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Graph-Regularized Tensor Regression: A Domain-Aware Framework for Interpretable Multi-Way Financial Modelling

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  • Yao Lei Xu
  • Kriton Konstantinidis
  • Danilo P. Mandic

Abstract

Analytics of financial data is inherently a Big Data paradigm, as such data are collected over many assets, asset classes, countries, and time periods. This represents a challenge for modern machine learning models, as the number of model parameters needed to process such data grows exponentially with the data dimensions; an effect known as the Curse-of-Dimensionality. Recently, Tensor Decomposition (TD) techniques have shown promising results in reducing the computational costs associated with large-dimensional financial models while achieving comparable performance. However, tensor models are often unable to incorporate the underlying economic domain knowledge. To this end, we develop a novel Graph-Regularized Tensor Regression (GRTR) framework, whereby knowledge about cross-asset relations is incorporated into the model in the form of a graph Laplacian matrix. This is then used as a regularization tool to promote an economically meaningful structure within the model parameters. By virtue of tensor algebra, the proposed framework is shown to be fully interpretable, both coefficient-wise and dimension-wise. The GRTR model is validated in a multi-way financial forecasting setting and compared against competing models, and is shown to achieve improved performance at reduced computational costs. Detailed visualizations are provided to help the reader gain an intuitive understanding of the employed tensor operations.

Suggested Citation

  • Yao Lei Xu & Kriton Konstantinidis & Danilo P. Mandic, 2022. "Graph-Regularized Tensor Regression: A Domain-Aware Framework for Interpretable Multi-Way Financial Modelling," Papers 2211.05581, arXiv.org.
  • Handle: RePEc:arx:papers:2211.05581
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    References listed on IDEAS

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    1. Dat Thanh Tran & Martin Magris & Juho Kanniainen & Moncef Gabbouj & Alexandros Iosifidis, 2017. "Tensor Representation in High-Frequency Financial Data for Price Change Prediction," Papers 1709.01268, arXiv.org, revised Nov 2017.
    2. Hua Zhou & Lexin Li & Hongtu Zhu, 2013. "Tensor Regression with Applications in Neuroimaging Data Analysis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 540-552, June.
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