Making accurate forecast or prediction is a challenging task in the big data era, in particular for those datasets involving highdimensional variables but short-term time series points,which are generally available from real-world systems.

To address this issue, Prof. CHEN Luonan from the Institute of Biochemistry and Cell Biology (SIBCB),Chinese Academy of Sciences (CAS) together with Profs. MA Huanfei (Soochow University), AIHARA Kazuyuki (University of Tokyo) and LIN Wei (Fudan University) proposed a new model-free theoretical framework, namely “Randomly Distributed Embedding”(RDE), for achieving accurate future state prediction based on short-term high-dimensional data.

中国学生发展核心素养重心实为“培养全面发展的人”。在此重心之下，何为全面发展的人及如何培养全面发展的人便成为教育改革所面临的首要问题。基于核心素养培育的具体要求，“部编本”教材应运而生，意图尝试通过改变教材内容以创新教材教法，创新课程体系，最终创造21世纪全面发展的新人才。

Specifically, from the observed data of highdimensional variables, the RDE framework randomly generates a sufficient number of low-dimensional “nondelay embeddings” and maps each of them to a “delay embedding,” which is constructed from the data of a target variable to be predicted. Any of these mappings can perform as a low-dimensional weak predictor for future state prediction, and all of such mappings generate a distribution of predicted future states. This distribution actually patches all pieces of association information from various embeddings unbiasedly or biasedly into the whole dynamics of the target variable, which after operated by appropriate estimation strategies, creates a stronger predictor for achieving prediction in a more reliable and robust form.

Figure 1: RDE decodes high-dim correlation data to future dynamics. (Image by courtesy of CHEN Luonan's group)

Figure 2: Although the training data only covers small segments of the attractor, RDE predicts the future dynamics even with different behaviors. (Image by courtesy of CHEN Luonan's group)

Through applying the RDE framework to data from both representative models and real-world systems, including the expression level of different genes in the liver, wind speeds across Tokyo and the relation between pollution levels and hospital admissions, the team reveal that a high-dimension feature is no longer an obstacle but a source of information crucial to accurate prediction for shortterm data, even under noise deterioration. RDE can be expected to be applied to many areas including AI and brain science. In particular, RDE decodes high-dim correlation data to future dynamics of target variables(low-dim), or can be viewed to transform high-dim small sample size into low-dim large size, shown in figure 1.

Although the training data only covers small segments of the attractor, RDE predicts the future dynamics even with different behaviors, as shown in figure 2. Considering the RDE problem as a learning process, we can view it as a “wide-learning” scheme(with small sample size but high-dimension inputs)against the traditional “deep-learning” scheme (with large sample size but usually low-dimension inputs),thus opening a new way to the study of machine learning, AI and brain intelligence.

在控制回路上作业时，要尽量避免出现寄生回路现象。在进行保护校验时，继保工作人员要明确区分失灵回路、闸刀切换回路及跳闸回路。在进行传动试验过程中要对传动进行出口间隔。在涉及到电压互感器、电流互感器的二次回路的工作时，继保工作人员要在接线、拆线时防止电压互感器二次侧短路、电流互感器二次侧开路。

This work entitled “Randomly Distributed Embedding Making Short-term High-dimensional Data Predictable” was published in Proceedings of the National Academy of Sciences of the United States of America on October 8, 2018. This work was supported by the grants from CAS, the National Key R&D Program of China, and the National Natural Science Foundation of China. The publication is available at: http://www.pnas.org/content/early/2018/10/04/1802987115.