Research map / Probabilistic and scientific modeling / Uncertainty and Gaussian processes
Simultaneous identification of models and parameters of scientific simulators
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Proposes simulation-based model inference (SBMI), an amortized NPE method that jointly infers discrete model components (via mixtures of multivariate binary Grassmann distributions) and their continuous parameters (via a marginalizing MDN) from black-box simulators.
Problem
Inferring joint posteriors over which discrete model components a scientific simulator includes and their associated parameters, when likelihoods are intractable and model components may be redundant.
Approach
Factorizes the joint posterior as p(M|x)p(θ|M,x) with a conditional mixture of Grassmann binary distributions for the model posterior and a Gaussian MDN over the full parameter space that is marginalized over absent components, trained end-to-end with NPE losses from prior samples generated via a graph-based model prior.
Key results
- On the additive model, SBMI model posterior marginals reach 0.86 (0.09) vs. 0.88 (0.15) for reference posterior with KL 0.28 vs. prior 11.26.
- Categorical model posterior performs much worse than MoGr on the 11-component additive model and fails to reach the RMSE lower bound.
- On Hodgkin-Huxley synthetic traces, mean marginal model posterior performance is 0.85 (0.16), rising to 0.96 (0.03) for traces with spikes.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use SBMI instead of the prior for additive-model inference | Additive model (6 components) · Additive model (6 components) | marginal performance: 0.53 (0.12) -> 0.86 (0.09) | Helped |
| Replace the MoGr model posterior with a flat categorical distribution (ablation) | SBMI on the additive model · Additive model | data efficiency | Hurt |
| Use MoGr rather than categorical model posterior distributions (ablation) | SBMI on the additive model · Additive model (11 components) | RMSE | Helped |
| Increase the number of MoGr and Gaussian MDN mixture components from three to twelve (ablation) | SBMI on the additive model · Additive model (11 components) | RMSE | No clear effect |
| Use MoGr rather than a categorical model posterior (ablation) | SBMI on the additive model · Additive model (20 components) | predictive performance | Helped |
| Replace the structured Hodgkin-Huxley model prior with a fully connected prior (ablation) | SBMI · Hodgkin-Huxley synthetic samples and Allen Cell Types recordings | MSE on summary statistics: 0.06±0.09 -> 0.10 ± 0.14; 0.24 ±0.11 -> 0.48 ± 0.55 | Mixed |
| Use SBMI posterior predictives rather than ground-truth resampling | SBMI on DDMs · DDM synthetic test set | MSE on densities (· 10⁻²): 3.14 (5.83) -> 3.23 (6.57) | Hurt |
| Condition Hodgkin-Huxley inference on traces that contain spikes | SBMI · Hodgkin-Huxley synthetic test traces | marginal model posterior performance: 0.85±0.16 -> 0.96±0.03 | Helped |
Surprising findings
- On the Allen recordings, the fully connected model prior produced substantially worse posterior predictive performance (MSE 0.48) than the domain-informed prior (MSE 0.24).
Limitations
- Model vector is an ordered fixed-length binary vector, restricting the model space representation.
- Reference posteriors are computationally infeasible for larger model spaces, limiting direct accuracy evaluation.
- DDM evaluation relies on posterior predictives and model posteriors because no efficient likelihood is available.
Experimental setup
Datasets: simulated additive model data simulated drift-diffusion data monkey random dot motion decision-making data simulated Hodgkin-Huxley traces Allen Cell Types database voltage recordings
Benchmarks: additive model reference posteriors DDM posterior predictives Hodgkin-Huxley posterior predictives Allen Cell Types recordings
Metrics: KL divergence RMSE marginal model posterior performance c2st simulation-based calibration MSE on posterior predictives
Baselines: categorical model posterior MADE fully connected model prior pyDDM point estimates reference posterior via importance sampling
Builds on: neural posterior estimation sbi toolbox Grassmann distributions (Arai) pyDDM symbolic regression
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