High-dimensional density estimation with tensorizing flow

Ren, Yinuo; Zhao, Hongli; Khoo, Yuehaw; Ying, Lexing

doi:10.1007/s40687-023-00395-x

High-dimensional density estimation with tensorizing flow

Journal Article · 21 June 2023 · Research in the Mathematical Sciences (Print)

DOI:https://doi.org/10.1007/s40687-023-00395-x· OSTI ID:2422101

^[1]; Zhao, Hongli; Khoo, Yuehaw; Ying, Lexing

OSTI

Not provided.

Research Organization:: Univ. of Chicago, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

DOE Contract Number:: SC0022232

OSTI ID:: 2422101

Journal Information:: Research in the Mathematical Sciences (Print), Journal Name: Research in the Mathematical Sciences (Print) Journal Issue: 3 Vol. 10; ISSN 2522-0144

Publisher:: SpringerOpen

Country of Publication:: United States

Language:: English

References (33)

Tensor Train Neighborhood Preserving Embedding Wang, Wenqi; Aggarwal, Vaneet; Aeron, Shuchin IEEE Transactions on Signal Processing, Vol. 66, Issue 10 https://doi.org/10.1109/TSP.2018.2816568	journal	May 2018
On the Best Rank-1 and Rank-( R ₁ , R ₂ ,. . ., R _N ) Approximation of Higher-Order Tensors De Lathauwer, Lieven; De Moor, Bart; Vandewalle, Joos SIAM Journal on Matrix Analysis and Applications, Vol. 21, Issue 4 https://doi.org/10.1137/S0895479898346995	journal	January 2000
Tensor Networks and Hierarchical Tensors for the Solution of High-Dimensional Partial Differential Equations Bachmayr, Markus; Schneider, Reinhold; Uschmajew, André Foundations of Computational Mathematics, Vol. 16, Issue 6 https://doi.org/10.1007/s10208-016-9317-9	journal	April 2016
Tree tensor networks for generative modeling Cheng, Song; Wang, Lei; Xiang, Tao Physical Review B, Vol. 99, Issue 15 https://doi.org/10.1103/PhysRevB.99.155131	journal	April 2019
Approximation and sampling of multivariate probability distributions in the tensor train decomposition Dolgov, Sergey; Anaya-Izquierdo, Karim; Fox, Colin Statistics and Computing, Vol. 30, Issue 3 https://doi.org/10.1007/s11222-019-09910-z	journal	November 2019
Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models Bond-Taylor, Sam; Leach, Adam; Long, Yang IEEE Transactions on Pattern Analysis and Machine Intelligence https://doi.org/10.1109/TPAMI.2021.3116668	journal	January 2021
TT-cross approximation for multidimensional arrays Oseledets, Ivan; Tyrtyshnikov, Eugene Linear Algebra and its Applications, Vol. 432, Issue 1 https://doi.org/10.1016/j.laa.2009.07.024	journal	January 2010
Generative Adversarial Networks are special cases of Artificial Curiosity (1990) and also closely related to Predictability Minimization (1991) Schmidhuber, Jürgen Neural Networks, Vol. 127 https://doi.org/10.1016/j.neunet.2020.04.008	journal	July 2020
The density matrix renormalization group in chemistry and molecular physics: Recent developments and new challenges Baiardi, Alberto; Reiher, Markus The Journal of Chemical Physics, Vol. 152, Issue 4 https://doi.org/10.1063/1.5129672	journal	January 2020
An introduction to the Ginzburg–Landau theory of phase transitions and nonequilibrium patterns Hohenberg, P. C.; Krekhov, A. P. Physics Reports, Vol. 572 https://doi.org/10.1016/j.physrep.2015.01.001	journal	April 2015
Hierarchical Singular Value Decomposition of Tensors Grasedyck, Lars SIAM Journal on Matrix Analysis and Applications, Vol. 31, Issue 4 https://doi.org/10.1137/090764189	journal	January 2010
A Multilinear Singular Value Decomposition De Lathauwer, Lieven; De Moor, Bart; Vandewalle, Joos SIAM Journal on Matrix Analysis and Applications, Vol. 21, Issue 4 https://doi.org/10.1137/S0895479896305696	journal	January 2000
Exponential Decay of Correlations Implies Area Law Brandão, Fernando G. S. L.; Horodecki, Michał Communications in Mathematical Physics, Vol. 333, Issue 2 https://doi.org/10.1007/s00220-014-2213-8	journal	November 2014
Stochastic Matrix Product States Temme, Kristan; Verstraete, Frank Physical Review Letters, Vol. 104, Issue 21 https://doi.org/10.1103/PhysRevLett.104.210502	journal	May 2010
Riemannian Optimization for High-Dimensional Tensor Completion Steinlechner, Michael SIAM Journal on Scientific Computing, Vol. 38, Issue 5 https://doi.org/10.1137/15M1010506	journal	January 2016
Computation of extreme eigenvalues in higher dimensions using block tensor train format Dolgov, S. V.; Khoromskij, B. N.; Oseledets, I. V. Computer Physics Communications, Vol. 185, Issue 4 https://doi.org/10.1016/j.cpc.2013.12.017	journal	April 2014
