Bayesian Model Averaging for Ensemble-Based Estimates of Solvation-Free Energies

Gosink, Luke; Overall, Christopher C.; Reehl, Sarah; Whitney, Paul D.; Mobley, David L.; Baker, Nathan A.

doi:10.1021/acs.jpcb.6b09198

Cited by 9 publications

(7 citation statements)

References 101 publications

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“…Such solvation models require the coordinates of the solute atoms as well as atomic charge distributions and a representation of the solute-solvent interface. Charges and interfaces are generally modeled through parameterized empirical representations; however, these parameterizations are often under-determined, leading to uncertainty in the resulting parameter sets [4][5][6]. The Poisson equation is a popular model for implicit solvent electrostatics and serves as a good example for exploring the influence of this uncertainty on properties such as molecular solvation energy [1][2][3]7].…”

Section: Introductionmentioning

confidence: 99%

“…Implicit solvent models and their applications have been the subject of numerous previous reviews. − Such solvation models require the coordinates of the solute atoms as well as atomic charge distributions and a representation of the solute–solvent interface. Charges and interfaces are generally modeled through parametrized empirical representations; however, these parametrizations are often underdetermined, leading to uncertainty in the resulting parameter sets. − The Poisson equation is a popular model for implicit solvent electrostatics and serves as a good example for exploring the influence of this uncertainty on properties such as molecular solvation energy. − , In this paper, we use the term “solvation energy” to refer to the energy returned from the Poisson equation and to emphasize that we are not sampling over solute conformational states for a true free energy. This is a partial differential equation for the electrostatic potential where is the problem domain, ∂Ω is the domain boundary, ϵ : Ω → [1,∞) is a dielectric coefficient, is the charge distribution, and φ D is a reference potential function (e.g., Coulomb’s law) used for the Dirichlet boundary condition.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Atomic Radius and Charge Parameter Uncertainty in Biomolecular Solvation Energy Calculations

Yang¹,

Lei²,

Gao³

et al. 2018

J. Chem. Theory Comput.

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Atomic radii and charges are two major parameters used in implicit solvent electrostatics and energy calculations. The optimization problem for charges and radii is underdetermined, leading to uncertainty in the values of these parameters and in the results of solvation energy calculations using these parameters. This paper presents a new method for quantifying this uncertainty in implicit solvation calculations of small molecules using surrogate models based on generalized polynomial chaos (gPC) expansions. There are relatively few atom types used to specify radii parameters in implicit solvation calculations; therefore, surrogate models for these low-dimensional spaces could be constructed using least-squares fitting. However, there are many more types of atomic charges; therefore, construction of surrogate models for the charge parameter space requires compressed sensing combined with an iterative rotation method to enhance problem sparsity. We demonstrate the application of the method by presenting results for the uncertainties in small molecule solvation energies based on these approaches. The method presented in this paper is a promising approach for efficiently quantifying uncertainty in a wide range of force field parametrization problems, including those beyond continuum solvation calculations. The intent of this study is to provide a way for developers of implicit solvent model parameter sets to understand the sensitivity of their target properties (solvation energy) on underlying choices for solute radius and charge parameters.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Atomic Radius and Charge Parameter Uncertainty in Biomolecular Solvation Energy Calculations

Yang¹,

Lei²,

Gao³

et al. 2018

J. Chem. Theory Comput.

Self Cite

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“…There are many directions for improvement and future work. (1) Since we use only a small number of base classifiers, would Bayesian modeling, as shown in [11] lead to a more effective determination of the µ(x), σ 2 (x) parameters?…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…See appendix section A.1 for more details10 See appendix section A.3 for more details11 See appendix section A.4 for more details…”

mentioning

confidence: 99%

Efficient Estimation of Generalization Error and Bias-Variance Components of Ensembles

Mahajan,

Gupta,

Keerthi

et al. 2017

Preprint

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For many applications, an ensemble of base classifiers is an effective solution. The tuning of its parameters (number of classifiers, amount of data on which each classifier is to be trained on, etc.) requires G, the generalization error of a given ensemble. The efficient estimation of G is the focus of this paper. The key idea is to approximate the variance of the class scores/probabilities of the base classifiers over the randomness imposed by the training subset by normal/beta distribution at each point x in the input feature space. We estimate the parameters of the distribution using a small set of randomly chosen base classifiers and use those parameters to give efficient estimation schemes for G. We give empirical evidence for the quality of the various estimators. We also demonstrate their usefulness in making design choices such as the number of classifiers in the ensemble and the size of subset of data used for training that are needed to achieve a certain value of generalization error. Our approach also has great potential for designing distributed ensemble classifiers.

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“…The random forest resembled the gating hierarchy of flow cytometry ( Popescu et al, 2019 ). It is an ensemble classifier with a decision tree as base classifier ( Cheng et al, 2018 ), has been well established in bioinformatics ( Gosink et al, 2017 ). We applied the random Survival Forest (RSF) method to rank the gene importance.…”

Section: Methodsmentioning

confidence: 99%

An Immune-Gene-Based Classifier Predicts Prognosis in Patients With Cervical Squamous Cell Carcinoma

Yang

Han

Hao

2021

Front. Mol. Biosci.

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Objective: Immunity plays a vital role in the human papilloma virus (HPV) persistent infection, and closely associates with occurrence and development of cervical squamous cell carcinoma (CSCC). Herein, we performed an integrated bioinformatics analysis to establish an immune-gene signature and immune-associated nomogram for predicting prognosis of CSCC patients.Methods: The list of immunity-associated genes was retrieved from ImmPort database. The gene and clinical information of CSCC patients were obtained from The Cancer Genome Atlas (TCGA) website. The immune gene signature for predicting overall survival (OS) of CSCC patients was constructed using the univariate Cox-regression analysis, random survival forests, and multivariate Cox-regression analysis. This signature was externally validated in GSE44001 cohort from Gene Expression Omnibus (GEO). Then, based on the established signature and the TCGA cohort with the corresponding clinical information, a nomogram was constructed and evaluated via Cox regression analysis, concordance index (C-index), receiver operating characteristic (ROC) curves, calibration plots and decision curve analyses (DCAs).Results: A 5-immune-gene prognostic signature for CSCC was established. Low expression of ICOS, ISG20 and high expression of ANGPTL4, SBDS, LTBR were risk factors for CSCC prognosis indicating poor OS. Based on this signature, the OS was significantly worse in high-risk group than in low-risk group (p-value < 0.001), the area under curves (AUCs) for 1-, 3-, 5-years OS were, respectively, 0.784, 0.727, and 0.715. A nomogram incorporating the risk score of signature and the clinical stage was constructed. The C-index of this nomogram was 0.76. AUC values were 0.811, 0.717, and 0.712 for 1-, 3-, 5-years OS. The nomogram showed good calibration and gained more net benefits than the 5-immune-gene signature and the clinical stage.Conclusion: The 5-immune-gene signature may serve as a novel, independent predictor for prognosis in patients with CSCC. The nomogram incorporating the signature risk score and clinical stage improved the predictive performance than the signature and clinical stage alone for predicting 1-year OS.

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Bayesian Model Averaging for Ensemble-Based Estimates of Solvation-Free Energies

Cited by 9 publications

References 101 publications

Atomic Radius and Charge Parameter Uncertainty in Biomolecular Solvation Energy Calculations

Atomic Radius and Charge Parameter Uncertainty in Biomolecular Solvation Energy Calculations

Efficient Estimation of Generalization Error and Bias-Variance Components of Ensembles

An Immune-Gene-Based Classifier Predicts Prognosis in Patients With Cervical Squamous Cell Carcinoma

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