ISyE Seminar Series: Shiqian Ma
 "Riemannian Optimization for Projection Robust Optimal Transport"Presentation by Shiqian Ma Wednesday, March 2 |
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About the seminar: The optimal transport problem is known to suffer the curse of dimensionality. A recently proposed approach to mitigate the curse of dimensionality is to project the sampled data from the high dimensional probability distribution onto a lower-dimensional subspace, and then compute the optimal transport between the projected data. However, this approach requires to solve a max-min problem over the Stiefel manifold, which is very challenging in practice. In this talk, we propose a Riemannian block coordinate descent (RBCD) method to solve this problem. We analyze the complexity of arithmetic operations for RBCD to obtain an $\epsilon$-stationary point, and show that it significantly improves the corresponding complexity of existing methods. Numerical results on both synthetic and real datasets demonstrate that our method is more efficient than existing methods, especially when the number of sampled data is very large. We will also discuss how the same idea can be used to solve the projection robust Wasserstein barycenter problem. "A Riemannian Block Coordinate Descent Method for Computing the Projection Robust Wasserstein Distance" (pdf) "Projection Robust Wasserstein Barycenters" (pdf) |
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Bio:
Shiqian Ma is an associate professor in the Department of Mathematics at the University of California, Davis. He received his PhD in IEOR from Columbia University in 2011. Shiqian was an NSF postdoctoral fellow in the Institute for Mathematics and its Applications at the University of Minnesota during 2011-2012 and an assistant professor in the Department of Systems Engineering and Engineering Management at the Chinese University of Hong Kong during 2012-2017. His main research areas are optimization and machine learning. Shiqian served as the area chair for ICML 2021 and 2022, and currently serves on the editorial board of Journal of Scientific Computing.
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