Unsupervised Generative Modeling Using Matrix Product States

Generative modeling, which learns joint probability distribution from training data and generates samples according to it, is an important task in machine learning and artificial intelligence. Inspired by probabilistic interpretation of quantum physics, we propose a generative model using matrix product states, which is a tensor network originally proposed for describing (particularly one-dimensional) entangled quantum states. Our model enjoys efficient learning by utilizing the density matrix renormalization group method which allows dynamic adjusting dimensions of the tensors, and offers an efficient direct sampling approach, Zipper, for generative tasks. We apply our method to generative modeling of several standard datasets including the principled Bars and Stripes, random binary patterns and the MNIST handwritten digits, to illustrate ability of our model, and discuss features as well as drawbacks of our model over popular generative models such as Hopfield model, Boltzmann machines and generative adversarial networks. Our work shed light on many interesting directions for future exploration on the development of quantum-inspired algorithms for unsupervised machine learning, which is of possibility of being realized by a quantum device.