REVIEW
A regularization-independent Information Criterion for correlated data
High Energy Physics - Lattice · Submitted 9 Nov 2026 · 19 references
Pith's verdict: RIAIC is a clean, well-derived fix for a real problem in lattice QCD model selection; the main limitation (correct specification assumption) is stated, and the numerical test is honest but limited to a regime where the assumption holds.
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Referee report
The paper
The paper claims
A regularization-independent Akaike Information Criterion (RIAIC) is derived for model and data subset selection with regularized fits on correlated data, and shown to reproduce standard correlated AIC selection on lattice QCD data.
The reading
This paper introduces the RIAIC, a new information criterion that is on average independent of the regularization. It achieves this by estimating the Kullback-Leibler divergence of the correlated (non-regularized) model, rather than the regularized one. The regularization effects are absorbed into a bias correction. The RIAIC has the same expectation value as the standard correlated AIC, so it can be used for model and data subset selection even when regularized fits are necessary. A Bayesian extension, the RIBAIC, is also derived.
The authors test the RIAIC on lattice QCD data for nucleon correlation functions. They show that while the naive regularized AIC systematically favors less regularized datasets and can select the wrong model, the RIAIC reproduces the selection of the standard correlated AIC within statistical uncertainties. This enables reliable model and data subset selection in regularized fits, which is common in lattice QCD and other fields with correlated data.
Extended reading notes
Core claim
The central claim is that the RIAIC, defined in eq. (3.4), is an unbiased estimator of the correlated model-dependent contribution to the Kullback-Leibler divergence and is on average regularization-independent. Its expectation value equals that of the standard correlated AIC, enabling model and data subset selection with regularized fits. This is stated in the abstract and Sec. 3.
Load-bearing premise
The weakest assumption is that the model is correctly specified (the data-generating distribution belongs to the set of candidate models) and that the regularization only removes poorly-estimated information that is irrelevant for parameter estimation. If the regularization removes information that is relevant for a correct estimation of the model parameters, the RIAIC may deviate from the correlated AIC (Sec. 3, paragraph after eq. (3.5), and b122). Additionally, the derivation assumes independence between fitted and non-fitted datasets (b55), which may not hold in practice; the paper notes this is left for future work.
Original abstract
We generalize the Akaike Information Criterion (AIC) to allow model and data subset selection when regularized fits are performed on correlated data. While the standard generalization to regularized fits is inherently dependent on the type of regularization applied to the data covariance matrix, our definition, the RIAIC, is, on average, regularization-independent. The regularization-independence is achieved by defining the new Information Criterion as an estimator of the model-dependent contribution to the correlated Kullback--Leibler divergence. The Bayesian extension is derived as well. We test the new criterion on lattice QCD data by performing regularized fits and show that it reproduces the selection properties of the standard correlated AIC, with fluctuations which are compatible with the expected statistical uncertainties. These results enable the application of subset and model selection techniques to cases where regularizations are applied to the covariance matrix of the fitted dataset.
Figures
Figures reproduced from arXiv:2611.12877 by the authors.
References
Discussion
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