Erratum: Probabilistic performance estimators for computational chemistry methods: Systematic improvement probability and ranking probability matrix. I. Theory [J. Chem. Phys. 152, 164108 (2020)]

Pernot, Pascal; Savin, Andreas

doi:10.1063/5.0031156

Cited by 2 publications

(3 citation statements)

References 3 publications

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“…In particular, the user should be able to input the expectations he has from the method, find out what the risks are, and decide whether he is willing to take them. A wider set of examples illustrating these points is presented in reference [7] .…”

Section: Discussionmentioning

confidence: 97%

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Acknowledging User Requirements for Accuracy in Computational Chemistry Benchmarks

Savin

Pernot

2020

Zeitschrift anorg allge chemie

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Computational chemistry has become an important complement to experimental measurements. In order to choose among the multitude of the existing approximations, it is common to use benchmark data sets, and to issue recommendations based on numbers such as mean absolute errors. We argue, using as an example band gaps calculated with density functional approximations, that a more careful study of the benchmark data is needed, stressing that the user's requirements play a role in the choice of an appropriate method. We also appeal to those who measure data capable of being used as a reference, to publish error estimates. We show how the latter can affect the judgment of approximations used in computational chemistry.

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Section: Discussionmentioning

confidence: 97%

“…If it is positive, LDA is better than HSE06. The fraction of systems having negative difference gives the systematic improvement probability (SIP) [6] of HSE06 over LDA. Please notice that SIP = 0.5 would mean that there is equal probability of improvement or worsening by changing from LDA to HSE06.…”

Section: Pairwise Comparisonmentioning

confidence: 99%

Acknowledging User Requirements for Accuracy in Computational Chemistry Benchmarks

Savin

Pernot

2020

Zeitschrift anorg allge chemie

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“…This lack of correlation supports the main message of this work: The number of fitted parameters does not represent an effective measure of the transferability of a functional. More reliable statistical criteria—such as those developed in this work, or alternatively, the probabilistic performance estimator recently introduced by Pernot and Savin [ 91,92 ] —should be used to evaluate the reliability of new and existing xc functionals.…”

Section: Statistical Criteria Of Bias–variance Tradeoff and Analysis mentioning

confidence: 99%

Fitting elephants in the density functionals zoo: Statistical criteria for the evaluation of density functional theory methods as a suitable replacement for counting parameters

Peverati

2020

Int J of Quantum Chemistry

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Counting parameters has become customary in the density functional theory community as a way to infer the transferability of popular approximations to the exchangecorrelation 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, here, we show that it is possible to represent every modern exchange-correlation functional approximations 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, Vapnik-Chervonenkis criterion, and cross-validation criterion and are used in a preliminary assessment to rank 60 exchange-correlation functional approximations using the ASCDB database of chemical data.

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Erratum: Probabilistic performance estimators for computational chemistry methods: Systematic improvement probability and ranking probability matrix. I. Theory [J. Chem. Phys. 152, 164108 (2020)]

Cited by 2 publications

References 3 publications

Acknowledging User Requirements for Accuracy in Computational Chemistry Benchmarks

Acknowledging User Requirements for Accuracy in Computational Chemistry Benchmarks

Fitting elephants in the density functionals zoo: Statistical criteria for the evaluation of density functional theory methods as a suitable replacement for counting parameters

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