On low-rank approximability of solutions to high-dimensional operator equations and eigenvalue problems Kressner, Daniel; Uschmajew, André Linear Algebra and its Applications, Vol. 493 https://doi.org/10.1016/j.laa.2015.12.016	journal	March 2016
Generative modeling via tree tensor network states Tang, Xun; Hur, YoonHaeng; Khoo, Yuehaw Research in the Mathematical Sciences, Vol. 10, Issue 2 https://doi.org/10.1007/s40687-023-00381-3	journal	April 2023
Streaming Tensor Train Approximation Kressner, Daniel; Vandereycken, Bart; Voorhaar, Rik SIAM Journal on Scientific Computing, Vol. 45, Issue 5 https://doi.org/10.1137/22M1515045	journal	October 2023
Variational Inference: A Review for Statisticians Blei, David M.; Kucukelbir, Alp; McAuliffe, Jon D. Journal of the American Statistical Association, Vol. 112, Issue 518 https://doi.org/10.1080/01621459.2017.1285773	journal	July 2016
Modeling sequences with quantum states: a look under the hood Bradley, Tai-Danae; Stoudenmire, E. M.; Terilla, John Machine Learning: Science and Technology, Vol. 1, Issue 3 https://doi.org/10.1088/2632-2153/ab8731	journal	July 2020
Density estimation by dual ascent of the log-likelihood Tabak, Esteban G.; Vanden-Eijnden, Eric Communications in Mathematical Sciences, Vol. 8, Issue 1 https://doi.org/10.4310/CMS.2010.v8.n1.a11	journal	January 2010
Normalizing Flows: An Introduction and Review of Current Methods Kobyzev, Ivan; Prince, Simon; Brubaker, Marcus IEEE Transactions on Pattern Analysis and Machine Intelligence https://doi.org/10.1109/TPAMI.2020.2992934	journal	January 2020
An Introduction to Fluid Dynamics Batchelor, G. K. https://doi.org/10.1017/CBO9780511800955	book	June 2012
Deep Residual Learning for Image Recognition He, Kaiming; Zhang, Xiangyu; Ren, Shaoqing 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) https://doi.org/10.1109/CVPR.2016.90	conference	June 2016
Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-Way Data Analysis and Blind Source Separation Cichocki, Andrzej; Zdunek, Rafal; Phan, Anh Huy https://doi.org/10.1002/9780470747278	book	September 2009
Direct sampling of projected entangled-pair states Vieijra, Tom; Haegeman, Jutho; Verstraete, Frank Physical Review B, Vol. 104, Issue 23 https://doi.org/10.1103/PhysRevB.104.235141	journal	December 2021
Minimum action method for the study of rare events E., Weinan; Ren, Weiqing; Vanden-Eijnden, Eric Communications on Pure and Applied Mathematics, Vol. 57, Issue 5 https://doi.org/10.1002/cpa.20005	journal	January 2004
Tensor-Train Decomposition Oseledets, I. V. SIAM Journal on Scientific Computing, Vol. 33, Issue 5 https://doi.org/10.1137/090752286	journal	January 2011
Training Products of Experts by Minimizing Contrastive Divergence Hinton, Geoffrey E. Neural Computation, Vol. 14, Issue 8 https://doi.org/10.1162/089976602760128018	journal	August 2002
Fast adaptive interpolation of multi-dimensional arrays in tensor train format Savostyanov, Dmitry; Oseledets, Ivan The 2011 International Workshop on Multidimensional (nD) Systems https://doi.org/10.1109/nDS.2011.6076873	conference	September 2011
Density-matrix algorithms for quantum renormalization groups White, Steven R. Physical Review B, Vol. 48, Issue 14 https://doi.org/10.1103/PhysRevB.48.10345	journal	October 1993
The Density Matrix Renormalization Group in Quantum Chemistry Chan, Garnet Kin-Lic; Sharma, Sandeep Annual Review of Physical Chemistry, Vol. 62, Issue 1 https://doi.org/10.1146/annurev-physchem-032210-103338	journal	May 2011

Similar Records

Generative modeling via tensor train sketching

Journal Article · 2023 · Applied and Computational Harmonic Analysis · OSTI ID:2576309

Analysis of a Computational Framework for Bayesian Inverse Problems: Ensemble Kalman Updates and MAP Estimators under Mesh Refinement

Journal Article · 2024 · SIAM/ASA Journal on Uncertainty Quantification · OSTI ID:2580021

A tensor density measure of topological charge in three dimensional nematic phases

Journal Article · 2024 · Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences · OSTI ID:2426768

Related Subjects

Mathematics

High-dimensional density estimation with tensorizing flow

Citation Formats

References (33)

Similar Records

Related Subjects