In 1960, Wigner published an article famously titled “The Unreasonable Effectiveness of Mathematics in the Natural Sciences”. In this talk we will, in a small way, follow the spirit of Wigner’s coinage, and explore the unreasonable effectiveness of negatively associated (i.e., self-repelling) stochastic systems far beyond their context of origin.

As a particular class of such models, determinantal processes (a.k.a. DPPs) originated in quantum and statistical physics, but have emerged in recent years to be a powerful toolbox for many fundamental learning problems. In this talk, we aim to explore the breadth and depth of these applications. On one hand, we will explore a class of Gaussian DPPs and the novel stochastic geometry of their parameter modulation, and their applications to the study of directionality in data and dimension reduction. At the other end, we will consider the fundamental paradigm of stochastic gradient descent, where we leverage connections with orthogonal polynomials to design a minibatch sampling technique based on data-sensitive DPPs ; with provable guarantees for a faster convergence exponent compared to traditional sampling. Principally based on the following works:

[1] Gaussian determinantal processes: A new model for directionality in data, with P. Rigollet, Proceedings of the National Academy of Sciences, vol. 117, no. 24 (2020), pp. 13207–13213 (PNAS Direct Submission)

[2] Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD, with R. Bardenet and M. Lin Advances in Neural Information Processing Systems 34 (Spotlight Paper at NeurIPS 2021)

Subhro Ghosh is an assistant professor at the Department of Mathematics National University of Singapore, jointly with the Dept of Statistics and Data Science and a faculty affiliate at the Institute of Data Science, NUS. He is broadly interested in stochastics, focusing on problems from the math of data and statistical physics, and their interactions. Subhro received his Bachelor in Statistics and Master in Mathematics degrees from the Indian Statistical Institute. He obtained his PhD from the University of California, Berkeley under the supervision of Yuval Peres, and was subsequently a postdoc at Princeton University prior to joining NUS.

Subhro’s research interests encompass constrained stochastic systems and their applications, including problems of learning under complex structure (e.g., latent symmetries or community structure), dimension reduction, sampling and optimization, statistical networks and signal processing. The investigation of these problems naturally brings together a wide array of tools and techniques from probability, Fourier analysis, persistent homology and group representations. His work on the mathematics of data has been recognized as a Finalist for the Bell Labs Prize, 2022.

For more information about the ESD Seminar, please email esd_invite@sutd.edu.sg