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Fitting Elephants in the Density Functionals Zoo: Statistical Criteria for the Evaluation of DFT methods as a Suitable Replacement for Counting Parameters
  • Roberto Peverati
Roberto Peverati
IJQC Special Issue
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Abstract

Counting parameters has become customary in the density functional theory community as a way to infer the transferability of popular approximations to the exchange–correlation functionals. Recent work in data science, however, has demonstrated that the number of parameters of a fitted model is not related to the complexity of the model itself, nor to its eventual overfitting. Using similar arguments, we show here that it is possible to represent every modern exchange–correlation functional approximation using just one single parameter. This procedure proves the futility of the number of parameters as a measure of transferability. To counteract this shortcoming, we introduce and analyze the performance of three statistical criteria for the evaluation of the transferability of exchange–correlation functionals. The three criteria are called Akaike information criterion (AIC), Vapnik–Chervonenkis criterion (VCC), and cross-validation criterion (CVC) and are used in a preliminary assessment to rank 60 exchange–correlation functional approximations using the ASCDB database of chemical data.

Peer review status:Published

17 Dec 2019Submitted to IJQC Special Issue
17 Dec 2019Reviewer(s) Assigned
21 May 2020Review(s) Completed, Editorial Evaluation Pending
25 May 20201st Revision Received
15 Jun 2020Editorial Decision: Accept
Published in 10.1002/qua.26379
10.22541/au.159223873.32760428
Anonymous IJQC Reviewer posted a review
In this manuscript, the authors present, discuss, and assess several criteria to evaluate the transferability of approximations to the exchange-correlation functional of density functional theory (DFT). In the first part of the paper they demonstrate that one criteria often used to assess such transferability -  the number of parameters in a given functional - is clearly inadequate for the task. In the second part of the paper, the authors introduce three statistical criteria with roots in statistics and machine learning and apply them to
10.22541/au.159223871.15927637
Anonymous IJQC Reviewer posted a review
In his present contribution, Peverati addresses whether the number of degrees of freedom influence the accuracy and applicability of a density functional. Overall, this question is of interest, particularly to DFT developers and Peverati answers it appropriately. Therefore, I find this work suitable for IJQC. That being said, I have to raise two major points and a couple of minor ones that should be addressed before this manuscript can be accepted for publication. I therefore recommend a revision. Note that I prefer to remain
10.22541/au.159223869.97401481
Roberto Peverati posted a review
Dear Dr. Cavalleri, I hereby resubmit my paper entitled “Fitting Elephants in the Density Functionals Zoo: Statistical Criteria for the Evaluation of DFT methods as a Suitable Replacement for Counting Parameters” with modifications that address all the concerns raised by the Referees. As such, I believe the manuscript is now ready for publication in the Authorea special issue of the International Journal of Quantum Chemistry. I want to thank the Referees for the clear and very useful remarks. For your convenience, I report below a point-by-point