TY - GEN

T1 - Accelerated flow for probability distributions

AU - Taghvaei, Amirhossein

AU - Mehta, Prashant G.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - This paper presents a methodology and numerical algorithms for constructing accelerated gradient flows on the space of probability distributions. In particular, we extend the recent variational formulation of accelerated methods in (Wibisono et al., 2016) from vector valued variables to probability distributions. The variational problem is modeled as a mean-field optimal control problem. A quantitative estimate on the asymptotic convergence rate is provided based on a Lyapunov function construction, when the objective functional is displacement convex. An important special case is considered where the objective functional is the relative entropy. For this case, two numerical approximations arc presented to implement the Hamilton's equations as a system of N interacting particles. The algorithm is numerically illustrated and compared with the MCMC and Hamiltonian MCMC algorithms.

AB - This paper presents a methodology and numerical algorithms for constructing accelerated gradient flows on the space of probability distributions. In particular, we extend the recent variational formulation of accelerated methods in (Wibisono et al., 2016) from vector valued variables to probability distributions. The variational problem is modeled as a mean-field optimal control problem. A quantitative estimate on the asymptotic convergence rate is provided based on a Lyapunov function construction, when the objective functional is displacement convex. An important special case is considered where the objective functional is the relative entropy. For this case, two numerical approximations arc presented to implement the Hamilton's equations as a system of N interacting particles. The algorithm is numerically illustrated and compared with the MCMC and Hamiltonian MCMC algorithms.

UR - http://www.scopus.com/inward/record.url?scp=85078037083&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85078037083&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85078037083

T3 - 36th International Conference on Machine Learning, ICML 2019

SP - 10632

EP - 10641

BT - 36th International Conference on Machine Learning, ICML 2019

PB - International Machine Learning Society (IMLS)

T2 - 36th International Conference on Machine Learning, ICML 2019

Y2 - 9 June 2019 through 15 June 2019

ER -