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An Entropy-based Coefficient of Determination with Adjustment of Optimization Bias — arXiv:2608.06624

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.06624
License (as archived): CC0-1.0
Archived: 2026-10-19T11:04:33.557Z
SHA-256 of the archived text: 0eb2e58edd5f6a47b55c34539fae9c0b6e1e1c16fb4c23aad6576462e7e913da
Stable URL of this page: https://metraipolis.com/documento/dc_3eeac37833fa

How to cite

An Entropy-based Coefficient of Determination with Adjustment of Optimization Bias — arXiv:2608.06624 — arXiv (en), https://arxiv.org/abs/2608.06624 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_3eeac37833fa (Metraipolis archive dc_3eeac37833fa, sha256 0eb2e58edd5f6a47b55c34539fae9c0b6e1e1c16fb4c23aad6576462e7e913da)

BibTeX

@misc{dc3eeac37833fa,
  title = {An Entropy-based Coefficient of Determination with Adjustment of Optimization Bias — arXiv:2608.06624},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.06624},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_3eeac37833fa; sha256 0eb2e58edd5f6a47b55c34539fae9c0b6e1e1c16fb4c23aad6576462e7e913da},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.06624. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Classical likelihood-ratio tests and $\Delta$AIC exacerbate the statistical significance crisis by scaling with sample size, often flagging negligible improvements as highly significant. While causal estimands like the average treatment effect (ATE) quantify practical magnitude, their reliance on the expectation operator ties them to the data's original coordinate scale. Furthermore, existing pseudo-$R^2$ metrics are inadequate: variance-based measures ignore higher-order distributional changes, and current formulations lack invariance to monotone transformations. We resolve these limitations by introducing Entropic Variance (EV) as a rigorous, scale-independent generalization of error variance in ordinary least squares. We define the population EV-based parameter, $\rho^2_V$, which projects unbounded cross-entropy onto a standardized $[0,1]$ scale, and establish that the EV-based $F_\text{V}$ statistic asymptotically follows an $F$-distribution. Building on these distributional properties, we propose two estimators: the empirical population $R^2_{\text{SV}}$ and the out-of-sample predictive $R^2_{\text{SVP}}$. Both are derived by exponentiating per-observation cross-entropy and incorporate a degrees-of-freedom correction for training optimism. Leveraging the $F_\text{V}$-distribution, we derive refined $p$-values and confidence intervals for $\rho^2_V$ without requiring intractable Fisher information matrices. Simulation studies and a Parkinson's disease microbiome application demonstrate the superiority of variable selection via these EV-$R^2$ metrics. Notably, evaluating the $R^2_{\text{SVP}}$ of a LASSO path via data-splitting reduced false discovery rates from 80% to 6% in simulations while fully preserving signal recall.

Tema degli esploratori: statistica e scienza dei dati (retro-catalogo arXiv: annunci del 2026-08-10 in stat.ME).
Categorie arXiv: Methodology (stat.ME) ; Information Theory (cs.IT); Genomics (q-bio.GN).
Pagina del lavoro: https://arxiv.org/abs/2608.06624 — 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 2026-10-19T11:02:56.760Z dalla pagina https://arxiv.org/catchup/stat.ME/2026-08-10?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).