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Hamiltonian Monte Carlo using an adjoint-differentiated Laplace approximation: Bayesian inference for latent Gaussian models and beyond
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use adjoint method with a single reverse sweep instead of forward-mode dK/dphi | Laplace marginal gradient · SKIM, p=200 | wall time per differentiation (s): 1.47 s -> 0.009 s | Helped |
| Marginalize latent Gaussian with embedded Laplace approximation | Dynamic HMC · Prostate cancer horseshoe regression | divergent transitions: 13 -> 0 | Helped |
| Marginalize latent Gaussian with embedded Laplace approximation | Dynamic HMC · SKIM, 200 covariates, delta_a=0.8 | divergent transitions: 36 -> 0 | Helped |
| Marginalize latent Gaussian with embedded Laplace approximation | Dynamic HMC · SKIM, full prostate data | estimated run time (hours): ~20 hours -> ~10 hours | Helped |
| Marginalize latent Gaussian with embedded Laplace approximation | Dynamic HMC · Disease map GP | warmup time (s): ~200 seconds -> ~10 seconds | Helped |
| Use analytical cotangent w in the adjoint method (ablation) | Adjoint differentiation · SKIM | differentiation speed | Helped |
| Raise delta_a from 0.8 to 0.99 for full HMC (ablation) | Full HMC · SKIM, 200 covariates | divergent transitions: 36 -> 0 | Helped |
| Raise delta_a from 0.8 to 0.99 for full HMC (ablation) | Full HMC (non-centered) · Prostate horseshoe regression | divergent transitions: ~150 -> 186 | Hurt |
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