Research map / Probabilistic and scientific modeling / Uncertainty and Gaussian processes
Addressing Misspecification in Simulation-based Inference through Data-driven Calibration
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Proposes RoPE, which fine-tunes NPE's summary network on a small labeled real calibration set and couples simulated and real observations with entropic semi-balanced optimal transport to produce calibrated posteriors under simulator misspecification.
Problem
Simulation-based inference yields unreliable, miscalibrated posteriors when the simulator is misspecified relative to real-world data, which blocks SBI use where only misspecified simulators exist.
Approach
Model the sim-to-real misspecification as an entropic semi-balanced optimal transport coupling between learned summary representations of real and simulated observations (summaries fine-tuned on a small calibration set), and form the real-data posterior as an OT-weighted mixture of NPE posteriors.
Key results
- RoPE returns well-calibrated or slightly underconfident posteriors across all six tasks with fixed gamma=0.5 and tau=0.9 for RoPE*, while significantly reducing uncertainty versus the prior.
- On the light tunnel task, RoPE remains the best approach even with calibration sets above 1000 examples, while J-NPE and MLP are overconfident (positive ACAUC) for larger calibration sets.
- Ablations show the OT step is crucial: OT-only matches RoPE on tasks A, D, and F but tuning-only performs poorly except on task B.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add the OT step to tuning-only (ablation) | RoPE · Tasks A, C, D, E, F | LPP and ACAUC | Helped |
| Add fine-tuning to OT-only (ablation) | RoPE · Tasks C and E | LPP and ACAUC | Helped |
| Add the OT step to tuning-only (ablation) | RoPE · Task B (SIR) | LPP and ACAUC | No clear effect |
| Add fine-tuning to OT-only (ablation) | RoPE · Tasks A, D, and F | LPP and ACAUC | No clear effect |
| Increase calibration set size | RoPE · Six benchmark tasks | LPP and ACAUC | Helped |
| Increase entropic regularization to gamma >= 5 | RoPE · Light Tunnel (Task E) | LPP and ACAUC | Hurt |
| Use unbalanced OT with tau < 1 | RoPE · Light Tunnel (Task E), misspecified prior | LPP | Helped |
| Use unbalanced OT with lower tau | RoPE · Pendulum (Task C), increasing prior misspecification | LPP and ACAUC | Helped |
| Use tau = 1 instead of lower tau | RoPE · Pendulum (Task C), correctly specified prior | LPP and ACAUC | Helped |
| Apply RoPE instead of NPE trained on simulated data | SIR (Task B) · SIR | LPP | Hurt |
| Apply RoPE instead of J-NPE or MLP | Six benchmark tasks · Six benchmark tasks, small calibration sets | LPP and ACAUC | Helped |
| Apply RoPE instead of J-NPE or MLP | Six benchmark tasks · Larger calibration sets | LPP | Mixed |
Surprising findings
- Standard NPE trained on simulations achieves the best results on the SIR benchmark, suggesting its misspecification is not a challenging test case.
- The standard statistical definition of misspecification can hold while posteriors remain biased, motivating a redefinition of misspecification in terms of posterior transferability.
Limitations
- Curse of dimensionality: higher-dimensional parameter spaces may require more calibration data and simulations; experiments are low-dimensional.
- Assumes calibration set is i.i.d. with the test distribution; non-iid calibration can degrade performance.
- Sinkhorn OT cost is quadratic in number of real observations, limiting scalability to large test sets.
Experimental setup
Datasets: CS simulator (cancer and stromal cell development) SIR stochastic epidemic simulator Pendulum simulator Hemodynamics PDE simulator Light tunnel dataset Wind tunnel dataset
Benchmarks: CS SIR Pendulum Hemodynamics Light tunnel Wind tunnel
Metrics: log-posterior probability (LPP) average coverage AUC (ACAUC)
Baselines: NPE J-NPE MLP NPE-RS Noisy NPE HVAE prior SBI posterior
Builds on: neural posterior estimation semi-balanced optimal transport Sinkhorn algorithm robust neural posterior estimation (RNPE)
Closest papers by meaning
- Inductive Domain Transfer In Misspecified Simulation-Based Inference (NeurIPS 2025 · similarity 0.91)
- Consistency Models for Scalable and Fast Simulation-Based Inference (NeurIPS 2024 · similarity 0.90)
- Learning Likelihood-Free Reference Priors (ICML 2025 · similarity 0.87)
- Model-Free Assessment of Simulator Fidelity via Quantile Curves (NeurIPS 2026 · similarity 0.87)
- Robust Simulation-Based Inference under Missing Data via Neural Processes (ICLR 2025 · similarity 0.86)
- Active Sequential Posterior Estimation for Sample-Efficient Simulation-Based Inference (NeurIPS 2024 · similarity 0.85)
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