Research map / Probabilistic and scientific modeling / Variational and generative sampling
Improving Gradient-Guided Nested Sampling for Posterior Inference
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes GGNS, a gradient-guided nested sampling algorithm using self-tuning Hamiltonian slice sampling with autodiff gradients, parallel dynamic live-point updates, clustering, and a new termination criterion, and combines it with GFlowNets for posterior/partition-function estimation.
Problem
Nested sampling for Bayesian evidence and posterior inference scales poorly with dimensionality and struggles with multimodal distributions; existing gradient-based step samplers (Hamiltonian slice sampling) are inefficient and unreliable in public implementations.
Approach
Use Hamiltonian slice sampling with gradients obtained via differentiable programming (autodiff) and adaptive time steps, trajectory preservation, parallel dynamic live-point replacement, cluster-based mode-collapse mitigation, and a termination criterion based on X·L, so that the number of live points need not scale with dimension; additionally, use GGNS samples to bootstrap GFlowNet/SDE sampler
Key results
- On the funnel and Gaussian mixture tasks, GGNS is the only method with log-evidence bias unbiased at one sigma (Gaussian mixture 0.029±0.132; funnel -0.051±0.353).
- GGNS likelihood-evaluation scaling is roughly linear in dimension at fixed n_live=200, versus quadratic for PolyChord and dynesty slice mode.
- Mode-collapse mitigation increased modes found for n_live=20 from 3.6 to 4.1 on a nine-Gaussian mixture (averaged over 10 runs).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add mode-collapse mitigation (ablation) | GGNS · Nine-Gaussian mixture, n_live = 20 | average number of modes found: $3.6$ -> $4.1$ | Helped |
| add mode-collapse mitigation (ablation) | GGNS · Nine-Gaussian mixture, n_live = 50 | average number of modes found: $6.4$ -> $6.4$ | No clear effect |
| add mode-collapse mitigation (ablation) | GGNS · Nine-Gaussian mixture, n_live = 100 | average number of modes found: $8.2$ -> $8.4$ | Helped |
| add mode-collapse mitigation (ablation) | GGNS · Nine-Gaussian mixture, n_live = 200 | average number of modes found: $8.9$ -> $9$ | Helped |
| replace adaptive step size with fixed dt = 0.5 (ablation) | GGNS · Gaussian likelihood, dimensionality scaling experiment | log-evidence estimation bias | Hurt |
| replace adaptive step size with fixed dt = 0.1 (ablation) | GGNS · Gaussian likelihood, dimensionality scaling experiment | likelihood evaluations | Hurt |
| replace trajectory preservation with a fixed number of steps and keep the last sample (ablation) | GGNS · Gaussian likelihood, dimensionality scaling experiment | log-evidence estimation bias | Hurt |
| use fixed n_steps = 20 instead of trajectory preservation (ablation) | GGNS · Gaussian likelihood, dimensionality scaling experiment | log-evidence estimation bias | Hurt |
| use fixed n_steps = 200 instead of trajectory preservation (ablation) | GGNS · Gaussian likelihood, dimensionality scaling experiment | log-evidence estimation bias | Hurt |
| remove momentum noise from preserved trajectories (ablation) | GGNS · Gaussian likelihood, dimensionality scaling experiment | log-evidence estimation bias | Hurt |
| replace the GGNS termination criterion with the conventional criterion (ablation) | GGNS · Gaussian likelihood, d = 128 | likelihood evaluations: $ \sim 5.8 \cdot 10^6$ vs $ \sim 5.4 \cdot 10^6$ | Mixed |
| train the GFlowNet with on-policy trajectory balance only | GFlowNet stochastic control model · 25-Gaussian mixture | mode coverage | Hurt |
Surprising findings
- The log-evidence error for the torus molecule task decreases with dimensionality because the KL divergence between posterior and prior decreases in that example.
- Hamiltonian slice sampling in dynesty is described by its own documentation as substantially less efficient and reliable than other gradient-based approaches.
Limitations
- Log-evidence error has higher variance than other methods and only decreases sublinearly with n_live; hyperparameter tuning is claimed to be minimal but not fully demonstrated.
- Ablation of pruning and parallel evolution was not performed; FAB could not be trained on the torus task for comparison.
- Application to real molecular conformations is left for future work because no fully differentiable chemical simulator was used.
Experimental setup
Datasets: synthetic Gaussian likelihoods funnel distribution Gaussian mixture (9 and 81 modes) torus reward many-well (32-D) 25-Gaussian mixture strong lensing image inference (256-D)
Benchmarks: Gaussian likelihood log-evidence scaling funnel distribution Gaussian mixture torus reward normalization many-well 32-D mixture of 40 Gaussians 25-Gaussian GFlowNet mixture
Metrics: log-evidence bias number of likelihood evaluations number of modes found KDE visual comparison of samples
Baselines: PolyChord dynesty Hamiltonian Monte Carlo Sequential Monte Carlo Path Integral Sampler GFlowNet trajectory balance FAB
Builds on: nested sampling Hamiltonian slice sampling dynamic nested sampling PolyChord trajectory balance
Closest papers by meaning
- Functional Gradient Flows for Constrained Sampling (NeurIPS 2024 · similarity 0.86)
- Posterior Inference in Latent Space for Scalable Constrained Black-box Optimization (NeurIPS 2026 · similarity 0.86)
- End-to-end Learning of Gaussian Mixture Priors for Diffusion Sampler (ICLR 2025 · similarity 0.86)
- Provable Posterior Sampling with Denoising Oracles via Tilted Transport (NeurIPS 2024 · similarity 0.86)
- Annealing in variational inference mitigates mode collapse: a theoretical study on Gaussian mixtures (NeurIPS 2026 · similarity 0.85)
- Consistency Posterior Sampling for Diverse Image Synthesis (CVPR 2025 · similarity 0.85)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.