• Corpus ID: 235683103

Probabilistic Graphical Models and Tensor Networks: A Hybrid Framework

@article{Miller2021ProbabilisticGM,
  title={Probabilistic Graphical Models and Tensor Networks: A Hybrid Framework},
  author={Jacob Miller and Geoffrey Roeder and Tai-Danae Bradley},
  journal={ArXiv},
  year={2021},
  volume={abs/2106.15666}
}
We investigate a correspondence between two formalisms for discrete probabilistic modeling: probabilistic graphical models (PGMs) and tensor networks (TNs), a powerful modeling framework for simulating complex quantum systems. The graphical calculus of PGMs and TNs exhibits many similarities, with discrete undirected graphical models (UGMs) being a special case of TNs. However, more general probabilistic TN models such as Born machines (BMs) employ complex-valued hidden states to produce novel… 
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41 References

Quantum Tensor Networks, Stochastic Processes, and Weighted Automata

This work shows how stationary or uniform versions of popular quantum tensor network models have equivalent representations in the stochastic processes and weighted automata literature, in the limit of infinitely long sequences.

Expressive power of tensor-network factorizations for probabilistic modeling, with applications from hidden Markov models to quantum machine learning

This work provides a rigorous analysis of the expressive power of various tensor-network factorizations of discrete multivariate probability distributions, and introduces locally purified states (LPS), a new factorization inspired by techniques for the simulation of quantum systems with provably better expressive power than all other representations considered.

Tensor Networks for Probabilistic Sequence Modeling

A novel generative algorithm is introduced giving trained u-MPS the ability to efficiently sample from a wide variety of conditional distributions, each one defined by a regular expression, which permits the generation of richly structured text in a manner that has no direct analogue in current generative models.

Enhancing Generative Models via Quantum Correlations

This paper presents a parallel version of the Celada–Seiden cellular automaton that automates the very labor-intensive and therefore time-heavy and therefore expensive and expensive way of simulating quantum mechanics.

Unsupervised Generative Modeling Using Matrix Product States

This work proposes a generative model using matrix product states, which is a tensor network originally proposed for describing (particularly one-dimensional) entangled quantum states, and enjoys efficient learning analogous to the density matrix renormalization group method.

Quantum Graphical Models and Belief Propagation

Perfect Sampling with Unitary Tensor Networks

This work proposes perfect sampling schemes, with vanishing equilibration and autocorrelation times, for unitary tensor networks, namely, unitary versions of the matrix product state and tree tensor network (TTN), and the multiscale entanglement renormalization Ansatz (MERA).

Modeling sequences with quantum states: a look under the hood

An understanding of the extra information contained in the reduced densities allow us to examine the mechanics of this DMRG algorithm and study the generalization error of the resulting model.

Norm-Observable Operator Models

A novel variant of OOMs is proposed, called norm-observable operator models (NOOMs), which avoid the NPP by design, and it is proved that NOOMs capture all Markov chain (MC) describable processes.

Duality of Graphical Models and Tensor Networks

The duality between tensor networks and undirected graphical models with discrete variables is shown and it is shown that belief propagation corresponds to a known algorithm for tensor network contraction.