Truyen  Nguyen

Research Interests

• Machine Learning

• Monge-Kantorovich Optimal Transport, Calculus of Variations and Optimal Control

• Partial Differential Equations

• Information theory

Publications

Book Chapters

• 1. Interior Hölder Estimates for Second Derivatives (with C. Gutierrez and Q. Huang). This appears as Chapter 8 in the book "The Monge-Ampère Equation, Birkhäuser Verlag, 2016" by C. Gutierrez.

Published Articles

Papers in machine learning:

(*: equal contribution)

1.  Optimal Transport for Measures with Noisy Tree Metric
   International Conference on Artificial Intelligence and Statistics (AISTATS), 2024.
   Tam Le*, Truyen Nguyen, Kenji Fukumizu.

2. Dynamic Flows on Curved Space Generated by Labeled Data
   International Joint Conference on Artificial Intelligence (IJCAI), 2023. (Acceptance rate: 15% out of 4566 submissions)
   Xinru Hua, Truyen Nguyen, Tam Le, Jose Blanchet, Viet Anh Nguyen

3. Scalable Unbalanced Sobolev Transport for Measures on a Graph
   International Conference on Artificial Intelligence and Statistics (AISTATS), 2023.
   Tam Le*, Truyen Nguyen*, Kenji Fukumizu

4. Sobolev Transport: A Scalable Metric for Probability Measures with Graph Metrics
   International Conference on Artificial Intelligence and Statistics (AISTATS), 2022.
   Tam Le*, Truyen Nguyen*, Dinh Phung, Viet Anh Nguyen

5. Adversarial Regression with Doubly Non-negative Weighting Matrices
   Neural Information Processing Systems (NeurIPS/NIPS), 2021. (Acceptance rate: 26.0% from 9122 submissions)
   Tam Le*, Truyen Nguyen*, Makoto Yamada, Jose Blanchet, Viet Anh Nguyen

6. MOST: Multi-Source Domain Adaptation via Optimal Transport for Student-Teacher Learning
   37th Conference on Uncertainty in Artificial Intelligence (UAI), 2021.
   Tuan Nguyen, Trung Le,  He Zhao, Quan Hung Tran, Truyen Nguyen, Dinh Phung

7. TIDOT: A Teacher Imitation Learning Approach for Domain Adaptation with Optimal Transport
   30th International Joint Conference on Artificial Intelligence (IJCAI), 2021.
   Tuan Nguyen, Trung Le,  Nhan Dam, Quan Hung Tran, Truyen Nguyen, Dinh Phung

8. Entropy Partial Transport with Tree Metrics: Theory and Practice
   International Conference on Artificial Intelligence and Statistics (AISTATS), 2021. (Oral rate: 48/1527=3.1%)
   Tam Le*, Truyen Nguyen*
   (This paper was selected for oral presentation. Oral : acceptance : submissions = 48 : 455 : 1527)

9. On the convergence of gradient descent in GANs: MMD GAN as a gradient flow
   International Conference on Artificial Intelligence and Statistics (AISTATS), 2021.
   Youssef Mroueh*, Truyen Nguyen* 

Papers in information theory:

1. Ranjbar, N. H. Tran, M Vu, T. V. Nguyen,  M. C. Gursoy, "Capacity Region and Capacity-Achieving Signaling Schemes for 1-bit ADC Multiple Access Channels in Rayleigh Fading'', IEEE Transactions on Wireless Communications, vol. 19, no. 9, pp. 6162--6178, 2020.

2. Ranjbar, N. H. Tran, T. V. Nguyen,  M. C. Gursoy, "On the Sum-Capacity-Achieving Distributions and Sum-Capacity of 1-Bit ADC MACs in Rayleigh Fading",  IEEE ICC, January 1, 2019.

3. M. Vu, N. H. Tran, H. D. Tuan, T. V. Nguyen, and Duy H.N. Nguyena, "Optimal Signaling Schemes and Capacities of Non-Coherent Correlated MISO Channels under Per-Antenna Power Constraints", in IEEE Transactions on Communications PP(99):1-1 DOI:10.1109/tcomm.2018.2863391, August 2018.

4. Ranjbar, N. H. Tran, T. V. Nguyen,  M. C. Gursoy, and H. Nguyen-Le, "Capacity-Achieving Signals for Point-to-Point and Multiple-Access Channels under Non-Gaussian Noise and Peak Power Constraint",  in IEEE Access PP(99):1-1 DOI:10.1109/ACCESS.2018.2837056,  May 2018.

5. Ranjbar, N. H. Tran, T. V. Nguyen, and M. C. Gursoy, “Optimal Inputs of Single-User and Multi-User non-Gaussian Aggregate Interference Channels”, in Proc. IEEE Int. Conf. on Commun. (ICC) – Commun. Theory, Kansas, USA, May 2018, pp. 1-6.

6. H. V. Vu, N. H. Tran, T. V. Nguyen, and S. I. Hariharan, “Estimating Shannon and Constrained Capacities of Bernoulli-Gaussian Impulsive Noise Channels in Rayleigh Fading”, IEEE Transactions on Communications, vol. 62 , pp. 1845-1856, June 2014.

7. H. V. Vu, N. H. Tran, T. V. Nguyen, and S. I. Hariharan, “Estimating Information Rates of Bernoulli-Gaussian Impulsive Noise Channels in Rayleigh Fading”, in Proc. IEEE Int. Conf. on Commun. (ICC) – Wireless Commun., Sydney, Australia, Jun. 2014, pp. 5859-5864.

