September 15\, 2023 11:00 AM Singapore

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

As a pa rticular class of such models\, determinantal processes (a.k.a. DPPs) origi nated in quantum and statistical physics\, but have emerged in recent years to be a powerful toolbox for many fundamental learning problems. In this t alk\, 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 g eometry of their parameter modulation\, and their applications to the study of directionality in data and dimension reduction. At the other end\, we w ill consider the fundamental paradigm of stochastic gradient descent\, wher e we leverage connections with orthogonal polynomials to design a minibatch sampling technique based on data-sensitive DPPs \; with provable guarantee s for a faster convergence exponent compared to traditional sampling. Princ ipally 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 proce sses based on orthogonal polynomials for sampling minibatches in SGD\, with R. Bardenet and M. Lin Advances in Neural Information Processing Syste ms 34 (Spotlight Paper at NeurIPS 2021)

Sub hro Ghosh is an assistant professor at the Department of Mathematics Nation al University of Singapore\, jointly with the Dept of Statistics and Data S cience and a faculty affiliate at the Institute of Data Science\, NUS. He i s 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 S tatistical Institute. He obtained his PhD from the University of California \, Berkeley under the supervision of Yuval Peres\, and was subsequently a p ostdoc at Princeton University prior to joining NUS.

Subhro's researc h interests encompass constrained stochastic systems and their applications \, including problems of learning under complex structure (e.g.\, latent sy mmetries or community structure)\, dimension reduction\, sampling and optim ization\, statistical networks and signal processing. The investigation of these problems naturally brings together a wide array of tools and techniqu es from probability\, Fourier analysis\, persistent homology and group repr esentations. His work on the mathematics of data has been recognized as a F inalist for the Bell Labs Prize\, 2022.

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