SLICE: Sequential Likelihood-Free Inference via Conformal E-Values
Abstract
Many scientific models can be simulated but have intractable likelihoods, making frequentist uncertainty quantification difficult. We construct exact anytime-valid confidence sequences for the parameters of such models. At each observation, fresh simulations from each candidate null conformalize a positive predictable score into a conditional e-value; their product is a test martingale, which we invert over the parameter. Validity holds for any such score, whatever its accuracy. We show that the oracle likelihood-ratio score maximizes expected log growth, which motivates approximating it with an amortized neural ratio estimator. On synthetic benchmarks, an audit of model routing in an LLM API, and microlensing data, the resulting confidence sequences stay valid under continuous monitoring, where fixed-sample methods do not, and neural scores remain competitive with exact likelihood ratios and application-specific scores.
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BibTeX
@misc{cortinovis2026slice,
title = {{SLICE: Sequential Likelihood-Free Inference via Conformal E-Values}},
author = {Stefano Cortinovis and Laura Battaglia and François Caron},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13855},
eprint = {2610.13855},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13855},
}
RIS
TY - UNPB
TI - SLICE: Sequential Likelihood-Free Inference via Conformal E-Values
AU - Stefano Cortinovis
AU - Laura Battaglia
AU - François Caron
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.13855
UR - https://arxiv.org/abs/2610.13855
AB - Many scientific models can be simulated but have intractable likelihoods, making frequentist uncertainty quantification difficult. We construct exact anytime-valid confidence sequences for the parameters of such models. At each observation, fresh simulations from each candidate null conformalize a positive predictable score into a conditional e-value; their product is a test martingale, which we invert over the parameter. Validity holds for any such score, whatever its accuracy. We show that the oracle likelihood-ratio score maximizes expected log growth, which motivates approximating it with an amortized neural ratio estimator. On synthetic benchmarks, an audit of model routing in an LLM API, and microlensing data, the resulting confidence sequences stay valid under continuous monitoring, where fixed-sample methods do not, and neural scores remain competitive with exact likelihood ratios and application-specific scores.
ER -