Statistics Final Defense - Jaideep Pralhad Mahajan "Fast and Efficient Log-Concave Sampling"

Ph.D. Final Examination for Jaideep Pralhad Mahajan will be held on June 25, 2026, at 10:00 AM, at Lincoln Hall, Room 1060, and via Zoom. This examination is open to the academic community, and we encourage both students and faculty to attend. 

Thesis Title: : Fast and Efficient Log-Concave Sampling

Abstract:
 We study parallel sampling from high-dimensional strongly log-concave distributions. Langevin-based samplers converge rapidly in continuous time, but their discretizations are typically sequential and often require polynomially many steps in the dimension, the target accuracy, or both. Picard-based parallel sampling methods reduce this sequential depth to a polylogarithmic scale by solving for many time-discretization points in parallel; however, existing guarantees often require a polynomial number of processors, leading to substantial memory and gradient-evaluation costs in high dimensions.

We show that higher-order Langevin structure can reduce this parallel resource burden while preserving polylogarithmic sequential depth. Our method combines arbitrary-order Langevin dynamics with blockwise Lagrange polynomial interpolation. This sharper discretization reduces the number of parallel points required to achieve a target accuracy. Our results cover both higher-order smooth potentials and ridge-separable potentials, including models such as Bayesian logistic regression and two-layer neural networks, and improve upon the space complexity of the current literature on parallel log-concave sampling.

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