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# Confidence Sequence

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  1. arXiv

    LLM labels stop being ground truth: AAELI spends human audits where they matter, reaching the same precision with about 21% fewer labels

    Large language models can label every instance cheaply, but their judgments are biased and their errors correlated, so treating them as human labels can mislead statistical inference. AAELI uses model outputs as auxiliary information to guide a limited human audit and builds anytime-valid confidence sequences from predictable empirical-likelihood processes, so coverage survives data-dependent stopping. On Chatbot Arena, AAELI needs about 870 human labels on average to reach a confidence-sequence width of 0.10, versus about 1,100 on average for the strongest baseline, RASI, a saving of roughly 21%.

    National University of Singapore
    Hongfu Gao（First author）
    Empirical Likelihood InferenceAAELIConfidence SequenceAdaptive Human Auditing
  2. arXiv

    Simulators run but likelihoods do not: an anytime-valid confidence sequence for parameters, with neural scores near exact ratios

    For models that can be simulated but whose likelihood cannot be evaluated, SLICE treats fresh simulations under each candidate parameter as references, normalizes the observed score into a conditional e-value, and multiplies these factors into a test martingale that is inverted into an anytime-valid confidence sequence. Validity holds for any positive predictable score, while the score only sets how fast the sequence shrinks; on synthetic benchmarks, a semi-synthetic audit of model routing in an LLM API, and OGLE-IV microlensing data, amortized neural ratio scores come close to exact likelihood ratios and application-specific scores.

    University of Oxford
    Stefano Cortinovis（First author）
    SLICE: Sequential Likelihood-Free Inference via Conformal E-ValuesConfidence SequenceNeural Ratio EstimationConformal PredictionSimulation-Based Inference

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