Scalable and Privacy-Aware Online Learning of Nonlinear Structural Equation Models

Rohan Money*, Joshin Krishnan, Baltasar Beferull-Lozano, Elvin Isufi

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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An online topology estimation algorithm for nonlinear structural equation models (SEM) is proposed in this paper, addressing the nonlinearity and the non-stationarity of real-world systems. The nonlinearity is modeled using kernel formulations, and the curse of dimensionality associated with the kernels is mitigated using random feature approximation. The online learning strategy uses a group-lasso-based optimization framework with a prediction-corrections technique that accounts for the model evolution. The proposed approach has three properties of interest. First, it enjoys node-separable learning, which allows for scalability in large networks. Second, it offers privacy in SEM learning by replacing the actual data with node-specific random features. Third, its performance can be characterized theoretically via a dynamic regret analysis, showing that it is possible to obtain a linear dynamic regret bound under mild assumptions. Numerical results with synthetic and real data corroborate our findings and show competitive performance w.r.t. state-of-the-art alternatives.
Original languageEnglish
Pages (from-to)61-70
Number of pages10
JournalIEEE Open Journal of Signal Processing
Publication statusPublished - 2023


  • Network topology inference
  • time-varying graph learning
  • structural equation models
  • random feature approximation


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