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In this paper, we propose a low-rank approximation method based on discreteleast-squares for the approximation of a multivariate function from random,noisy-free observations. Sparsity inducing regularization techniques are usedwithin classical algorithms for low-rank approximation in order to exploit thepossible sparsity of low-rank approximations. Sparse low-rank approximationsare constructed with a robust updated greedy algorithm which includes anoptimal selection of regularization parameters and approximation ranks usingcross validation techniques. Numerical examples demonstrate the capability ofapproximating functions of many variables even when very few functionevaluations are available, thus proving the interest of the proposed algorithmfor the propagation of uncertainties through complex computational models.

A least-squares method for sparse low rank approximation of multivariate functions