Modeling the joint distribution of high-dimensional data is a central task in unsupervised machine learning. In recent years, many interests have been attracted to developing learning models based on tensor networks, which have the advantages of a principle understanding of the expressive power using entanglement properties, and as a bridge connecting classical computation and quantum computation. Despite the great potential, however, existing tensor network models for unsupervised machine learning only work as a proof of principle, as their performance is much worse than the standard models such as restricted Boltzmann machines and neural networks. In this Letter, we present autoregressive matrix product states (AMPS), a tensor network model combining matrix product states from quantum many-body physics and autoregressive modeling from machine learning. Our model enjoys the exact calculation of normalized probability and unbiased sampling. We demonstrate the performance of our model using two applications, generative modeling on synthetic and real-world data, and reinforcement learning in statistical physics. Using extensive numerical experiments, we show that the proposed model significantly outperforms the existing tensor network models and the restricted Boltzmann machines, and is competitive with state-of-the-art neural network models.

翻译：对高维数据联合分布进行建模是无监督机器学习的核心任务。近年来，基于张量网络的学习模型因其利用纠缠性质原则性理解表达能力，以及作为连接经典计算与量子计算的桥梁而备受关注。然而，尽管潜力巨大，现有用于无监督机器学习的张量网络模型仅起到原理验证作用，其性能远逊于受限玻尔兹曼机和神经网络等标准模型。本文提出自回归矩阵乘积态（AMPS），一种结合量子多体物理矩阵乘积态与机器学习自回归建模的张量网络模型。该模型可实现归一化概率的精确计算与无偏采样。我们通过生成建模（针对合成数据与真实数据）和统计物理中的强化学习两个应用验证模型性能。大量数值实验表明，所提模型显著优于现有张量网络模型及受限玻尔兹曼机，并能与最先进的神经网络模型相媲美。