# Generative Modeling via Tree Tensor Network States

arXiv: https://arxiv.org/abs/2209.01341 · HTML: https://mlsanity.com/paper/2209.01341/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 40 references that are in the map.
- First posted on arXiv 3 Sep 2022.

## Builds on (most cited first, 16 of 16)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [An Introduction to Matrix Concentration Inequalities](https://mlsanity.com/paper/1501.01571/) (2015)
- [Sketching as a Tool for Numerical Linear Algebra](https://mlsanity.com/paper/1411.4357/) (2014)
- [Spectral Methods for Data Science: A Statistical Perspective](https://mlsanity.com/paper/2012.08496/) (2020)
- [Unsupervised Generative Modeling Using Matrix Product States](https://mlsanity.com/paper/1709.01662/) (2017)
- [A statistical model for tensor PCA](https://mlsanity.com/paper/1411.1076/) (2014)
- [Tree Tensor Networks for Generative Modeling](https://mlsanity.com/paper/1901.02217/) (2019)
- [Expressive power of tensor-network factorizations for probabilistic modeling, with applications from hidden Markov models to quantum machine learning](https://mlsanity.com/paper/1907.03741/) (2019)
- [Near-Optimal Learning of Tree-Structured Distributions by Chow-Liu](https://mlsanity.com/paper/2011.04144/) (2020)
- [Modeling Sequences with Quantum States: A Look Under the Hood](https://mlsanity.com/paper/1910.07425/) (2019)
- [Learning a Tree-Structured Ising Model in Order to Make Predictions](https://mlsanity.com/paper/1604.06749/) (2016)
- [Generative modeling via tensor train sketching](https://mlsanity.com/paper/2202.11788/) (2022)

## Built on by (most cited first, 5 of 5)

- [Generative Modeling via Hierarchical Tensor Sketching](https://mlsanity.com/paper/2304.05305/) (2023)
- [High-dimensional density estimation with tensorizing flow](https://mlsanity.com/paper/2212.00759/) (2022)
- [Tensorization of neural networks for improved privacy and interpretability](https://mlsanity.com/paper/2501.06300/) (2025)
- [Plastic tensor networks for interpretable generative modeling](https://mlsanity.com/paper/2504.06722/) (2025)
- [Combining Monte Carlo and Tensor-network Methods for Partial Differential Equations via Sketching](https://mlsanity.com/paper/2305.17884/) (2023)

## 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.