  This paper introduces an efficient sparse recovery approach for Polynomial
Chaos (PC) expansions, which promotes the sparsity by breaking the
dimensionality of the problem. The proposed algorithm incrementally explores
sub-dimensional expansions for a sparser recovery, and shows success when
removal of uninfluential parameters that results in a lower coherence for
measurement matrix, allows for a higher order and/or sparser expansion to be
recovered. The incremental algorithm effectively searches for the sparsest PC
approximation, and not only can it decrease the prediction error, it can also
reduce the dimensionality of PCE model. Four numerical examples are provided to
demonstrate the validity of the proposed approach. The results from these
examples show that the incremental algorithm substantially outperforms
conventional compressive sampling approaches for PCE, in terms of both solution
sparsity and prediction error.
