Stochastic Gradient Hamiltonian Monte Carlo

[xukai92]

Reference

Chen, T., Fox, E. B., & Guestrin, C. (2014, February 17). Stochastic Gradient Hamiltonian Monte Carlo. arXiv.org.

The proposal below is naive.

The Stochastic HMC can use the current code with only making some changes to observe():

1. Count the total number of observations in the first run of the model
2. For later iterations
i. Choose a subset of observations for each iteration (according to obs_frac (observation fraction) set by user)
ii. Only accumulate logpdf of those chosen observations (Note: the subset is fixed for each HMC iteration)

This two changes are done in this branch: https://github.com/yebai/Turing.jl/tree/stochhmc and some simple tests are done, which initially looks fine.

Followed our discussion on correlation last time, I think of using the following way to generate correlated observation sets:

1. User set a correlation ratio corr_rate
2. When generating new observation subset, fix a fraction of observations according to corr_rate and sample the remaining

Expected problem: when obs_frac is large, we would not able to do so. E.g.

We have 10 obs and obs_frac is 0.8. Say our first subset is [1,2,3,4,5,6,7,8].

User pick corr_rate to be 0.125. Then we need to fix one obs, say [1] and sample 7 obs from [9, 10], which is impossible.

[xukai92]

Wrong way to do this. Will re-do it after new interface.