Generative modeling, which learns joint probability distribution fromtraining data and generates samples according to it, is an important task inmachine learning and artificial intelligence. Inspired by probabilisticinterpretation of quantum physics, we propose a generative model using matrixproduct states, which is a tensor network originally proposed for describing(particularly one-dimensional) entangled quantum states. Our model enjoysefficient learning by utilizing the density matrix renormalization group methodwhich allows dynamic adjusting dimensions of the tensors, and offers anefficient direct sampling approach, Zipper, for generative tasks. We apply ourmethod to generative modeling of several standard datasets including theprincipled Bars and Stripes, random binary patterns and the MNIST handwrittendigits, to illustrate ability of our model, and discuss features as well asdrawbacks of our model over popular generative models such as Hopfield model,Boltzmann machines and generative adversarial networks. Our work shed light onmany interesting directions for future exploration on the development ofquantum-inspired algorithms for unsupervised machine learning, which is ofpossibility of being realized by a quantum device.
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