FAR) 降低。截止点设置为与 SPE 相关的M2 耀斑的累积分布显示中断的地方，这反映了地球和东半球耀斑之间的磁连接不良。使用 SMOTE 算法获得最佳性能，检测概率为 0.83，FAR 为 0.39。尽管如此，我们证明了预测的相关 FAR 是样本基本率的自然结果。从贝叶斯的角度来看，我们发现 FAR 明确包含关于类分布的先验知识。这是任何统计方法的关键问题，它需要通过保留训练和测试数据集中的类分布来执行模型验证。