  Uncertainty quantification based on stochastic spectral methods suffers from
the curse of dimensionality. This issue was mitigated recently by low-rank
tensor methods. However, there exist two fundamental challenges in low-rank
tensor-based uncertainty quantification: how to automatically determine the
tensor rank and how to pick the simulation samples. This paper proposes a novel
tensor regression method to address these two challenges. Our method uses an
$\ell_{q}/ \ell_{2}$-norm regularization to determine the tensor rank and an
estimated Voronoi diagram to pick informative samples for simulation. The
proposed framework is verified by a 19-dim phonics bandpass filter and a 57-dim
CMOS ring oscillator, capturing the high-dimensional uncertainty well with only
90 and 290 samples respectively.
