Fetching the paper…
Reading the bibliography…
Continuous normalizing flows (CNFs) are a generative method for learning probability distributions, which is based on ordinary differential equations.
Robbins, H. E
1955
Earlier work this paper cites.
[author] Hatsell, Charles P.C. P. and Nolte, Loren W.L. W. (1971). Some geometric properties of the likelihood ratio (Corresp.). IEEE Transactions on Information Theory 17 616-618
1971
Earlier work this paper cites.
[author] Brascamp, Herm J.H. J. and Lieb, Elliott H.E. H. (1976). On extensions of the Brunn-Minkowski and Prékopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation. Journal of Functional Analysis 22 366–389
1976
Earlier work this paper cites.
[author] Stone, Charles JC. J. (1982). Optimal global rates of convergence for nonparametric regression. The Annals of Statistics 10 1040–1053
1982
Earlier work this paper cites.
[author] DeVore, Ronald A.R. A., Howard, RalphR. and Micchelli, CharlesC. (1989). Optimal nonlinear approximation. Manuscripta mathematica 63 469–478
1989
Earlier work this paper cites.
[author] McCann, Robert J.R. J. (1997). A convexity principle for interacting gases. Advances in Mathematics 128 153–179
1997
Earlier work this paper cites.
Bartlett, P
1998
Earlier work this paper cites.
[author] Anthony, MartinM. and Bartlett, Peter L.P. L. (1999). Neural Network Learning: Theoretical Foundations 9. Cambridge University Press
1999
Earlier work this paper cites.
[author] Ledoux, MichelM. (2001). The Concentration of Measure Phenomenon. Mathematical Surveys and Monographs 89. American Mathematical Society
2001
Earlier work this paper cites.
2002
Earlier work this paper cites.
[author] Györfi, LászlóL., Kohler, MichaelM., Krzyzak, AdamA. and Walk, HarroH. (2002). A Distribution-Free Theory of Nonparametric Regression. Springer
2002
Earlier work this paper cites.
[author] Hartman, PhilipP. (2002). Existence. In Ordinary Differential Equations II, 8-23. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA
2002
Earlier work this paper cites.
[author] Adams, Robert A.R. A. and Fournier, John J. F.J. J. F. (2003). Sobolev Spaces, second ed. Pure and Applied Mathematics 140. Academic Press
2003
Earlier work this paper cites.
[author] Brenner, Susanne C.S. C. and Scott, L. RidgwayL. R. (2008). The Mathematical Theory of Finite Element Methods, third ed. Texts in Applied Mathematics 15 4, 93–127. Springer New York, New York, NY
2008
Earlier work this paper cites.
[author] Villani, CédricC. (2009). Displacement interpolation. In Optimal Transport: Old and New 113–162. Springer Berlin Heidelberg, Berlin, Heidelberg
2009
Earlier work this paper cites.
[author] Evans, Lawrence C.L. C. (2010). Partial Differential Equations, second ed. Graduate Studies in Mathematics 19. American Mathematical Society
2010
Earlier work this paper cites.
[author] Efron, BradleyB. (2011). Tweedie’s formula and selection bias. Journal of the American Statistical Association 106 1602–1614
2011
Earlier work this paper cites.
[author] Tabak, Esteban G.E. G. and Turner, Cristina V.C. V. (2013). A family of nonparametric density estimation algorithms. Communications on Pure and Applied Mathematics 66 145–164
2013
Earlier work this paper cites.
[author] Cattiaux, PatrickP. and Guillin, ArnaudA. (2014). Semi log-concave Markov diffusions. In Séminaire de probabilités XLVI (CatherineC. Donati-Martin, AntoineA. Lejay and AlainA. Rouault, eds.) 231–292. Springer International Publishing, Cham
2014
Earlier work this paper cites.
[author] Goodfellow, IanI., Pouget-Abadie, JeanJ., Mirza, MehdiM., Xu, BingB., Warde-Farley, DavidD., Ozair, SherjilS., Courville, AaronA. and Bengio, YoshuaY. (2014). Generative adversarial nets. In Advances in Neural Information Processing Systems 27 2672–2680
2014
Earlier work this paper cites.
Kingma, D. P
2014
Earlier work this paper cites.
[author] LeCun, YannY., Bengio, YoshuaY. and Hinton, GeoffreyG. (2015). Deep learning. Nature 521 436–444
2015
Earlier work this paper cites.
Rezende, D
2015
Earlier work this paper cites.
[author] Salakhutdinov, RuslanR. (2015). Learning deep generative models. Annual Review of Statistics and Its Application 2 361–385
2015
Earlier work this paper cites.
Sohl-Dickstein, J
2015
Earlier work this paper cites.
[author] Dalalyan, Arnak S.A. S. (2017). Theoretical guarantees for approximate sampling from smooth and log-concave densities. Journal of the Royal Statistical Society Series B: Statistical Methodology 79 651-676
2017
Earlier work this paper cites.
