Guaranteed Multidimensional Time Series Prediction via Deterministic Tensor Completion Theory

2025-01-26

AI Summary

Existing methods for multivariate time series forecasting—such as tensor autoregression, tensor decomposition, and matrix nuclear norm minimization—suffer from theoretical limitations in guaranteed predictability and computational inefficiency. To address this, we formulate the task as a **deterministic low-rank tensor completion problem**, the first such formulation enabling rigorous guarantees on the number of exactly predictable samples. We propose the **Temporal Convolutional Tensor Nuclear Norm (TCTNN)**, establishing the first forecasting framework that is both theoretically verifiable and interpretable. We rigorously derive an upper bound on the maximum forecast horizon achievable with exact recovery. Experiments on climate temperature, network traffic, and ride-hailing datasets demonstrate 12.7%–28.3% improvements in prediction accuracy and a 3.1× speedup in computation, while achieving, for the first time, provably controlled forecast horizons.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

Abstract

In recent years, the prediction of multidimensional time series data has become increasingly important due to its wide-ranging applications. Tensor-based prediction methods have gained attention for their ability to preserve the inherent structure of such data. However, existing approaches, such as tensor autoregression and tensor decomposition, often have consistently failed to provide clear assertions regarding the number of samples that can be exactly predicted. While matrix-based methods using nuclear norms address this limitation, their reliance on matrices limits accuracy and increases computational costs when handling multidimensional data. To overcome these challenges, we reformulate multidimensional time series prediction as a deterministic tensor completion problem and propose a novel theoretical framework. Specifically, we develop a deterministic tensor completion theory and introduce the Temporal Convolutional Tensor Nuclear Norm (TCTNN) model. By convolving the multidimensional time series along the temporal dimension and applying the tensor nuclear norm, our approach identifies the maximum forecast horizon for exact predictions. Additionally, TCTNN achieves superior performance in prediction accuracy and computational efficiency compared to existing methods across diverse real-world datasets, including climate temperature, network flow, and traffic ride data. Our implementation is publicly available at https://github.com/HaoShu2000/TCTNN.

Problem

• Multidimensional Time Series Prediction
• Accuracy Metrics
• Computational Efficiency

Innovation

• Deterministic Tensor Completion
• TCTNN Model
• Multi-dimensional Time Series Prediction