Research map / Probabilistic and scientific modeling / Uncertainty and Gaussian processes
Variational Inference with Coverage Guarantees in Simulation-Based Inference
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes CANVI, which wraps amortized variational posteriors with split conformal prediction, selects the most efficient candidate by estimated volume, and recalibrates on a fresh set to give marginal coverage guarantees in simulation-based inference.
Problem
Amortized variational inference in simulation-based inference yields posterior approximations with no guarantees on calibration (coverage), and existing calibration fixes are heuristic or require tuning.
Approach
Apply split conformal prediction with the score 1/q(theta|x) on top of amortized VI posteriors, pick the candidate approximator minimizing estimated predictive efficiency (Lebesgue volume of regions), then recalibrate on a separate dataset so that marginal coverage holds after selection; requires only forward-model samples.
Key results
- CANVI calibrates NPE on SBI benchmarks in under one second, with calibration curves lying on the y=x line while baseline BNRE, NPE, NRE, and related methods are miscalibrated.
- On ARCH, FAVI-trained posteriors after CANVI recalibration give higher predictive efficiency than ELBO- and IWBO-trained ones (e.g., volume 0.7451 for FAVI vs 1.3184 for ELBO at 1-alpha=0.95 level reported in table for alpha=0.05 threshold).
- For galaxy spectra (PROVABGS), CANVI with FAVI achieves nearly perfect calibration with minimal enlargement of high-density regions, while ELBO-based regions become too large to be informative.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Conformalize the ELBO posterior | ELBO posterior · ARCH, target coverage 0.50 | coverage: 0.0007 -> 0.4970 | Helped |
| Conformalize the IWBO posterior | IWBO posterior · ARCH, target coverage 0.95 | coverage: 0.4074 -> 0.9548 | Helped |
| Conformalize the FAVI posterior | FAVI posterior · ARCH, target coverage 0.95 | coverage: 0.9260 -> 0.9487 | Helped |
| Conformalize the ELBO posterior | ELBO posterior · SED, target coverage 0.95 | coverage: 0.6824 -> 0.9499 | Helped |
| Conformalize the IWBO posterior | IWBO posterior · SED, target coverage 0.95 | coverage: 0.9248 -> 0.9510 | Helped |
| Conformalize the FAVI posterior | FAVI posterior · SED, target coverage 0.95 | coverage: 0.9532 -> 0.9461 | No clear effect |
| Use 10 mixed samplers instead of only the variational posterior as the volume-estimation sampler (ablation) | CANVI volume estimator · ARCH | volume estimate accuracy | Helped |
| Use 10 mixed samplers instead of only the variational posterior as the volume-estimation sampler (ablation) | CANVI volume estimator · ARCH, ELBO volume estimate | estimated volume: 50.6595 (8.1313) -> 1.4151 (0.2181) | Helped |
| Use 10 mixed samplers instead of only the variational posterior as the volume-estimation sampler (ablation) | CANVI volume estimator · ARCH, IWBO volume estimate | estimated volume: 69.6484 (2.2495) -> 1.5206 (0.1114) | Helped |
Surprising findings
- The ELBO-trained approximator on the galaxy spectra task was so underdispersed that the conformal quantile was zero up to machine precision, yielding an infinite volume estimate.
- Conformal correction can either enlarge or shrink regions depending on the direction of miscalibration of the underlying variational posterior.
Limitations
- Guarantees are marginal rather than conditional; group-conditional extension only sketched in appendix.
- Efficiency guarantee relies on Assumptions about Lipschitz efficiency and a Monte Carlo estimator assumption that are not proven in general and only validated empirically.
- Requires exact forward-model samples; extension to misspecified forward models left to future work.
Experimental setup
Datasets: SBI benchmark tasks (Gaussian Linear, Gaussian Linear Uniform, SLCP with Distractors, Bernoulli GLM Raw, Gaussian Mixtur PROVABGS galaxy spectra simulator
Benchmarks: SBI benchmark tasks ARCH time-series model PROVABGS galaxy spectral energy distributions
Metrics: expected coverage predictive efficiency (expected Lebesgue volume of predictio calibration curves
Baselines: BNRE BNRE C NPE NRE NRE C Ratio BNPE ELBO IWBO FAVI
Builds on: split conformal prediction VFCP (validity-first conformal prediction) FAVI normalizing flows HPD-based conformal calibration
Closest papers by meaning
- All-in-one simulation-based inference (ICML 2024 · similarity 0.87)
- EigenVI: score-based variational inference with orthogonal function expansions (NeurIPS 2024 · similarity 0.87)
- Compositional simulation-based inference for time series (ICLR 2025 · similarity 0.87)
- Least squares variational inference (NeurIPS 2025 · similarity 0.87)
- VIKING: Deep variational inference with stochastic projections (NeurIPS 2025 · similarity 0.87)
- Closing the Approximation Gap in Simulation-free Latent SDEs (NeurIPS 2026 · similarity 0.86)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.