Research map / Probabilistic and scientific modeling / Variational and generative sampling
Path-Guided Particle-based Sampling
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Proposes path-guided particle-based sampling (PGPS), which learns a neural vector field that moves particles along a partition-free Log-weighted Shrinkage density path from an initial distribution to the posterior, with a Wasserstein error bound and experiments against SVGD, LD/SGLD and PFG.
Problem
Particle-based Bayesian inference (e.g., gradient-flow samplers like SVGD and Langevin dynamics) mixes slowly and misses or misweights posterior modes, hurting calibration and accuracy for multimodal targets such as BNN posteriors.
Approach
Instead of descending a KL functional, particles follow an ODE whose neural vector field is trained to match the Fokker-Planck equation of a designed partition-free density path (Log-weighted Shrinkage), so intermediate targets guide particles across modes; the loss needs no partition function.
Key results
- On Noisy MNIST with 10 particles, PGPS reaches 0.8788 ACC vs 0.8282 (SVGD), 0.6419 (SGLD), 0.7119 (PFG), with ECE 0.1716 vs 0.1941 for SVGD.
- On UCI, PGPS has the best ECE on 4 of 7 datasets (e.g., WINERED 0.0366 vs 0.0402 SVGD) and best accuracy on several datasets.
- On the mode-seeking Gaussian mixture, PGPS recovers the right mode (score_1 near the true 0.49) while LD, SVGD, and PFG fail.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use the LwS path to guide particles rather than gradient-flow sampling | PGPS · Gaussian mixture mode discovery | right-mode score | Helped |
| use the LwS path to guide particles rather than gradient-flow sampling | PGPS · Gaussian mixture with negligible left mode | score_2 | Helped |
| use PGPS rather than LD | Bayesian sampling of four 8-dimensional Gaussian mixture · Gaussian mixture weight recovery | weight mismatch error: 0.3314 average for LD | Helped |
| use PGPS rather than gradient-flow baselines | BNN inference · Noisy MNIST | ACC: 0.8282 -> 0.8788 | Helped |
| use PGPS rather than gradient-flow baselines | BNN inference · Noisy MNIST | NLL: 1.8202 ± 0.019; SGLD: 1.8184 ± 0.127 | Mixed |
| use PGPS rather than gradient-flow baselines | BNN inference · Noisy MNIST | ECE: 0.1752 -> 0.1716 | Helped |
| use the learned vector field instead of training-free Langevin adjustment (ablation) | PGPS · Noisy MNIST, 10 particles | ACC: 0.8380 ±0.0504 -> 0.8683 ±0.0193 | Helped |
| use the learned vector field instead of training-free Langevin adjustment (ablation) | PGPS · Noisy MNIST, 10 particles | ECE: 0.1659 ±0.0083 -> 0.1680 ±0.0132 | Hurt |
| use the learned vector field instead of training-free Langevin adjustment (ablation) | PGPS · Noisy MNIST, 50 particles | NLL: 1.8467 ±0.0108 -> 1.8473 ±0.0101 | Hurt |
| use the learned vector field instead of training-free Langevin adjustment (ablation) | PGPS · Noisy MNIST, 50 particles | ACC: 0.8672 ±0.0298 -> 0.9006 ±0.0071 | Helped |
| use the learned vector field instead of training-free Langevin adjustment (ablation) | PGPS · Noisy MNIST, 100 particles | ACC: 0.8956 ±0.0259 -> 0.9182 ±0.0036 | Helped |
| add shrinkage to the log-weighted path (ablation) | tf-PGPS · Two-Gaussian mode discovery | right-mode capture | Helped |
Surprising findings
- SVGD performs worse than LD on the weight recovery task, which the authors attribute to curse of dimensionality.
- Training-free PGPS (Langevin adjustment only) is competitive with trained PGPS on several metrics, and NLL increases as particle count grows.
Limitations
- Standard PGPS requires training a neural network vector field, which adds cost compared with training-free methods.
- Theoretical bound relies on Lipschitz and bounded-vector-field assumptions; finite-particle generalization is not analyzed.
- Hyperparameters (alpha, beta, step sizes) affect performance and must be chosen.
Experimental setup
Datasets: UCI datasets (SONAR, WINEWHITE, WINERED, AUSTRALIAN, HEART, GLASS, COVERTYPE) MNIST (with Gaussian noise perturbation) synthetic Gaussian mixtures
Benchmarks: UCI classification datasets Noisy MNIST synthetic Gaussian mixture mode seeking
Metrics: ECE accuracy NLL mode-capture score weight mismatch error
Baselines: SVGD SGLD PFG LD
Builds on: Stein variational gradient descent Langevin dynamics preconditioned functional gradient flow annealed Langevin dynamics
Closest papers by meaning
- Variance Reduction in Stochastic Particle-Optimization Sampling (ICML 2020 · similarity 0.88)
- Scalable approximate Bayesian inference for particle tracking data (ICML 2018 · similarity 0.88)
- Sampling in Unit Time with Kernel Fisher-Rao Flow (ICML 2024 · similarity 0.87)
- Functional Gradient Flows for Constrained Sampling (NeurIPS 2024 · similarity 0.86)
- To discretize continually: Mean shift interacting particle systems for Bayesian inference (NeurIPS 2026 · similarity 0.86)
- Particle Guidance: non-I.I.D. Diverse Sampling with Diffusion Models (ICLR 2024 · similarity 0.86)
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