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Utilizing the CLT Structure in Stochastic Approximations of Sampling Algorithms

Series: Bangalore Theory Seminars

Speaker: Dheeraj Nagaraj Google Research

Date/Time: Mar 03 11:00:00

Location: CSA Lecture Hall (Room No. 112, Ground Floor)

Abstract:
We consider stochastic approximations of sampling algorithms like Langevin Monte Carlo and Interacting Particle Dynamics with random batches. These are heavily deployed in Bayesian inference, and the physical sciences. The noise induced by random batches is approximately Gaussian (due to the Central Limit Theorem) while the Brownian motion driving the algorithm is exactly Gaussian.

We utilize this structure to provide improved guarantees for sampling algorithms under significantly weaker assumptions. We also propose covariance correction, which rescales the brownian motion to approximately remove the random batch error. We show that covariance corrected algorithms enjoy even better convergence.

Joint work with: Aniket Das (Google) and Anant Raj (INRIA and UIUC)


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We are grateful to the Kirani family for generously supporting the theory seminar series


Hosts: Rahul Madhavan, Rameesh Paul, Aditya Subramanian and Aditya Abhay Lonkar