Kelvin Shuangjian Zhang
I am a Postdoctoral Fellow at the Department of Statistics and Actuarial Science, University of Waterloo, working with Professor David Saunders and Professor Mario Ghossoub.
I received my Ph.D. degree from the Department of Mathematics, University of Toronto in 2018, under the supervision of Professor Robert J. McCann. During summer 2018, I visited Professor Guillaume Carlier at MOKAPLAN, INRIA. Then I worked with Professor Marco Cuturi as a Postdoctoral Fellow at CREST - ENSAE ParisTech (2018.09-2019.05), before I moved to ENS Paris and worked with Professor Gabriel Peyré at Department of Mathematics and Applications (2019.06-2021.08).
Optimal Transport, and its applications in
- - Economics (Screening, Auction)
- - Machine Learning (GANs)
- - Statistics (MCMC)
Interested Topics Include:
- Prescribed Jacobian equation, Monge–Ampère equation
- Langevin Monte Carlo, Fokker–Planck equation
- The principal-agent framework, Duopoly models
- Wasserstein GANs
Publications and Preprints:
 Cyclical ascent: a fast algorithm for computing Wasserstein barycenters, with Robert J. McCann, David Wu. In preparation.
 The Kantorovich optimal transport problem for capacities on finite spaces [pdf], with Mario Ghossoub, David Saunders. Submitted. [Slides]
 A duality and free boundary approach to adverse selection [pdf], with Robert J. McCann. Appendix by Cale Rankin. arXiv:2301.07660. [Slides by McCann]
 Wasserstein Control of Mirror Langevin Monte Carlo [pdf]. Kelvin Shuangjian Zhang, Gabriel Peyré, Jalal Fadili, Marcelo Pereyra. In Proc. COLT'20, 2020. [Slides]
 Existence of solutions to principal-agent problems with adverse selection under minimal assumptions [pdf], with Guillaume Carlier. J. Math. Econ. 88 (2020) 64-71.
 Existence in multidimensional screening with general nonlinear preferences [pdf]. Econ. Theory 67(2) (2019) 463-485.
 On concavity of the monopolist's problem facing consumers with nonlinear price preferences [pdf], with Robert J. McCann. Comm. Pure Appl. Math. 72(7) (2019) 1386-1423.
 Existence, Uniqueness, Concavity and Geometry of the Monopolist’s Problem Facing Consumers with Nonlinear Price Preferences [pdf]. PhD Thesis, University of Toronto, 2018.
 Implicit manifold learning on generative adversarial networks [pdf]. Kry Yik Chau Lui, Yanshuai Cao, Maxime Gazeau, Kelvin Shuangjian Zhang. ICML2017 Workshop on Implicit Generative Models, Sydney, 2017.
 Circular cone: a novel approach for protein ligand shape matching using modified PCA [pdf]. Kelvin Shuangjian Zhang, Jun Du, Liang Zhang, Cheng Zeng, Qiao Liu, Tao Zhang and Gang Hu. Computer Methods and Programs in Biomedicine 108(1) (2012) 168-175.
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