On Reducing the Coherence in Sparse System Identification

One of the major contributions to sparse learning has been to quantify how the correlation between the regressors affect the ability to recover a sparse parameter vector. Roughly, the inverse of the maximum correlation controls how many non-zero parameters can be exactly recovered from an under-determined system of equations. This result is of importance also in system identification where observations are noisy. Unfortunately, for such problems the regressors are highly correlated making sparse identification difficult. In this contribution we address this problem by applying a linear transformation to the regressors, selected in such a way that the correlation is reduced. The latter is achieved by formulating a constrained optimization problem which is solved using a proximal method. The method can be seen as a pre-processing step that can be used prior to any sparse estimation algorithm. Simulations are used to demonstrate the usefulness of the method.