Robust Identification of Graph Structure

Partial correlations (PCs) and the related inverse covariance matrix adopted by graphical lasso, are widely applicable tools for learning graph connectivity given nodal observations. The resultant estimators however, can be sensitive to outliers. Robust approaches developed so far to cope with outliers do not (explicitly) account for nonlinear interactions possibly present among nodal processes. This can hurt the identification of graph connectivity, merely due to model mismatch. To overcome this limitation, a novel formulation of robust PC is introduced based on nonlinear kernel functions. The proposed scheme leverages robust ridge regression techniques, spectral Fourier feature based kernel approximants, and robust association measures. Numerical tests on synthetic and real data illustrate the potential of the novel approach.