A Closed-Form Estimator and Diagnostic Battery for Anchor-Judge Error Correlation, Under a Single-Common-Factor Model
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单共同因子模型下锚点与评判器误差相关的闭式估计及诊断
- 研究问题
- 在用外部锚点分解大语言模型评判器误差时，如何估计锚点与共同误差的相关性，并判断单共同因子模型是否适用？
- 方法与思路
- 作者利用至少两个评判器与两个锚点构造闭式识别，配套协方差、过度识别和家族分块诊断，并使用自助区间及弱识别筛查。
- 材料陈述的贡献
- 摘要称，作者刻画识别失败边界与有序评分的识别层级；真实面板均被预检拒绝，估计器验证来自模拟及半合成压力测试。
- 阅读关注点
- 应核对共同因子模型的不可检验部分、诊断能漏掉哪些违背，以及家族分块修正、弱识别筛查与有序评分结果的条件。
- 阅读边界
- 这是 arXiv 预印本，同行评审及接收状态未核实；尚无真实面板通过模型预检，摘要未提供区间覆盖数值，不能声称真实数据估计已获验证。
原文摘要
When an external reference set (an anchor) is used to decompose an LLM-judge panel's error into a quality signal and a shared common-mode error, standard practice assumes the anchor is uncontaminated: its error uncorrelated with the judges' shared error. We study when that assumption can be dropped and replaced by an estimate. Under a single-common-factor model, >=2 judges and >=2 anchors point-identify the quality variance, the common-mode variance, and each anchor's contamination correlation rho_k in closed form, with an exact per-anchor-pair failure boundary; a designated clean-anchor estimator, by contrast, reports a contaminated companion anchor as fully clean once its trusted anchor is itself contaminated. Because the single-common-factor assumption is itself untestable, the estimator ships gated behind a calibrated diagnostic battery (judge-covariance dispersion; over-identification; a family-block test from judge metadata, with a family-blocked estimator that removes family-level shared-residual bias exactly), bootstrap confidence intervals with measured coverage, and a weak-identification screen. A proposition maps which violations bias rho_k, in which direction, and which evade detection. For ordinal scores we show an identification hierarchy: with all variables ordinal, rho_k is not identified at any number of anchors; with ordinal judges and >=3 continuous anchors it is, and we give an estimator for that case. On real data the validation is asymmetric, and we say so plainly: the diagnostics are validated in the rejecting direction (both real panels we test are correctly rejected by the model-adequacy pre-test), while the estimator is validated in simulation and stress-tested semi-synthetically under oracle calibration; no real panel has yet passed the pre-test, and the pre-test exists precisely to say so. All results replay offline from shipped, checksummed artifacts.