Reflective Hamiltonian Monte Carlo with Leafrog steps for exponential sampling #143
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Comment: This PR is redundant since the Hamiltonian Monte Carlo with Leapfrog integrator is implemented in #138 . This PR shall be updated when the previous PR is merged into develop. |
papachristoumarios
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Mar 9, 2021
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The contents of this PR can be inferred from #138 .
More specifically, you could use the IsotropicLinearFunctor class from include/ode_solvers/oracle_functors.hpp to do exponential sampling.
For the R interface:
What can be a good addition, is creating the functor in R and giving it as an argument (rather than parsing functions from Rcpp which is rather slow; especially if you need a "famous" density) which would yield a considerable speedup.
Thank you in advance!
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This PR implements the Reflective Hamiltonian Monte Carlo with leapfrog integrator to sample from the exponential distribution restricted to a convex polytope.
Algorithmic details:
-- We exploit the simple form of the gradient to reduce the cost per step.
-- When the trajectory hits the boundary it is reflected.
Implementation details:
-- The sampler is implemented by a new structure.
-- The PR extends the C++ interface for exponential sampling.
-- The sampler is integrated into the R interface of volesti.
-- This implementation is more stable than the case of exact HMC for exp. sampling, when the variance is extremely small.