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In this work, we discuss the problem of approximating a multivariate function via ℓ_1 minimization method, using a random chosen sub-grid of the corresponding tensor grid of Gaussian points. The independent variables of the function are assumed to be random variables, and thus, the framework provides a non-intrusive way to construct the generalized polynomial chaos expansions, stemming from the motivating application of Uncertainty Quantification (UQ). We provide theoretical analysis on thearXiv:1602.00995v2 fatcat:75pfrhgz7jcxnlu6uae7pnvnhm