[author] Durmus, AlainA. and Moulines, ÉricÉ. (2017). Nonasymptotic convergence analysis for the unadjusted Langevin algorithm. The Annals of Applied Probability 27 1551 – 1587
2017
Earlier work this paper cites.
[author] Yarotsky, DmitryD. (2017). Error bounds for approximations with deep ReLU networks. Neural Networks 94 103–114
2017
Earlier work this paper cites.
Chen, R. T. Q
2018
Cited alongside, same era.
[author] Eldan, RonenR. and Lee, James R.J. R. (2018). Regularization under diffusion and anticoncentration of the information content. Duke Mathematical Journal 167 969–993
2018
Cited alongside, same era.
[author] Petersen, PhilippP. and Voigtlaender, FelixF. (2018). Optimal approximation of piecewise smooth functions using deep ReLU neural networks. Neural Networks 108 296–330
2018
Cited alongside, same era.
[author] Vershynin, RomanR. (2018). High-Dimensional Probability: An Introduction with Applications in Data Science 47. Cambridge University Press
2018
Cited alongside, same era.
Yarotsky, D
2018
Cited alongside, same era.
2022
Later among the works it cites.
2022
Later among the works it cites.
2023
Later among the works it cites.
Albergo, M. S
2023
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
[author] Bartlett, Peter L.P. L., Harvey, NickN., Liaw, ChristopherC. and Mehrabian, AbbasA. (2019). Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networks. The Journal of Machine Learning Research 20 2285–2301
2019
Cited alongside, same era.
[author] Bauer, BenediktB. and Kohler, MichaelM. (2019). On deep learning as a remedy for the curse of dimensionality in nonparametric regression. The Annals of Statistics 47 2261 – 2285
2019
Cited alongside, same era.
[author] Dwivedi, RaazR., Chen, YuansiY., Wainwright, Martin JM. J. and Yu, BinB. (2019). Log-concave sampling: Metropolis-Hastings algorithms are fast. Journal of Machine Learning Research 20 1–42
2019
Cited alongside, same era.
Suzuki, T
2019
Cited alongside, same era.
Vempala, S
2019
Cited alongside, same era.
[author] Gühring, IngoI., Kutyniok, GittaG. and Petersen, PhilippP. (2020). Error bounds for approximations with deep ReLU neural networks in W s , p \mathit{W}^{s,p} norms. Analysis and Applications 18 803-859
2020
Cited alongside, same era.
[author] Nakada, RyumeiR. and Imaizumi, MasaakiM. (2020). Adaptive approximation and generalization of deep neural network with intrinsic dimensionality. Journal of Machine Learning Research 21 1–38
2020
Cited alongside, same era.
2023
Later among the works it cites.
2023
Later among the works it cites.
2023
Later among the works it cites.
2023
Later among the works it cites.
[author] Dytso, AlexA., Poor, H. VincentH. V. and Shamai Shitz, ShlomoS. (2023). Conditional mean estimation in Gaussian noise: A meta derivative identity with applications. IEEE Transactions on Information Theory 69 1883-1898
2023
Later among the works it cites.
[author] Fan, JianqingJ. and Gu, YihongY. (2023). Factor augmented sparse throughput deep ReLU neural networks for high dimensional regression. Journal of the American Statistical Association just-accepted 1–28
2023
Later among the works it cites.
2023
Later among the works it cites.
2023
Later among the works it cites.
2023
Later among the works it cites.
[author] Jiao, YulingY., Wang, YangY. and Yang, YunfeiY. (2023). Approximation bounds for norm constrained neural networks with applications to regression and GANs. Applied and Computational Harmonic Analysis 65 249-278
2023
Later among the works it cites.
[author] Jiao, YulingY., Shen, GuohaoG., Lin, YuanyuanY. and Huang, JianJ. (2023). Deep nonparametric regression on approximate manifolds: Nonasymptotic error bounds with polynomial prefactors. The Annals of Statistics 51 691–716
2023
Later among the works it cites.
Lipman, Y
2023
Later among the works it cites.
2023
Later among the works it cites.
Neklyudov, K
2023
Later among the works it cites.
2023
Later among the works it cites.
[author] Siegel, Jonathan W.J. W. (2023). Optimal approximation rates for deep ReLU neural networks on Sobolev and Besov spaces. Journal of Machine Learning Research 24 1–52
2023
Later among the works it cites.
2023
Later among the works it cites.
[author] Benton, JoeJ., Deligiannidis, GeorgeG. and Doucet, ArnaudA. (2024). Error bounds for flow matching methods. Transactions on Machine Learning Research
2024
Closest in time.
Benton, J
2024
Closest in time.
2024
Closest in time.
2024
Closest in time.
2024
Closest in time.