One World Seminar Series on the
Mathematics of Machine Learning
The One World Seminar Series on the Mathematics of Machine Learning is an online platform for research seminars, workshops and seasonal schools in theoretical machine learning. The focus of the series lies on theoretical advances in machine learning and deep learning as a complement to the one world seminars on probability, on Information, Signals and Data (MINDS), on methods for arbitrary data sources (MADS), and on imaging and inverse problems (IMAGINE).
The series was started during the Covid-19 epidemic in 2020 to bring together researchers from all over the world for presentations and discussions in a virtual environment. It follows in the footsteps of other community projects under the One World Umbrella which originated around the same time.
We welcome suggestions for speakers concerning new and exciting developments and are committed to providing a platform also for junior researchers. We recognize the advantages that online seminars provide in terms of flexibility, and we are experimenting with different formats. Any feedback on different events is welcome.
Geometric Methods for Machine Learning and Optimization
Many machine learning applications involve non-Euclidean data, such as graphs, strings or matrices. In such cases, exploiting Riemannian geometry can deliver algorithms that are computationally superior to standard (Euclidean) nonlinear programming approaches. This observation has resulted in an increasing interest in Riemannian methods in the optimization and machine learning community.
In the first part of the talk, we consider the task of learning a robust classifier in hyperbolic space. Such spaces have received a surge of interest for representing large-scale, hierarchical data, due to the fact that they achieve better representation accuracy with lower dimensions. We present the first theoretical guarantees for the (robust) large-margin learning problem in hyperbolic space and discuss conditions under which hyperbolic methods are guaranteed to surpass the performance of their Euclidean counterparts. In the second part, we introduce Riemannian Frank-Wolfe (RFW) methods for constraint optimization on manifolds. Here, the goal of the theoretical analysis is two-fold: We first show that RFW converges at a nonasymptotic sublinear rate, recovering the best-known guarantees for its Euclidean counterpart. Secondly, we discuss how to implement the method efficiently on matrix manifolds. Finally, we consider applications of RFW to the computation of Riemannian centroids and Wasserstein barycenters, which are crucial subroutines in many machine learning methods.
Based on joint work with Suvrit Sra (MIT) and Manzil Zaheer, Ankit Singh Rawat, Aditya Menon and Sanjiv Kumar (all Google Research).
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Seminars are held online on Zoom. The presentations are recorded and video is made available on our youtube channel. A list of past seminars can be found here. All seminars, unless otherwise stated, are held on Wednesdays at 12 noon ET. The invitation will be shared on this site before the talk and distributed via email.