In this paper we introduce a sketching algorithm for constructing a tensor train representation of a probability density from its samples. Our method deviates from the standard recursive SVD-based procedure for constructing a tensor train. Instead we formulate and solve a sequence of small linear systems for the individual tensor train cores. This approach can avoid the curse of dimensionality that threatens both the algorithmic and sample complexities of the recovery problem. Specifically, for Markov models, we prove that the tensor cores can be recovered with a sample complexity that is constant with respect to the dimension. Finally, we illustrate the performance of the method with several numerical experiments.

翻译：在本文中,我们引入了用于建造从样本中代表概率密度的高压列车的草图算法。 我们的方法偏离了用于建造高压列车的标准递归 SVD 程序。 相反,我们为单个高压列车核心制定和解决一个小线性系统的序列。 这种方法可以避免威胁恢复问题算法和样本复杂性的维度诅咒。 具体地说, 对于Markov 模型来说, 我们证明, 抗压列车核心可以用一个与维度相一致的样本复杂性来回收。 最后, 我们用几个数字实验来说明该方法的性能。