Slide 8
Slide 8 text
First-order optimization algorithms
Sampling methods turns out to be first-order gradient descent methods
in probability space. It has many generalizations:
I Fisher-Rao metric and natural gradient methods (Amari, Ny, Zhang,
et.al.);
I Wasserstein metric and Wasserstein gradient descent (Jordan,
Kinderlehrer, Otto, Villani, Carillo, Slepcev, Liu, Lu, Gao, Ambrosio,
Gigli, Savare, Gangbo, et.al.);
I Stein metric and Stein variational gradient descent (Liu, Wang);
I Wasserstein-Kalman metric and Ensemble Kalman sampling
(Garbuno-Inigo, Ho↵man, Li, Stuart);
I Wasserstein Newton’s metric and Wasserstein Newton’s flow (Wang,
Li);
I Projected Wasserstein metric and Project Wasserstein gradient flow
(Wang, Chen, Li);
I Entropy-Entropy flux-metric and Flux-gradient flows (Li, Liu, Osher,
Shu).
8
(Wang, Chen, Pilanci, Li);