mlsanityData to 7 Oct 2026

Tensor-Train Density Estimation

arXiv 2108.00089 ↗First posted 30 Jul 2021cs.LG cs.AI stat.MLcited by 30

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Abstract (arXiv)

Estimation of probability density function from samples is one of the central problems in statistics and machine learning. Modern neural network-based models can learn high dimensional distributions but have problems with hyperparameter selection and are often prone to instabilities during training and inference. We propose a new efficient tensor train-based model for density estimation (TTDE). Such density parametrization allows exact sampling, calculation of cumulative and marginal density functions, and partition function. It also has very intuitive hyperparameters. We develop an efficient non-adversarial training procedure for TTDE based on the Riemannian optimization. Experimental results demonstrate the competitive performance of the proposed method in density estimation and sampling tasks, while TTDE significantly outperforms competitors in training speed.

Key facts. Cited by 30 papers in the map (data through 7 Oct 2026). Builds on 15 of its 29 references that are in the map. First posted on arXiv 30 Jul 2021.

Builds on

15 of 29 references.

References · 15

  1. 2013Auto-Encoding Variational Bayescited by 3,980
  2. 2016Density estimation using Real NVPcited by 2,029
  3. 2018Glow: Generative Flow with Invertible 1x1 Convolutionscited by 1,539
  4. 2016Pixel Recurrent Neural Networkscited by 814
  5. 2017Masked Autoregressive Flow for Density Estimationcited by 680
  6. 2018FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Modelscited by 584
  7. 2020Glow-TTS: A Generative Flow for Text-to-Speech via Monotonic Alignment Searchcited by 269
  8. 2015On the Expressive Power of Deep Learning: A Tensor Analysiscited by 97
  9. 2019Block Neural Autoregressive Flowcited by 62
  10. 2017Expressive power of recurrent neural networkscited by 30
  11. 2019Nonparametric Density Estimation for High-Dimensional Data - Algorithms and Applicationscited by 18
  12. 2017Tensors, Learning, and 'Kolmogorov Extension' for Finite-alphabet Random Vectorscited by 16
3 more
  1. 2020Low-rank Characteristic Tensor Density Estimation Part I: Foundationscited by 15
  2. 2019Learning Mixtures of Smooth Product Distributions: Identifiability and Algorithmcited by 14
  3. 2018Black-Box Autoregressive Density Estimation for State-Space Modelscited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 7; 2023: 7; 2024: 11; 2025: 3; 2026: 2.

30 papers.

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  1. 2023Subtractive Mixture Models via Squaring: Representation and Learningcited by 39
  2. 2024What is the Relationship between Tensor Factorizations and Circuits (and How Can We Exploit it)?cited by 22
  3. 2023How to Turn Your Knowledge Graph Embeddings into Generative Modelscited by 20
  4. 2024On the Relationship Between Monotone and Squared Probabilistic Circuitscited by 14
  5. 2022Generative modeling via tensor train sketchingcited by 13
  6. 2022Permutation Search of Tensor Network Structures via Local Samplingcited by 13
  7. 2024EigenVI: score-based variational inference with orthogonal function expansionscited by 11
  8. 2023Generative Learning of Continuous Data by Tensor Networkscited by 9
  9. 2023Generative Modeling via Hierarchical Tensor Sketchingcited by 8
  10. 2024Guaranteed Nonconvex Factorization Approach for Tensor Train Recoverycited by 8
  11. 2025SHAP Meets Tensor Networks: Provably Tractable Explanations with Parallelismcited by 8
  12. 2025How to Square Tensor Networks and Circuits Without Squaring Themcited by 5
18 more
  1. 2022High-dimensional density estimation with tensorizing flowcited by 4
  2. 2024Coarse-To-Fine Tensor Trains for Compact Visual Representationscited by 4
  3. 2023Sample Complexity Using Infinite Multiview Modelscited by 3
  4. 2024Efficient Nonparametric Tensor Decomposition for Binary and Count Datacited by 3
  5. 2024Language Modeling Using Tensor Trainscited by 3
  6. 2022Tensor Train for Global Optimization Problems in Roboticscited by 2
  7. 2023TERM Model: Tensor Ring Mixture Model for Density Estimationcited by 2
  8. 2024On Faster Marginalization with Squared Circuits via Orthonormalizationcited by 2
  9. 2022Error Analysis of Tensor-Train Cross Approximationcited by 1
  10. 2022Deep importance sampling using tensor trains with application to a priori and a posteriori rare event estimationcited by 1
  11. 2023Tensorizing flows: a tool for variational inferencecited by 1
  12. 2022Counting Phases and Faces Using Bayesian Thermodynamic Integrationcited by 0
  13. 2024Tensor-Train Point Cloud Compression and Efficient Approximate Nearest-Neighbor Searchcited by 0
  14. 2024Joint Bayesian Parameter and Model Order Estimation for Low-Rank Probability Mass Tensorscited by 0
  15. 2024Tensor Network Estimation of Distribution Algorithmscited by 0
  16. 2025Explaining Anomalies with Tensor Networkscited by 0
  17. 2026On the Approximation Complexity of Matrix Product Operator Born Machinescited by 0
  18. 2026QuanVI: Score-based Variational Inference via Quantum Maximally Mixed Statescited by 0