Demonstrated 'delocalization of bias' in unadjusted Langevin algorithms, leading to nearly dimension-independent bias scaling under certain conditions.
Developed new derivative-free and derivative-based affine-invariant ensemble samplers that improve upon the emcee package, especially in high dimensions.
Introduced affine-invariant ensemble HMC achieving state-of-the-art dimensional scaling while maintaining affine invariance and embarrassingly parallel structure.
Established a design framework for gradient flows in sampling, focusing on Fisher-Rao geometry, and developed a Kalman-filter-type Gaussian mixture approximation for large-scale Bayesian inverse problems.
Proposed principled designs for noise and interpolation schedules in generative modeling of multiscale scientific data, introducing 'optimal averaged Lipschitzness' for improved numerical efficiency on ill-conditioned distributions.