Neural network gradient Hamiltonian Monte Carlo.
- Author(s): Li, Lingge
- Holbrook, Andrew
- Shahbaba, Babak
- Baldi, Pierre
- et al.
Published Web Locationhttps://doi.org/10.1007/s00180-018-00861-z
Hamiltonian Monte Carlo is a widely used algorithm for sampling from posterior distributions of complex Bayesian models. It can efficiently explore high-dimensional parameter spaces guided by simulated Hamiltonian flows. However, the algorithm requires repeated gradient calculations, and these computations become increasingly burdensome as data sets scale. We present a method to substantially reduce the computation burden by using a neural network to approximate the gradient. First, we prove that the proposed method still maintains convergence to the true distribution though the approximated gradient no longer comes from a Hamiltonian system. Second, we conduct experiments on synthetic examples and real data to validate the proposed method.