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Active Sequential Posterior Estimation for Sample-Efficient Simulation-Based Inference
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Proposes ASNPE, an SNPE variant that adds an active-learning acquisition over parameter candidates (disagreement between marginal and per-parameter posteriors under MC-dropout MAF) and applies it to Munich OD calibration and SBI benchmarks.
Problem
Simulation-based inference and origin-destination calibration require many expensive simulator runs; existing sequential NPE methods (SNPE) choose simulation parameters without explicitly accounting for the uncertainty of the neural density estimator.
Approach
Integrates an acquisition function into the SNPE loop that scores candidate parameters from the current proposal by the expected squared disagreement between the marginal posterior and posteriors induced by sampled NDE parameters (approximated with MC-dropout), trained with APT so that proposal correction is unchanged.
Key results
- On the Munich network under Prior I (Hours 5:00-6:00, Congestion A), ASNPE reaches RMSNE 0.147 ± 0.011 versus 0.201 for SNPE and 0.193 for PC-SPSA.
- ASNPE is outperformed by PC-SPSA in two Prior I settings for Hours 8:00-9:00, per the authors.
- On SBI benchmarks ASNPE beats SNPE-C on C2ST and MMD across all three tasks at 1024 simulations (e.g., Bernoulli GLM MMD 0.146 vs 0.210).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use active acquisition of simulation parameters instead of non-active SNPE-C (ablation) | SNPE-C posterior estimation · Bernoulli GLM | C2ST: 0.749 ± 0.017 -> 0.725 ± 0.012 | Helped |
| Use active acquisition of simulation parameters instead of non-active SNPE-C (ablation) | SNPE-C posterior estimation · Bernoulli GLM | MMD: 0.210 ± 0.024 -> 0.146 ± 0.057 | Helped |
| Use active acquisition of simulation parameters instead of non-active SNPE-C (ablation) | SNPE-C posterior estimation · SLCP distractors | C2ST: 0.987 ± 0.001 -> 0.985 ± 0.002 | Helped |
| Use active acquisition of simulation parameters instead of non-active SNPE-C (ablation) | SNPE-C posterior estimation · SLCP distractors | MMD: 0.172 ± 0.001 -> 0.148 ± 0.022 | Helped |
| Use active acquisition of simulation parameters instead of non-active SNPE-C (ablation) | SNPE-C posterior estimation · Gaussian mixture | C2ST: 0.773 ± 0.009 -> 0.771 ± 0.006 | Helped |
| Use active acquisition of simulation parameters instead of non-active SNPE-C (ablation) | SNPE-C posterior estimation · Gaussian mixture | MMD: 0.167 ± 0.006 -> 0.150 ± 0.025 | Helped |
| Use ASNPE instead of PC-SPSA | Munich OD calibration · Prior I, 8:00-9:00, congestion A | RMSNE: 0.159 ± 0.036 -> 0.165 ± 0.064 | Hurt |
| Use ASNPE instead of PC-SPSA | Munich OD calibration · Prior I, 8:00-9:00, congestion B | RMSNE: 0.159 ± 0.046 -> 0.161 ± 0.079 | Hurt |
Surprising findings
- PC-SPSA beats ASNPE in some high-dimensional traffic settings, which the authors attribute to batch updates versus serial per-simulation updates.
- ASNPE does not beat SNPE-C on SLCP distractors mean error and on Bernoulli GLM median distance, showing mixed gains on benchmarks.
Limitations
- Batched updates every 32 simulations delay incorporation of informative data relative to serial methods like PC-SPSA.
- Evaluated on a single traffic network and small sample horizons (128 simulations; 1024 on benchmarks) with five trials.
Experimental setup
Datasets: Munich traffic network (SUMO simulations) SBI benchmarks SLCP distractors, Bernoulli GLM, Gaussian mixture (sbibm)
Benchmarks: Munich traffic network OD calibration (RMSNE) SLCP distractors Bernoulli GLM Gaussian mixture
Metrics: RMSNE C2ST MMD posterior median distance posterior mean error
Baselines: SPSA PC-SPSA MC-ABC SNPE SNPE-C
Builds on: SNPE-C (APT) SNPE Bayesian active learning / expected information gain MC-dropout SPSA
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