  The problem of Bayesian reduced rank regression is considered in this paper.
We propose, for the first time, to use Langevin Monte Carlo method in this
problem. A spectral scaled Student prior distrbution is used to exploit the
underlying low-rank structure of the coefficient matrix. We show that our
algorithms are significantly faster than the Gibbs sampler in high-dimensional
setting. Simulation results show that our proposed algorithms for Bayesian
reduced rank regression are comparable to the state-of-the-art method where the
rank is chosen by cross validation.
