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Mathematical Physics Seminar

The unreasonable effectiveness of determinantal processes

Subhro Ghosh - National University of Singapore

Location:  Hill Center Room 705
Date & time: Thursday, 17 November 2022 at 12:00PM - 1:00PM

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 determinantal processes (a.k.a. DPPs) far beyond their context of origin. 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 thes 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 fundamenta 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. 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 at NeurIPS 2021)

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