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

2025-11-17

AI Summary

A fundamental trade-off exists in time-series modeling between the high accuracy but low interpretability of neural networks and the high interpretability yet poor performance of traditional white-box models. Method: This paper proposes an interpretable white-box framework integrating quantum physics and tensor networks. It maps time-series data into a reproducing kernel Hilbert space (RKHS) via kernel mean embedding, constructs a one-dimensional spin-chain Hamiltonian, solves the Schrödinger equation for uncertainty quantification, and incorporates perturbation theory to enhance robustness. Contribution/Results: The framework retains full analytical tractability while substantially narrowing the performance gap between white-box models and black-box neural networks. Experiments demonstrate superior performance over state-of-the-art white-box methods on change-point detection and time-series clustering—achieving high accuracy, explicit uncertainty modeling, and fully traceable decision processes—thereby establishing a new paradigm for trustworthy time-series analysis.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• Addresses uncertainty quantification in machine learning models
• Bridges interpretability gap between neural networks and probabilistic models
• Enhances time series analysis through quantum tensor networks

Innovation

• Quantum tensor network models time series data
• Mapping kernel mean embedding to Hilbert space
• Solving Schrödinger equation quantifies uncertainty