8. H. V. Vu, N. H. Tran, T. V. Nguyen, and S. I. Hariharan, “On the Capacity of Bernouli-Gaussian Impulsive Noise Channels in Rayleigh Fading”, in Proc. IEEE Inter. Symp. on Personal, Indoor and Mobile Radio Commun. (PIMRC), London, UK, Sept. 2013, pp. 1281-1285.

 Papers in kinetic theory, conservation laws, and calculus of variations and HJEs in the Wasserstein space:

1. One-dimensional pressureless gas systems with/without viscosity (with A. Tudorascu), Comm. Partial Differential Equations  40  (2015),  no. 9, 1619--1665.

2. Erratum to: Global magnetic confinement for the 1.5D Vlasov-Maxwell system (with Toan Nguyen and W. Strauss), Kinet. Relat. Models  8  (2015),  no. 3, 615--616.

3.  Global magnetic confinement for the 1.5D Vlasov-Maxwell system (with Toan Nguyen and W. Strauss), Kinet. Relat. Models  8  (2015), no. 1, 153--168, arXiv:1410.3003v1

4. Non-existence and non-uniqueness for multidimensional sticky particle systems (with A. Bressan), Kinet. Relat. Models  7  (2014),  no. 2, 205--218,  arXiv:1312.1636v1

5. Hamilton-Jacobi equations in space of measures associated with a system of conservation laws (with J. Feng), J. Math. Pures Appl. (9) 97 (2012), no. 4, 318--390.

6. On the existence, uniqueness and stability of entropy solutions to scalar conservation laws (with D. Golovaty),  J. Differential Equations  253  (2012),  no. 5, 1341--1375.

7. Euler-Poisson systems as action-minimizing paths in the Wasserstein space (with W. Gangbo and A. Tudorascu), Arch. Rat. Mech. Analysis, vol. 192, no. 3, 419--452, 2009.

8. Hamilton-Jacobi equations in the Wasserstein space (with W. Gangbo and A. Tudorascu), Methods and Applications of Analysis, vol. 15, no. 2, 155--183, 2008.            

9. Pressureless Euler/Euler-Poisson systems via adhesion dynamics and scalar conservation laws (with A. Tudorascu), SIAM J. Math. Analysis, vol. 40, no. 2, 754--775, 2008.

Papers in PDEs of elliptic and parabolic type:

1. Regularity estimates in weighted Morrey spaces for quasilinear elliptic equations (with G. Di Fazio), Revista  Matematica Iberoamericana, 36 (2020), no. 6, 1627--1658,  arXiv:1810.12496v1

2. Interior Calderón-Zygmund estimates for solutions to general parabolic equations of p-Laplacian type,  Calc. Var. Partial Differential Equations  56  (2017),  no. 6, Art. 173, 42 pp,  arXiv:1709.02847v1

3. Global W^{1,p} estimates for solutions to the linearized Monge-Ampère equations (with N. Le), J. Geom. Anal.  27  (2017),  no. 3, 1751--1788, arXiv:1602.02194v1

4. Interior gradient estimates for quasilinear elliptic equations (with T. Phan), Calc. Var. Partial Differential Equations  55  (2016),  no. 3, Art. 59, 33 pp.

5. Local gradient estimates for degenerate elliptic equations (with L. Hoang and T. Phan), Adv. Nonlinear Stud.  16  (2016),  no. 3, 479--489, arXiv:1505.01122v1

6. Interior second derivative estimates for solutions to the linearized Monge-Ampère equation (with C. Gutierrez), Trans. Amer. Math. Soc. 367 (2015), no. 7, 4537--4568,  arXiv:1208.5097v1

7. Gradient estimates and global existence of smooth solutions to a cross-diffusion system (with L. Hoang and T. Phan), SIAM J. Math. Anal.  47  (2015),  no. 3, 2122--2177, arXiv:1311.6828v1

8. A perturbation argument for a Monge-Ampère type equation arising in optimal transportations (with L. Caffarelli and M.d.M. González), Arch. Ration. Mech. Anal. 212 (2014), no. 2, 359--414.

9. Global W^{2,p} estimates for solutions to the linearized Monge-Ampère equations (with N. Le),  Math. Ann.  358  (2014),  no. 3-4, 629--700, arXiv:1209.1998v2

10. Geometric properties of boundary sections of solutions to the Monge-Ampère equation and applications (with N. Le),  J. Funct. Anal.  264  (2013),  no. 1, 337--361,  arXiv:1205.6882v1

11. Interior gradient estimates for solutions to the linearized Monge-Ampère equation (with C. Gutierrez), Advances in Mathematics, vol. 228, 2034--2070, 2011.

12. Weighted Sobolev's inequalities for bounded domains and singular elliptic equations (with D. M. Duc and N. C. Phuc) Indiana University Mathematics Journal, vol. 56, no. 2, 615--642, 2007.

13. On Monge-Ampère type equations arising in optimal transportation problems (with C. E. Gutierrez) Calc. Var. Partial Differential Equations, vol. 28, no. 3, 275--316, 2007. 

14. Homogenization and convergence of correctors in Carnot groups (with B. Franchi and C. E. Gutierrez) Comm. Partial Differential Equations, vol. 30, no. 10-12, 1817--1841, 2005.