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We consider the estimation of the state transition matrix in vectorautoregressive models, when time sequence data is limited but nonsequencesteady-state data is abundant. To leverage both sources of data, we formulatethe least squares minimization problem regularized by a Lyapunov penalty. Weimpose cardinality or rank constraints to reduce the complexity of theautoregressive model. We solve the resulting nonconvex, nonsmooth problem byusing the proximal alternating linearization method (PALM). We show that PALMis globally convergent to a critical point and that the estimation errormonotonically decreases. Furthermore, we obtain explicit formulas for theproximal operators to facilitate the implementation of PALM. We demonstrate theeffectiveness of the developed method on synthetic and real-world data. Ourexperiments show that PALM outperforms the gradient projection method in bothcomputational efficiency and solution quality.

Learning Low-Complexity Autoregressive Models via Proximal Alternating Minimization