• Short biography

    • I am moving to University of South Carolina as an assistant professor.
    • UCLA, CAM assistant professor in Mathematics, 2016-2020.
    • Georgia Tech, Ph.D. in Mathematics, 2016.
    • Georgia Tech, M.S. in Statistics, 2015.
    • Shandong University, B.S.in Mathematics, 2009.

    Research areas

      Google Scholar.
    • Machine Learning: theory, algorithm and applications;
    • Transport information geometry with applications in data science, statistics, optimization and data-driven scientific computing methods;
    • Numerical Mean field games, Schrodinger equation and Schrodinger Bridge problem.

    Website Links

    News

    • Draft "Information Newton flow: second-order optimization method in probability space" is online. We propose information Newton's flows for sampling optimization problems arised in inverse problem and Bayesisan statistics. Newton's Langvein dynamics, a.k.a Wasserstein Newton's flows of KL divergence, are derived. We propose second-order algorithms for Bayesian sampling problems, Jan 13, 2020. [PDF]
    • Paper "Ricci curvature for parametric statistics via optimal transport" has been accepted in Information Geometry, January 12, 2020.
    • Paper "Kernelized Wasserstein Natural Gradient" is accepted in ICLR 2020, Spotlight, Dec 20, 2019.
    • Draft "A Machine Learning Framework for Solving High-Dimensional Mean Field Game and Mean Field Control Problems" is online. We provide a computational method to approximate solutions of high dimenisonal potential mean field games, Dec 4, 2019. [PDF]
    • Draft "Tropical Optimal Transport in Phylogenetic Tree Space" is online. We study the dynamical optimal transport in Phylogenetic Tree Space. This is the first differential structure connection between optimal transport and Algebraic geometry with applications in biology, statistics and data science, Nov 13, 2019. [PDF]
    • Draft "Wasserstein information matrix" is online. We study statistical and estimation properties of Wasserstein informatin matrices. The Wasserstein score function, the Wasserstein-Cramer-Rao bound, the Wasserstein efficiency and the Poincare efficiency (interplay with Wasserstein and Fisher information matrices) are derived, Oct 24, 2019. [PDF]
    • Draft "Generalized Gamma z calculus via sub-Riemannian density manifold" (104 pages) is online. A sysmetic calculus for studying degenerate drift diffusion process is provided. The further study is to estimate convergence rates of degenerate Langvein dynamics type MCMCs with variable drift coefficents, Oct 16, 2019.[PDF]
    • Paper "Hessian transport gradient flows", is accepted in Research in the Mathematical Sciences, Oct 11, 2019.
    • Paper "Interacting Langevin Diffusions: Gradient Structure And Ensemble Kalman sampler", is accepted SIAM journal on Applied dynamical system, Oct 10, 2019.
    • Paper "Wasserstein Diffusion Tikhonov Regularization" is accepted in OTML Workshop NeurIPS, Oct 1, 2019.
    • Paper "Equilibrium slection via optimal transport" is accepted in SIAM journal on Applied Math, Sep 23, 2019.
    • Paper "Unnormalized Optimal transport", known as GLOP, is accepted in Journal of Computational Physics, Sep 6, 2019. [PDF]
    • Paper "Accelerated Information Gradient flow" is online. An accerlated gradient flow has been studied in probability space and Gaussian models for various information merics, including Fisher information metric and Wasserstein information metric, Sep 4, 2019. [PDF]
    • Paper "Wasserstein Hamiltonian flow" is accepted in Journal of differential equations, August 24, 2019. [PDF]
    • Draft "Fast algorithms for generalized unnormalized optimal transport" is online, August 12, 2019. [PDF]
    • Draft "Diffusion hypercontractivity via generalized density manifold" is online, July 29, 2019. [PDF]
    • Draft "Fisher information regularization schemes for Wasserstein gradient flows" is online, July 3, 2019. [PDF]
    • Draft "Hessian transport gradient flows" is online, May 11, 2019.[PDF]
    • Paper "Algorithm for Hamilton-Jacobi equation in density space" is accpeted in Journal of Scientific Computation, May 4, 2019.
    • Papers "Parametric Fokker-Planck equation", "Affine Natural Proximal Learning", "Hopf-Cole transformation and Schrodinger problems" are accpeted in Geometry science of information, April 25, 2019.
    • Paper "Wasserstein of Wasserstein Loss" is accepted in ICML, April 22, 2019.

    Highlights

    Wasserstein Information Matrix [Talk ] [Paper1]
    Mean Field Games with Applications. [Overview Talk ] [Generative network Talk]
    Accelerated Information Gradient flow. [Talk ] [pdf ]
    Unnormalized Optimal Transport. [Talk ] [pdf1][pdf2]
    Transport information geometric learning. [Talk ] [pdf1 ][pdf2] [pdf3] [pdf4][ pdf5 ][ pdf6 ]
    Evolutionary games via optimal transport. [Talk ] [pdf1 ][pdf2 ]
    Computational Mean field games. [Talk ] [pdf ]
    Hamiltonian flows via optimal transport. [Talk1] [Talk2] [pdf1 ][pdf 2][ pdf3] [pdf4]
    Gradient flows on graphs via optimal transport. [Talk ] [pdf1 ] [pdf2 ]
    L1 optimal transport with applications. [Talk ] [pdf1] [pdf2] [pdf3] [pdf4][pdf5]

    Contact

    • Office: MS 7620F, UCLA.
    • Email: wcli at math.ucla.edu