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:建模高维数据的共同分布是不受监督的机器学习的一项核心任务。近年来,许多兴趣被吸引到开发基于强力网络的学习模型上,这些模型具有利用缠绕特性对表达力进行原则性理解的优势,并且是连接古典计算和量量计算的一个桥梁。然而,尽管现有的无监督机器学习的强力网络模型作为原则的证明有很大潜力,但其性能比标准模型,如限制的波尔茨曼机器和神经网络要差得多。在本信中,我们介绍了自动反向矩阵产品州(AMPS),这是一种将量子多体物理学和机器学习的自动反向模型组合的矩阵产品国结合起来的强势网络模型。我们的模型享有对正常概率和不偏重的抽样的精确计算。我们用两种应用,即合成和现实世界数据的基因化模型模型,以及统计物理学的强化学习,来展示我们的模型的性能。我们通过广泛的数字实验,表明拟议的模型大大优于现有的高压网络模型和受限制的波尔茨曼机器,并且与州网络模型具有竞争力。