Exact Hamiltonian Monte Carlo for exponential sampling #142
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vissarion
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vissarion,
papachristoumarios and
elias-tsigaridas
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| // Exact HMC for sampling from the Exponential distribution restricted to a convex polytope | ||
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| struct HMCExponentialWalk |
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I think here you should change the name of the struct to agree with the one that's already in the develop branch, namely HMCExponentialWalk -> HamiltonianMonteCarloExactExponentialWalk.
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Thanks for the comment. I renamed it to "ExponentialHamiltonianMonteCarloExactWalk".
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| #include "random_walks/uniform_john_walk.hpp" | |||
| #include "random_walks/uniform_vaidya_walk.hpp" | |||
| #include "random_walks/uniform_accelerated_billiard_walk.hpp" | |||
| #include "random_walks/exponential_hamiltonian_monte_carlo_walk.hpp" | |||
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Please keep header names consistent. If the struct name has exponential after hmc, it should be better if it's the same here.
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I renamed it accordingly to the previous comment.
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| typename Walk | ||
| > | ||
| struct ExponentialRandomPointGenerator |
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Apply naming consistency if needed.
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I think this is consistent with the other structure names.
include/random_walks/exponential_hamiltonian_monte_carlo_walk.hpp
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Great! See my comments on #144 for a final change on the macro RVOLESTI.
| Point _v; | ||
| Point _c; | ||
| NT _Temp; | ||
| const double _tol = 1e-10; |
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Thanks for the comment. However, this will give us a compile error in the R interface.
I used #define IN_INSIDE_BODY_TOLLERANCE 1e-10.
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This is merged with #144 |
This PR implements exact Hamiltonian Monte Carlo for exponential sampling.
Algorithmic details:
-- The exact HMC for exponential sampling exploits quadratic polynomial trajectories in the interior of the polytope.
-- When the trajectory hits the boundary it is reflected.
Implementation details:
-- The sampler is implemented by a new structure.
-- The PR includes a new C++ interface for exponential sampling.
-- The sampler is integrated into the R interface of volesti.
-- There is a probability of failure for small values of variance. The implementation stops when it fails to generate the next point of the random walk.