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Robust Monte Carlo Sampling using Riemannian Nosé-Poincaré Hamiltonian Dynamics
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Riemannian Nosé-Poincaré dynamics (SGR-NPHMC) instead of SG-NHT | topic modeling with gamma-GP model · 20-Newsgroups | test perplexity: 758 to 723 | Helped |
| Riemannian Nosé-Poincaré dynamics (SGR-NPHMC) instead of SG-NHT | topic modeling with gamma-GP model · Reuters | test perplexity: 929 to 904 | Helped |
| Gamma-NB rather than gamma-GP prior in SGR-NPHMC (ablation) | SGR-NPHMC topic model · Reuters | test perplexity: 904 to 930 | Hurt |
| Riemannian Nosé-Poincaré dynamics with noise correction vs SG-NHT on 1D Gaussian | mean estimation · 1D Gaussian | RMSE (mu): 0.0375 (SG-NHT, A=1) to 0.0244 (SGR-NPHMC, A,B=0.001) | Helped |
| Riemannian Nosé-Poincaré dynamics vs SG-NHT on 1D Gaussian precision | precision estimation · 1D Gaussian | RMSE (tau): 0.0471 (SG-NHT) to 0.0466 (SGR-NPHMC) | Helped |
| Varying noise correction strength {A,B} from 0.01 to 0.0001 in SGR-NPHMC (ablation) | SGR-NPHMC on 1D Gaussian · 1D Gaussian | autocorrelation time (mu): 14.90 at 0.01, 13.63 at 0.001, 2.59 at 0.0001 | Mixed |
| Riemannian metric preconditioning with Nosé-Poincaré dynamics on Bayesian logistic regression | SGR-NPHMC · synthetic Bayesian logistic regression | RMSE for parameters | Helped |
| Fixed-point iterations instead of Newton updates for implicit system (ablation) | SGR-NPHMC on real datasets · real datasets | mixing stability | Hurt |
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