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

You are here

Top Reasons to Join SPS Today!

1. IEEE Signal Processing Magazine
2. Signal Processing Digital Library*
3. Inside Signal Processing Newsletter
4. SPS Resource Center
5. Career advancement & recognition
6. Discounts on conferences and publications
7. Professional networking
8. Communities for students, young professionals, and women
9. Volunteer opportunities
10. Coming soon! PDH/CEU credits
Click here to learn more.

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

Rohan Money; Joshin Krishnan; Baltasar Beferull-Lozano; Elvin Isufi

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.


Structural Equation Models (SEM) are a prevalent tool to model interactions in real-world networks due to their simplicity and ability to express instantaneous directed relationships between interacting entities [1][2][3]. The advantages of SEM over simple correlation-based models lie in leveraging the directionality, which is key to many applications, such as modeling the functional connectivity between brain regions [4] and interactions in financial networks [5], to name a few. SEM modeling and its topology estimation are challenging because real-life networks are large, dynamic, and comprise nonlinear interactions, as well as leveraging directly node-specific data may raise privacy concerns [1].

Although SEM-based topology est

SPS on Twitter

  • DEADLINE EXTENDED: The 2023 IEEE International Workshop on Machine Learning for Signal Processing is now accepting…
  • ONE MONTH OUT! We are celebrating the inaugural SPS Day on 2 June, honoring the date the Society was established in…
  • The new SPS Scholarship Program welcomes applications from students interested in pursuing signal processing educat…
  • CALL FOR PAPERS: The IEEE Journal of Selected Topics in Signal Processing is now seeking submissions for a Special…
  • Test your knowledge of signal processing history with our April trivia! Our 75th anniversary celebration continues:…

IEEE SPS Educational Resources

IEEE SPS Resource Center

IEEE SPS YouTube Channel