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

TL;DR

This paper introduces a Graph-Regularized Tensor Regression framework that incorporates economic domain knowledge via graph Laplacian regularization, enabling interpretable, efficient, and improved multi-way financial modeling.

Contribution

The paper presents a novel tensor regression model that integrates domain knowledge through graph regularization, enhancing interpretability and performance in financial data analysis.

Findings

Improved forecasting accuracy over competing models

Reduced computational costs compared to traditional tensor models

Enhanced interpretability of model parameters

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.