  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.
