Model selection based on validation criteria for Gaussian process regression: An application with highlights on the predictive variance

2021 ◽  
Author(s):  
Charles Demay ◽  
Bertrand Iooss ◽  
Loic Le Gratiet ◽  
Amandine Marrel
Keyword(s):  
Model Selection ◽  
Gaussian Process ◽  
Gaussian Process Regression ◽  
Validation Criteria

scholarly journals Model comparison of $$\Lambda $$CDM vs $$R_h=ct$$ using cosmic chronometers

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Haveesh Singirikonda ◽  
Shantanu Desai
Keyword(s):  
Model Selection ◽  
Gaussian Process ◽  
Bayesian Model ◽  
Model Comparison ◽  
Gaussian Process Regression ◽  
Acoustic Oscillations ◽  
Bayesian Model Comparison ◽  
Baryon Acoustic Oscillations ◽  
Best Fit

Abstract In 2012, Bilicki and Seikel (Mon Not R Astron Soc 425:1664, 2012) showed that H(z) data reconstructed using Gaussian Process Regression from cosmic chronometers and baryon acoustic oscillations, conclusively rules out the $$R_h=ct$$Rh=ct model. These results were disputed by Melia and collaborators in two different works (Melia and Maier in Mon Not R Astron Soc 432:2669, 2013; Melia and Yennapureddy in JCAP 2018:034, 2018), who showed using both an unbinned analysis and Gaussian Process reconstructed H(z) data from chronometers, that $$R_h=ct$$Rh=ct is favored over $$\Lambda $$ΛCDM model. To resolve this imbroglio, we carry out model comparison of $$\Lambda $$ΛCDM versus $$R_h=ct$$Rh=ct by independently reproducing the above claims using the latest chronometer data. We perform model selection between these two models using Bayesian model comparison. We find that no one model between $$\Lambda $$ΛCDM and $$R_h=ct$$Rh=ct is decisively favored when uniform priors on $$\Lambda $$ΛCDM parameters are used. However, if we use priors centered around the Planck best-fit values, then $$\Lambda $$ΛCDM is very strongly preferred over $$R_h=ct$$Rh=ct.

Model Selection for Gaussian Process Regression

2017 ◽  
pp. 306-318 ◽  
Author(s):  
Nico S. Gorbach ◽  
Andrew An Bian ◽  
Benjamin Fischer ◽  
Stefan Bauer ◽  
Joachim M. Buhmann
Keyword(s):  
Model Selection ◽  
Gaussian Process ◽  
Gaussian Process Regression ◽  
Selection For

Exchange Spin Coupling from Gaussian Process Regression

2020 ◽  
Author(s):  
Marc Philipp Bahlke ◽  
Natnael Mogos ◽  
Jonny Proppe ◽  
Carmen Herrmann
Keyword(s):  
Machine Learning ◽  
Gaussian Process ◽  
Gaussian Process Regression ◽  
Molecular Magnets ◽  
Molecular Structures ◽  
Spin Coupling ◽  
Structure Property ◽  
Data Set ◽  
Uncertainty Estimates

Heisenberg exchange spin coupling between metal centers is essential for describing and understanding the electronic structure of many molecular catalysts, metalloenzymes, and molecular magnets for potential application in information technology. We explore the machine-learnability of exchange spin coupling, which has not been studied yet. We employ Gaussian process regression since it can potentially deal with small training sets (as likely associated with the rather complex molecular structures required for exploring spin coupling) and since it provides uncertainty estimates (“error bars”) along with predicted values. We compare a range of descriptors and kernels for 257 small dicopper complexes and find that a simple descriptor based on chemical intuition, consisting only of copper-bridge angles and copper-copper distances, clearly outperforms several more sophisticated descriptors when it comes to extrapolating towards larger experimentally relevant complexes. Exchange spin coupling is similarly easy to learn as the polarizability, while learning dipole moments is much harder. The strength of the sophisticated descriptors lies in their ability to linearize structure-property relationships, to the point that a simple linear ridge regression performs just as well as the kernel-based machine-learning model for our small dicopper data set. The superior extrapolation performance of the simple descriptor is unique to exchange spin coupling, reinforcing the crucial role of choosing a suitable descriptor, and highlighting the interesting question of the role of chemical intuition vs. systematic or automated selection of features for machine learning in chemistry and material science.

SAMPL6 Challenge Results from pKa Predictions Based on a General Gaussian Process Model

2018 ◽  
Author(s):  
Caitlin C. Bannan ◽  
David Mobley ◽  
A. Geoff Skillman
Keyword(s):  
Gaussian Process ◽  
Process Model ◽  
Molecular Graph ◽  
Gaussian Process Regression ◽  
Ionization State ◽  
Training Set ◽  
Physiochemical Properties ◽  
Quantile Plots ◽  
Physical And Chemical ◽  
Good Agreement

<div>A variety of fields would benefit from accurate pK<sub>a</sub> predictions, especially drug design due to the affect a change in ionization state can have on a molecules physiochemical properties.</div><div>Participants in the recent SAMPL6 blind challenge were asked to submit predictions for microscopic and macroscopic pK<sub>a</sub>s of 24 drug like small molecules.</div><div>We recently built a general model for predicting pK<sub>a</sub>s using a Gaussian process regression trained using physical and chemical features of each ionizable group.</div><div>Our pipeline takes a molecular graph and uses the OpenEye Toolkits to calculate features describing the removal of a proton.</div><div>These features are fed into a Scikit-learn Gaussian process to predict microscopic pK<sub>a</sub>s which are then used to analytically determine macroscopic pK<sub>a</sub>s.</div><div>Our Gaussian process is trained on a set of 2,700 macroscopic pK<sub>a</sub>s from monoprotic and select diprotic molecules.</div><div>Here, we share our results for microscopic and macroscopic predictions in the SAMPL6 challenge.</div><div>Overall, we ranked in the middle of the pack compared to other participants, but our fairly good agreement with experiment is still promising considering the challenge molecules are chemically diverse and often polyprotic while our training set is predominately monoprotic.</div><div>Of particular importance to us when building this model was to include an uncertainty estimate based on the chemistry of the molecule that would reflect the likely accuracy of our prediction. </div><div>Our model reports large uncertainties for the molecules that appear to have chemistry outside our domain of applicability, along with good agreement in quantile-quantile plots, indicating it can predict its own accuracy.</div><div>The challenge highlighted a variety of means to improve our model, including adding more polyprotic molecules to our training set and more carefully considering what functional groups we do or do not identify as ionizable. </div>

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