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Inductive Domain Transfer In Misspecified Simulation-Based Inference
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Proposes FRISBI, an inductive, amortized version of RoPE for misspecified simulation-based inference that jointly trains encoder with closed-form mini-batch OT plus supervised calibration loss, then amortizes the OT posterior mixture with a conditional normalizing flow.
Problem
Simulation-based inference of latent parameters is degraded by model misspecification; the existing RoPE method is transductive, requiring a batch of test samples and simulator access at inference, which limits scalability and stability.
Approach
Use rho=0 entropic OT, which admits a closed-form coupling, to enable mini-batch SGD training of a real-observation encoder jointly with a supervised calibration loss; then distill the resulting OT-based posterior mixture into a conditional normalizing flow conditioned on embeddings, removing simulator access at test time.
Key results
- Across calibration sizes, FRISBI consistently outperforms the single-sample RoPE baseline in LPP while keeping ACAUC near zero for most sizes, and matches or exceeds full-test RoPE with larger calibration sets.
- On the cardiac biomarker (CO) estimation task with 200 calibration samples, FRISBI significantly outperforms all baselines including RoPE in LPP, with slight overconfidence (ACAUC < 0.2).
- The UDA NPE baseline fails completely under significant misspecification, showing the importance of a calibration set.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use FRISBI instead of single-sample RoPE | Inductive inference with calibration data · Benchmarks across calibration set sizes | LPP | Helped |
| Use FRISBI instead of single-sample RoPE | Inductive inference with calibration data · Benchmarks across calibration set sizes | ACAUC | Helped |
| Increase the calibration set size | FRISBI · Benchmarks across calibration set sizes | LPP | Mixed |
| Use FRISBI instead of standard NPE | SIR · SIR | LPP | Hurt |
| Use FRISBI instead of finetuning-only | CS · CS | LPP | No clear effect |
| Use joint training instead of amortizing RoPE's transductive solution (ablation) | FRISBI · Benchmarks across calibration set sizes | LPP | Helped |
| Use joint training instead of amortizing RoPE's transductive solution (ablation) | FRISBI · Benchmarks across calibration set sizes | ACAUC | Helped |
| Add posterior-mixture amortization to joint training (ablation) | FRISBI · Pendulum | LPP | Hurt |
| Add posterior-mixture amortization to joint training (ablation) | FRISBI · Light Tunnel, low-calibration regime | LPP | Helped |
| Increase the OT entropy regularization weight γ (ablation) | FRISBI · Light Tunnel, small calibration set | LPP | Helped |
| Reduce the OT entropy regularization weight γ (ablation) | FRISBI · Light Tunnel, calibration set of 1,000 samples | LPP | Helped |
| Increase the supervised-loss weight λ (ablation) | FRISBI · Light Tunnel, 10% label noise | ACAUC | Hurt |
Surprising findings
- Under minimal misspecification (CS and SIR), FRISBI and RoPE underperform vanilla NPE on SIR, indicating a standard NPE suffices there.
- The amortized RoPE-only variant performs worse than joint training, and the full pipeline gains are largely attributed to joint training.
Limitations
- Sensitivity to label noise in calibration pairs, especially at high noise levels.
- Joint training still involves two separate stages (joint OT-supervised training, then flow amortization).
- Experiments focus on low-dimensional problems; scalability to high dimensions is discussed but not tested.
Experimental setup
Datasets: synthetic pendulum (simulated and damped-pendulum emulated real) Causal Chambers wind tunnel Causal Chambers light tunnel MIMIC-II arterial blood pressure subset OpenBF simulator CS benchmark SIR benchmark
Benchmarks: synthetic pendulum Causal Chambers wind tunnel Causal Chambers light tunnel MIMIC-II cardiac biomarker estimation CS SIR
Metrics: log-posterior probability ACAUC
Baselines: RoPE full test RoPE single sample NPE UDA NPE OT-only (full test) OT-only (single sample) finetune-only SBI prior
Builds on: RoPE entropic optimal transport neural posterior estimation soft k-means mini-batch optimal transport
Closest papers by meaning
- Addressing Misspecification in Simulation-based Inference through Data-driven Calibration (ICML 2025 · similarity 0.91)
- Consistency Models for Scalable and Fast Simulation-Based Inference (NeurIPS 2024 · similarity 0.88)
- Learning Likelihood-Free Reference Priors (ICML 2025 · similarity 0.85)
- All-in-one simulation-based inference (ICML 2024 · similarity 0.85)
- Robust Simulation-Based Inference under Missing Data via Neural Processes (ICLR 2025 · similarity 0.85)
- Closing the Approximation Gap in Simulation-free Latent SDEs (NeurIPS 2026 · similarity 0.84)
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