Distributed Sparse Identification in Multivariate Stochastic Regression Model under Colored Noise

This paper investigates the distributed sparse identification problem in multivariate stochastic regression models under colored noise. A novel distributed extended least squares algorithm is proposed based on the [Formula: see text]-regularization, enhanced by a two-stage estimation scheme to promote sparsity. In the first stage, initial estimates of the sparse parameter matrix are obtained by locally applying an extended least squares method with information exchange among neighboring agents. In the second stage, these estimates are refined by minimizing a local cost function that combines cumulative estimation errors with an adaptively weighted [Formula: see text]-regularization term. Under the weakest possible cooperative nonpersistent excitation condition, the proposed algorithm establishes the set convergence of zero elements with a finite number of observations and the almost sure convergence of nonzero elements. Moreover, the prediction accuracy is characterized by analyzing the upper bound of the accumulated regret without any excitation conditions. These theoretical results effectively address the challenge of distributed sparse parameter identification under nonindependent and nonstationary observation sequences and enable the application of the proposed method to stochastic systems with feedback loops.