Unsupervised Generative Modeling Using Matrix Product States

By Zhaoyu Han, Jun Wang, Heng Fan, Lei Wang, Pan Zhang. Physical Review X, 2017

313 citations recorded by the source corpus.

Generative modeling, which learns joint probability distribution from 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 analogous to the density matrix renormalization group method, which allows dynamically adjusting dimensions of the tensors and offers an efficient direct sampling approach for generative tasks. We apply our method to generative modeling of several standard datasets including the Bars and Stripes, random binary patterns and the MNIST handwritten digits to illustrate the abilities, features and drawbacks of our model over popular generative models such as Hopfield model, Boltzmann machines and generative adversarial networks. Our work sheds light on many interesting directions of future exploration on the development of quantum-inspired algorithms for unsupervised machine learning, which are promisingly possible to be realized on quantum devices.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/5ed4617d39833a8dd8e931282ca2fcee136db634

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Citations in the corpus

Parameterized quantum circuits as machine learning models (2019, background): “[72] Zhao-Yu Han, Jun Wang, Heng Fan, Lei Wang, and”
Towards quantum machine learning with tensor networks (2018, background): “With classical resources, tensor network models already give very good results for supervised [12, 13, 15, 17] and unsupervised [17, 19] learning tasks.”
A high-bias, low-variance introduction to Machine Learning for physicists (2018, unknown): “, 2017), and generative models based on matrix product states have been developed (Han et al., 2017).”
A generative modeling approach for benchmarking and training shallow quantum circuits (2018, methodology): “Previous implementations of Born machines [25–28] often relied on the construction of tensor networks and their efficient manipulation through graphical-processing units.”