B0553
Title: Sampling from multimodal target distributions using tempered Hamiltonian transitions
Authors: Joonha Park - University of Kansas (United States) [presenting]
Abstract: Hamiltonian Monte Carlo (HMC) methods are widely used to draw samples from unnormalized target densities due to high efficiency and favorable scalability with respect to increasing space dimensions. However, HMC struggles when the target distribution is multimodal, because the maximum increase in the potential energy function (i.e., the negative log density function) along the simulated path is bounded by the initial kinetic energy, which follows a half of the chi-squared distribution with d degrees of freedom, where d is the space dimension. We develop a Hamiltonian Monte Carlo method that can construct paths that cross high potential energy barriers. This approach does not require the modes of the target distribution to be known. Our method constructs the Hamiltonian paths while continuously increasing and decreasing the mass of the simulated particle, and thus it can be viewed as a case of the tempered transitions method. We develop a practical tuning strategy for the mass schedule, aiming to achieve high mode-hopping frequency. In addition to highly competitive scalability with dimensions, our method has a practical advantage over other tempering methods in the Gibbs sampler settings, where the target distribution changes frequently. We demonstrate that our method can facilitate frequent mode hopping in high-dimensional distributions using mixtures of normal distributions and a sensor network self-localization problem.
