Block Toeplitz Sparse Precision Matrix Estimation for Large-Scale Interval-Valued Time Series Forecasting

2025-04-04

AI Summary

Scalable and efficient modeling of large-scale interval-valued time series (ITS) remains challenging due to structural complexity and high dimensionality. Method: This paper proposes an automatic segmentation-and-clustering-driven feature extraction framework. It formulates ITS structural learning as a block Toeplitz sparse precision matrix estimation problem—the first such formulation for ITS. Within a Majorization-Minimization (MM) framework, we design a provably convergent alternating optimization scheme integrating dynamic programming and the Alternating Direction Method of Multipliers (ADMM). Furthermore, we incorporate joint recurrence plots (JRPs) for image-based ITS representation and leverage transfer learning to achieve robust, invariant feature extraction. Contribution/Results: Experiments on real-world datasets demonstrate substantial improvements in forecasting accuracy. The framework delivers a scalable, interpretable, and high-performance paradigm for large-scale ITS modeling and prediction, with theoretical convergence guarantees and practical efficacy.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Modeling and forecasting interval-valued time series (ITS) have attracted considerable attention due to their growing presence in various contexts. To the best of our knowledge, there have been no efforts to model large-scale ITS. In this paper, we propose a feature extraction procedure for large-scale ITS, which involves key steps such as auto-segmentation and clustering, and feature transfer learning. This procedure can be seamlessly integrated with any suitable prediction models for forecasting purposes. Specifically, we transform the automatic segmentation and clustering of ITS into the estimation of Toeplitz sparse precision matrices and assignment set. The majorization-minimization algorithm is employed to convert this highly non-convex optimization problem into two subproblems. We derive efficient dynamic programming and alternating direction method to solve these two subproblems alternately and establish their convergence properties. By employing the Joint Recurrence Plot (JRP) to image subsequence and assigning a class label to each cluster, an image dataset is constructed. Then, an appropriate neural network is chosen to train on this image dataset and used to extract features for the next step of forecasting. Real data applications demonstrate that the proposed method can effectively obtain invariant representations of the raw data and enhance forecasting performance.

Problem

• Estimating Toeplitz sparse precision matrices for large-scale interval-valued time series
• Developing feature extraction via auto-segmentation, clustering, and transfer learning
• Enhancing forecasting performance using invariant representations and neural networks

Innovation

• Block Toeplitz sparse precision matrix estimation
• Dynamic programming and ADMM for optimization
• Joint Recurrence Plot for feature extraction