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Approximation and sampling of multivariate probability distributions in the tensor train decomposition. (arXiv:1810.01212v1 [math.NA])
来源于:arXiv
General multivariate distributions are notoriously expensive to sample from,
particularly the high-dimensional posterior distributions in PDE-constrained
inverse problems. This paper develops a sampler for arbitrary continuous
multivariate distributions that is based on low-rank surrogates in the
tensor-train format. We construct a tensor-train approximation to the target
probability density function using the cross interpolation, which requires a
small number of function evaluations. For sufficiently smooth distributions the
storage required for the TT approximation is moderate, scaling linearly with
dimension. The structure of the tensor-train surrogate allows efficient
sampling by the conditional distribution method. Unbiased estimates may be
calculated by correcting the transformed random seeds using a
Metropolis--Hastings accept/reject step. Moreover, one can use a more efficient
quasi-Monte Carlo quadrature that may be corrected either by a control-variate
strategy, or by importa 查看全文>>