Random Coordinate Langevin Monte Carlo

Understand

Langevin Monte Carlo (LMC) is a popular Markov chain Monte Carlo sampling method.

• One drawback is that it requires the computation of the full gradient at each iteration, an expensive operation if the dimension of the problem is high.
• We propose a new sampling method: Random Coordinate LMC (RC-LMC).
• At each iteration, a single coordinate is randomly selected to be updated by a multiple of the partial derivative along this direction plus noise, and all other coordinates remain untouched.