基于图核机器的学习算法及其在金融分析理论的研究

Kernel machines have been proven powerful for financial analysis. Kernel machines are instances of learning algorithms from statistical learning theory. Comparing to most traditional learning algorithms, kernel machines provide an elegant way of solving complex non-linear problems in a high dimensional linear space, and thus better characterize financial data. Unfortunately, existing kernel machines for financial analysis can only accommodate vectors directly constructed by original financial data that may ignore some information of financial data. As a result, these methods cannot comprehensively reflect the characteristics of financial data. One way to overcome this problem is to use graph-based kernel machines for graphs abstracted from financial data. However, most existing graph kernels are designed for simple graphs (e.g., un-directed graphs and un-weighted graphs). This limits the application of using graph-based kernel machines for financial analysis. ..To address the mentioned problems, we aim to develop novel approaches based on learning from graph-based kernel machines for the objective of financial analysis. The main contributions of this research are threefold. First, we use the continuous-time quantum walk as a means of establishing dynamical graph structures for financial data. The graph structures can capture richer characteristic for complex financial data, and thus overcome the shortcoming of ignoring co-relation of financial data that arises in existing methods. Second, we develop novel graph kernels based on the recent novel theories of continuous-time quantum walk, quantum mechanics and mutual information on graphs, which can easily accommodate complex graph structures abstracted from complicated financial data. Finally, associated with our new graph kernels and dynamical graph constructing method, we explore the financial analysis study from graph-based kernel machines. Our research can provide a powerful tool for financial analysis, and is significant for future development of using machine learning algorithms on financial analysis study.

核机器是金融分析领域重要的机器学习算法，具有比传统学习算法更好的分析复杂金融数据的能力。然而，目前应用于金融分析的核机器是基于向量数据设计的，如何使用基于图数据的核机器(即图核机器)进行金融分析尚无文献记录。为实现图核机器在金融分析理论的突破，本项目专注于使用图核机器进行金融分析，并探索与之相关的新理论与新方法。本项目的主要贡献有三点：1）使用连续量子漫步为金融数据构建动态图结构，通过金融数据的动态图，既可以体现金融数据的复杂性也可以反映金融数据的主要特征；2）通过使用连续量子漫步、量子力学、信息论等近年图核函数领域崭新理论，探索构造可处理各种复杂类型图的图核函数，以全面反映基于金融数据的图结构的特征；3）结合本项目新提出的动态图与图核函数方法，使用图核机器进行金融分析，并探索基于图核机器的金融分析理论方法。本项目研究成果可为金融决策人员与相关从业人员提供重要的支持，具有重要的学术价值。

为实现图核机器在金融数据分析理论的突破，本项目专注于使用图核机器等机器学习算法进行金融数据分析，并解决了本项目提出的三个重要问题。这些问题包括：1）现有工作在基于金融时间序列构建动态图结构数据时，无法自动鉴别最优关联时间序列子集，从而难以有效对时间序列数据进行图结构建模；2）现有图核函数研究工作大部分是针对无向稀疏图这一结构相对的图数据设计的，能够直接应用于全连接图权重图、高阶关系图等的图核函数很少，特别是缺乏能够应用于同时具有上述信息的复杂图结构的方法；3）现有工作缺乏使用图核函数进行金融数据分析的工作。本项目使用基于图数据的机器学习与模式识别方法，特别是图核函数展开了金融数据分析的工作，对相关新理论与新方法进行了深入研究。在本项目的支持下，课题组成员在国际重要学术期刊、会议发表论文29篇。其中，期刊论文包括国际重要期刊Pattern Recognition、Physical Review E、Pattern Recognition Letters、Neurocomputing等；会议论文包括：CIKM、ICPR、IEEE Big Data等。组织国际会议1st ICPR Workshop on Pattern Recognition in Intelligent Financial and Risk Management一次。本项目研究成果可为金融决策人员与相关从业人员提供重要的支持，具有重要的学术价值。