Practical Hamiltonian Monte Carlo on Riemannian Manifolds via Relativity Theory
Authors: Kai Xu, Hong Ge
ICML 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We implement all samplers studied in this paper using Advanced HMC.jl (Xu et al., 2020).3 Derivative implementation in (5.3) is tested by finite differentiation. Geweke tests (Geweke, 2004; Grosse & Duvenaud, 2014) are used to validate the correctness of samplers (detailed in appendix C). Appendix D lists default hyper-parameters used across experiments. |
| Researcher Affiliation | Collaboration | 1MIT-IBM Watson AI Lab, Cambridge MA, United States 2University of Cambridge, Cambridge, United Kingdom. |
| Pseudocode | Yes | Algorithm 1 Momentum sampling via Box Muller transform |
| Open Source Code | Yes | Available at https://github.com/Turing Lang/ Advanced HMC.jl |
| Open Datasets | Yes | We use the 2-dimensional Neal s funnel (Neal, 2011), hierarchical Bayesian logistic regression (HBLR) model and a log-Gaussian Cox point process (log GCPP) model, that are previously used to benchmark HMC algorithms (Heng & Jacob, 2019; Xu et al., 2021). The HBLR problem has a dimensionality of 26, and the log GCPP problem has a dimensionality of 64. |
| Dataset Splits | No | The paper does not provide specific dataset split information (e.g., train/validation/test percentages or counts) for the experiments. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., exact GPU/CPU models, memory amounts) used for running its experiments. |
| Software Dependencies | No | The paper mentions software like 'Advanced HMC.jl', 'MCMCDebugging.jl', 'Turing', 'Zygote.jl', and 'Forward Diff.jl', but does not provide specific version numbers for these dependencies. |
| Experiment Setup | Yes | Appendix D lists default hyper-parameters used across experiments. Table 4: Common hyper-parameters used across experiments in section 6. parameter name value comment the number of leapfrog steps 8 the number of fixed-point iterations 6 scale of identity matrix added to Hessian (λ) 1 10 2 we use H + λI to regularize the Hessian initial position distribution U( 1, 1) this follows Betancourt (2013) |