A Quantum Tensor Network-Based Viewpoint for Modeling and Analysis of Time Series Data

Pragatheeswaran Vipulananthan, Kamal Premaratne, Dilip Sarkar, Manohar N. Murthi

Abstract: Accurate uncertainty quantification is a critical challenge in machine learning. While neural networks are highly versatile and capable of learning complex patterns, they often lack interpretability due to their "black box" nature. On the other hand, probabilistic "white box" models, though interpretable, often suffer from a significant performance gap when compared to neural networks. To address this, we propose a novel quantum physics-based "white box" method that offers both accurate uncertainty quantification and enhanced interpretability. By mapping the kernel mean embedding (KME) of a time series data vector to a reproducing kernel Hilbert space (RKHS), we construct a tensor network-inspired 1D spin chain Hamiltonian, with the KME as one of its eigen-functions or eigen-modes. We then solve the associated Schrödinger equation and apply perturbation theory to quantify uncertainty, thereby improving the interpretability of tasks performed with the quantum tensor network-based model. We demonstrate the effectiveness of this methodology, compared to state-of-the-art "white box" models, in change point detection and time series clustering, providing insights into the uncertainties associated with decision-making throughout the process.