Learn kernel bandwidth

We investigate the validity of the BM method in selecting the bandwidth. The target density is a toy bi-modal distribution. MCMC represents the Langevin MCMC method. Samples from MCMC match the target distribution in a stochastic way; samples from MED collapse; samples from HE align tidily around contour lines; samples from BM arrange neatly and are closer to samples from MCMC. This indicates that the BM method makes the particle system behave similar to MCMC, though in a deterministic way.

[1] Chang Liu, Jingwei Zhuo, Pengyu Cheng, Ruiyi Zhang, Jun Zhu, and Lawrence Carin. Accelerated first-order methods on the Wasserstein space for Bayesian inference. arXiv preprint arXiv:1807.01750, 2018.