# On IoT-Friendly Skewness Monitoring for Skewness-Aware Online Edge Learning
###### Abstract
In the simplest case, the cumulative version of running skewness from several mathematical libraries can work for the basic online sequential learning (e.g., [15]). Nevertheless, we find that the corresponding algorithms are either inefficient or improper for skewness monitoring on the edge (cf. Sections 4.3.3 and 4.3.4). After observing frequent inquiries about running skewness in the open source community [16; 17; 18], we further affirmed the gap between practitioners' needs and the scientific research on this topic. In detail, by studying the existing running skewness algorithms and the relevant statistical methods (i.e., running mean and running variance), we identified that the currently inefficient algorithms of cumulative running skewness are due to the inefficient calculation of running variance. Meanwhile, the missing of the other running skewness versions is mainly due to the lack of an efficient (or concise) cumulative version. Driven by these findings, this research develops IoT-friendly equation systems for calculating three popular running skewness versions and initially validates the usefulness and significance of skewness awareness in the implementation of online edge learning. Correspondingly, this research makes a fourfold contribution:  
* From the statistics community's perspective, this research enriches skewness monitoring solutions in the running statistics domain. It is worth highlighting that our solutions can conveniently be implemented into efficient algorithms and deployed on IoT devices for practical usage. In fact, compared with the pervasive discussions about mean, median, and variance (or standard deviation), skewness has been considered \"a forgotten statistic\" [8], not to mention running skewness. In particular, this research reminds the statistics community of the real-world needs of running skewness in the context of IoT and edge learning. * From the machine learning community's perspective, this research paves the way for developing skewness-aware online learning techniques, which is particularly valuable and useful in the edge computing domain. It should be noted that although traditional skewness-aware machine learning has been studied [5; 19], their generic strategy of curing high skewness (i.e., data pre-processing) cannot be applied to the online mode. In particular, this research reminds the machine learning community of the significance and the available methods of online skewness monitoring. After all, the slightest difference at the model training stage can lead to a huge error in the machine learning results. * In addition, the shared formula derivation details (in Appendix A) can help both researchers and practitioners investigate other versions of running skewness and develop corresponding algorithms, so as to satisfy the diverse needs in practice. It should be noted that not only has our work developed an efficient cumulative version of running skewness, but we have also investigated the other two versions that can satisfy the forgetting mechanism in the modern edge learning proposals. This contribution essentially follows the spirit of open methods that can act \"as a higher-level strategy over open-source tools and open-access data\" to facilitate scientific work [20]. In fact, this research has revealed that the obscurity in some advanced statistical methods may hinder their recognition and employment (cf. Section 3.1.2). * Overall, our work advocates and fosters cross-community research efforts on IoT-friendly online edge learning. Given the booming of edge intelligence [21] accompanied with the resource limits of IoT equipment (e.g., the embedded RAM is only 4 KB in the current taxi-mounted GPS devices), multi-domain knowledge and expertise need to fuse together to address the challenges of online edge learning. Through this paper, we particularly expect to attract more attention from the statistics community and to inspire more skewness monitoring algorithms and techniques for the various needs in the diverse edge environments.