Interpretability of Matrix-variate Gaussian Processes with Kernels Structured using Kronecker Sum for Prediction of Vehicle Battery State of Charge

Abstract

This paper proposes a novel structured kernel that enhances the interpretability of a matrix-variate Gaussian process model for multi-step-ahead prediction of vehicle battery state of charge (SOC). Whereas conventional Kronecker-product structures mix contributions along the row and column directions of matrix data, making it difficult to separate those features, the proposed method employs a Kronecker sum to decompose the kernel matrix into distinct row and column components. As a result, the correlation structures in the row and column can each be interpreted independently. Experiments using real data from 100 vehicles show that the proposed model achieves superior prediction accuracy compared to both a baseline model and a Kronecker-product-based model. Furthermore, clustering based on the column kernel reveals meaningful vehicle groups characterized by their day-of-week usage patterns.