论文标题
高维密度估计随张力流量
High-dimensional density estimation with tensorizing flow
论文作者
论文摘要
我们提出了一种量化流量方法，用于估计观察到的数据的高维概率密度函数。该方法基于张量训练和基于流量的生成建模。我们的方法首先通过基于低维边缘的核密度估计量从线性系统中求解张量芯在张量形式中有效构建近似密度。然后，我们通过执行最大似然估计来训练从该张量训练密度到观察到的经验分布的连续时间流模型。提出的方法将张量训练的无优化特征与基于流量的生成模型的灵活性相结合。包括数值结果以证明所提出的方法的性能。
We propose the tensorizing flow method for estimating high-dimensional probability density functions from the observed data. The method is based on tensor-train and flow-based generative modeling. Our method first efficiently constructs an approximate density in the tensor-train form via solving the tensor cores from a linear system based on the kernel density estimators of low-dimensional marginals. We then train a continuous-time flow model from this tensor-train density to the observed empirical distribution by performing a maximum likelihood estimation. The proposed method combines the optimization-less feature of the tensor-train with the flexibility of the flow-based generative models. Numerical results are included to demonstrate the performance of the proposed method.
