mlsanityData to 7 Oct 2026

Generative Modeling via Tree Tensor Network States

arXiv 2209.01341 ↗First posted 3 Sep 2022stat.ML cs.LG quant-phcited by 5

Not on the map. Why?

Abstract (arXiv)

In this paper, we present a density estimation framework based on tree tensor-network states. The proposed method consists of determining the tree topology with Chow-Liu algorithm, and obtaining a linear system of equations that defines the tensor-network components via sketching techniques. Novel choices of sketch functions are developed in order to consider graphical models that contain loops. Sample complexity guarantees are provided and further corroborated by numerical experiments.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 16 of its 40 references that are in the map. First posted on arXiv 3 Sep 2022.

Builds on

16 of 40 references.

References · 16

  1. 2022Generative Adversarial Networkscited by 5,603
  2. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  3. 2013Auto-Encoding Variational Bayescited by 3,980
  4. 2015Variational Inference with Normalizing Flowscited by 2,161
  5. 2018Barren plateaus in quantum neural network training landscapescited by 624
  6. 2015An Introduction to Matrix Concentration Inequalitiescited by 391
  7. 2014Sketching as a Tool for Numerical Linear Algebracited by 285
  8. 2020Spectral Methods for Data Science: A Statistical Perspectivecited by 111
  9. 2017Unsupervised Generative Modeling Using Matrix Product Statescited by 87
  10. 2014A statistical model for tensor PCAcited by 72
  11. 2019Tree Tensor Networks for Generative Modelingcited by 63
  12. 2019Expressive power of tensor-network factorizations for probabilistic modeling, with applications from hidden Markov models to quantum machine learningcited by 55
4 more
  1. 2020Near-Optimal Learning of Tree-Structured Distributions by Chow-Liucited by 20
  2. 2019Modeling Sequences with Quantum States: A Look Under the Hoodcited by 19
  3. 2016Learning a Tree-Structured Ising Model in Order to Make Predictionscited by 14
  4. 2022Generative modeling via tensor train sketchingcited by 13

Built on by

Cited by year

Citing papers per year: 2022: 1; 2023: 2; 2024: 0; 2025: 2.

5 papers.

  1. 2023Generative Modeling via Hierarchical Tensor Sketchingcited by 8
  2. 2022High-dimensional density estimation with tensorizing flowcited by 4
  3. 2025Tensorization of neural networks for improved privacy and interpretabilitycited by 3
  4. 2025Plastic tensor networks for interpretable generative modelingcited by 1
  5. 2023Combining Monte Carlo and Tensor-network Methods for Partial Differential Equations via Sketchingcited by 0