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Graph-Based Testing of Conditional Mean Independence with Applications to Large Language Model Evaluation — arXiv:2611.01773

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.01773
License (as archived): CC0-1.0
Archived: 2026-11-03T18:43:37.170Z
SHA-256 of the archived text: fa27a9abec4ca9bb9a5ab2f6e618ced67ce2780fc68e49149a9394985fde1df1
Stable URL of this page: https://metraipolis.com/documento/dc_7a12cbf64da3

How to cite

Graph-Based Testing of Conditional Mean Independence with Applications to Large Language Model Evaluation — arXiv:2611.01773 — arXiv (en), https://arxiv.org/abs/2611.01773 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_7a12cbf64da3 (Metraipolis archive dc_7a12cbf64da3, sha256 fa27a9abec4ca9bb9a5ab2f6e618ced67ce2780fc68e49149a9394985fde1df1)

BibTeX

@misc{dc7a12cbf64da3,
  title = {Graph-Based Testing of Conditional Mean Independence with Applications to Large Language Model Evaluation — arXiv:2611.01773},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.01773},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_7a12cbf64da3; sha256 fa27a9abec4ca9bb9a5ab2f6e618ced67ce2780fc68e49149a9394985fde1df1},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.01773. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study whether a predictor $X$ provides additional information for predicting a scalar response $Y$ after adjustment for other variables $Z$, formalized by testing $\mathsf{H}_0:\E(Y\mid X,Z)=\E(Y\mid Z)$. Existing methods often require estimating nuisance functions involving $X$, which can be difficult for high-dimensional or structured predictors. We propose a graph-based test that extends the edge count principle to covariate adjustment. It represents $X$ through pairwise dissimilarities, estimates only the baseline regression $\E(Y\mid Z)$, and aggregates products of held-out residuals across graph edges. We develop sample-splitting and two-fold cross-fitting versions. Under regularity conditions, both have standard normal null limits, yielding analytic $p$-values, and are consistent under graph-smooth and graph-rough alternatives. Simulations with vector, image, and network predictors show good size control and power advantages over competing procedures, with cross-fitting improving power across the main alternatives. Applications examine human quality ratings, mathematical error labels, and LLM response preferences. Our method detects associations with quality ratings and an LLM judge's preferences after adjustment for text length and other recorded characteristics.

Tema degli esploratori: statistica e scienza dei dati (elenco arXiv stat.ME, nuovi lavori del giorno).
Categorie arXiv: Methodology (stat.ME).
Pagina del lavoro: https://arxiv.org/abs/2611.01773 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-03T18:13:53.113Z dalla pagina https://arxiv.org/list/stat.ME/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).