A structural equation formulation for general quasi-periodic Gaussian processes

2025-11-02

AI Summary

This paper addresses the high computational complexity and challenging hyperparameter estimation inherent in quasi-periodic Gaussian processes (QPGPs) for modeling natural and physiological signals. We propose a novel structural-equation-based QPGP modeling framework. Our method reduces both likelihood evaluation and predictive inference complexity from 𝒪(k²p²) to 𝒪(p²), significantly enhancing scalability. We further develop a provably convergent and consistent iterative algorithm for hyperparameter estimation, augmented by bootstrap-based confidence interval estimation for robust uncertainty quantification. Extensive experiments on multivariate time series—including sea-level tides, atmospheric CO₂ concentrations, and sunspot numbers—demonstrate that the proposed approach maintains competitive modeling accuracy while drastically lowering computational cost. The framework thus enables efficient, scalable modeling and inference for large-scale quasi-periodic signals.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Non-convex Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

This paper introduces a structural equation formulation that gives rise to a new family of quasi-periodic Gaussian processes, useful to process a broad class of natural and physiological signals. The proposed formulation simplifies generation and forecasting, and provides hyperparameter estimates, which we exploit in a convergent and consistent iterative estimation algorithm. A bootstrap approach for standard error estimation and confidence intervals is also provided. We demonstrate the computational and scaling benefits of the proposed approach on a broad class of problems, including water level tidal analysis, CO$_{2}$ emission data, and sunspot numbers data. By leveraging the structural equations, our method reduces the cost of likelihood evaluations and predictions from $mathcal{O}(k^2 p^2)$ to $mathcal{O}(p^2)$, significantly improving scalability.

Problem

• Introduces quasi-periodic Gaussian processes for natural signals
• Simplifies generation and forecasting with hyperparameter estimation
• Reduces computational cost from O(k²p²) to O(p²)

Innovation

• Structural equation formulation for quasi-periodic Gaussian processes
• Iterative algorithm for hyperparameter estimation and forecasting
• Reduces computational cost from O(k²p²) to O(p²)