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

• URL: http://arxiv.org/abs/2511.13514v1
• Date: Mon, 17 Nov 2025 15:49:17 GMT
• Title: A Quantum Tensor Network-Based Viewpoint for Modeling and Analysis of Time Series Data
• Abstract summary: We propose a novel quantum physics-based white box'' method that offers both accurate uncertainty quantification and enhanced interpretability.<n>By mapping the kernel mean embedding (KME) of a time series data vector to a reproducing a kernel Hilbert space (RKHS), we construct a tensor network-inspired 1D spin chain Hamiltonian.<n>We then solve the associated Schrdinger equation and apply perturbation theory to quantify uncertainty, thereby improving the interpretability of tasks performed with the quantum tensor network-based model.
• Score: 0.8399688944263844
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 Schr{ö}dinger 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.

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