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Scalable and Privacy-aware Online Learning of Nonlinear Structural Equation Models
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  • Rohan Money ,
  • Joshin P. Krishnan ,
  • Baltasar Beferull-Lozano ,
  • Elvin Isufi
Rohan Money
University of Agder

Corresponding Author:[email protected]

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Joshin P. Krishnan
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Baltasar Beferull-Lozano
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Elvin Isufi
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Abstract

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.
2023Published in IEEE Open Journal of Signal Processing volume 4 on pages 61-70. 10.1109/OJSP.2023.3241580