Unsupervised Generative Modeling Using Matrix Product States

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 stat...

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Published in:Physical review. X Vol. 8; no. 3; p. 031012
Main Authors: Han, Zhao-Yu, Wang, Jun, Fan, Heng, Wang, Lei, Zhang, Pan
Format: Journal Article
Language:English
Published: College Park American Physical Society 01.07.2018
Subjects:
Algorithms
Allocations
Artificial intelligence
Datasets
Entangled states
Generative adversarial networks
Handwriting
Machine learning
Mathematical models
Modelling
Parameters
Probability distribution
Probability theory
Quantum computing
Quantum phenomena
Quantum physics
Quantum theory
Representations
Samples
Sampling
Standard data
Statistical analysis
Statistical methods
Tensors
ISSN:2160-3308, 2160-3308
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Abstract 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 data sets 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 the Hopfield model, Boltzmann machines, and generative adversarial networks. Our work sheds light on many interesting directions of future exploration in the development of quantum-inspired algorithms for unsupervised machine learning, which are promisingly possible to realize on quantum devices.
AbstractList 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 data sets 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 the Hopfield model, Boltzmann machines, and generative adversarial networks. Our work sheds light on many interesting directions of future exploration in the development of quantum-inspired algorithms for unsupervised machine learning, which are promisingly possible to realize on quantum devices.
ArticleNumber 031012
Author Zhang, Pan
Wang, Lei
Han, Zhao-Yu
Wang, Jun
Fan, Heng
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  fullname: Zhang, Pan
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  year: 2016
  ident: PhysRevX.8.031012Cc37R1
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Snippet Generative modeling, which learns joint probability distribution from data and generates samples according to it, is an important task in machine learning and...
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StartPage 031012
SubjectTerms Algorithms
Allocations
Artificial intelligence
Datasets
Entangled states
Generative adversarial networks
Handwriting
Machine learning
Mathematical models
Modelling
Parameters
Probability distribution
Probability theory
Quantum computing
Quantum phenomena
Quantum physics
Quantum theory
Representations
Samples
Sampling
Standard data
Statistical analysis
Statistical methods
Tensors
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Title Unsupervised Generative Modeling Using Matrix Product States
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