Title: Scalable Estimation of Bidirectional Causal Influences via Large-Scale Online Kernel Learning

Abstract:

This research introduces a scalable online kernel learning framework designed to estimate bidirectional causal effects within systems defined by mutual dependence and heteroskedasticity. While conventional causal inference typically prioritizes unidirectional impacts, this approach addresses the prevalent bidirectional dynamics found in real-world scenarios. Leveraging identification strategies based on heteroskedasticity, the method synthesizes a quasi-maximum likelihood estimator for simultaneous equation models with large-scale online kernel learning. To accurately capture nonlinear conditional means and variances, the framework utilizes random Fourier feature approximations. Furthermore, an adaptive online gradient descent algorithm is implemented to maintain computational efficiency when processing high-dimensional and streaming data. Extensive simulations reveal that the proposed technique outperforms baselines based on single equations and polynomial approximations, delivering enhanced accuracy and stability with reduced bias and root mean squared error across diverse data-generating processes. These findings validate the approach’s capacity to model intricate bidirectional causal relationships with near-linear computational scaling. By merging econometric identification principles with contemporary machine learning methodologies, this framework provides a practical, scalable, and theoretically robust solution for large-scale causal inference in fields ranging from natural and social sciences to policy development, business, and industrial operations.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC