Xiang Zhao

This thesis defines a new class of vector-valued stochastic processes, called MARM (Multivariate Autoregressive Modular) Processes. It describes the construction of two flavors of MARM processes, MARM+ and MARM-, studies the statistics of MARM processes (transition structure and second order statistics), and devises MARM-based fitting and forecasting algorithms providing point estimators and confidence intervals. The key advantage of MARM processes is their ability to fit a strong statistical signature consisting of empirical first-order and second-order statistics simultaneously. More precisely, MARM processes exactly fit arbitrary multi-dimensional empirical histograms and approximately fit the leading empirical autocorrelations and cross-correlations functions. This ability appears to make the MARM modeling methodology unique in its goal of fitting a model to such a class of strong statistical signatures. Furthermore, the thesis proposes practical MARM modeling and forecasting methodologies of considerable generality, suitable for implementation on a computer. We demonstrate the efficacy of these methodologies with an example of a three-dimension time series vector, using a software environment, called MultiArmLab, which supports MARM modeling and forecasting.

Multivariate Autoregressive Modular Processes

Gang Li

Heng Tao Shen

Ye Yuan

Xiaoyang Wang

Huawen Liu

This two-volume set of LNAI 12274 and LNAI 12275 constitutes the refereed proceedings of the 13th International Conference on Knowledge Science, Engineering and Management, KSEM 2020, held in Hangzhou, China, in August 2020.* The 58 revised full papers and 27 short papers were carefully reviewed and selected from 291 submissions. The papers of the first volume are organized in the following topical sections: knowledge graph; knowledge representation; knowledge management for education; knowledge-based systems; and data processing and mining. The papers of the second volume are organized in the following topical sections: machine learning; recommendation algorithms and systems; social knowledge analysis and management; text mining and document analysis; and deep learning. *The conference was held virtually due to the COVID-19 pandemic.

Xiang Zhao

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