# Prediction of Atomization Energy Using Graph Kernel and Active Learning

arXiv: https://arxiv.org/abs/1810.07310 · HTML: https://mlsanity.com/paper/1810.07310/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Oct 2018.

## Built on by (most cited first, 6 of 6)

- [Detecting Label Noise via Leave-One-Out Cross-Validation](https://mlsanity.com/paper/2103.11352/) (2021)
- [Graphical Gaussian Process Regression Model for Aqueous Solvation Free Energy Prediction of Organic Molecules in Redox Flow Battery](https://mlsanity.com/paper/2106.08146/) (2021)
- [Optimal Sampling Density for Nonparametric Regression](https://mlsanity.com/paper/2105.11990/) (2021)
- [Nonlinear Matrix Approximation with Radial Basis Function Components](https://mlsanity.com/paper/2106.02018/) (2021)
- [Efficient Chemical Space Exploration Using Active Learning Based on Marginalized Graph Kernel: an Application for Predicting the Thermodynamic Properties of Alkanes with Molecular Simulation](https://mlsanity.com/paper/2209.00514/) (2022)
- [Evaluating Point-Prediction Uncertainties in Neural Networks for Drug Discovery](https://mlsanity.com/paper/2210.17043/) (2022)

## Abstract (arXiv)

Data-driven prediction of molecular properties presents unique challenges to the design of machine learning methods concerning data structure/dimensionality, symmetry adaption, and confidence management. In this paper, we present a kernel-based pipeline that can learn and predict the atomization energy of molecules with high accuracy. The framework employs Gaussian process regression to perform predictions based on the similarity between molecules, which is computed using the marginalized graph kernel. To apply the marginalized graph kernel, a spatial adjacency rule is first employed to convert molecules into graphs whose vertices and edges are labeled by elements and interatomic distances, respectively. We then derive formulas for the efficient evaluation of the kernel. Specific functional components for the marginalized graph kernel are proposed, while the effect of the associated hyperparameters on accuracy and predictive confidence are examined. We show that the graph kernel is particularly suitable for predicting extensive properties because its convolutional structure coincides with that of the covariance formula between sums of random variables. Using an active learning procedure, we demonstrate that the proposed method can achieve a mean absolute error of 0.62 +- 0.01 kcal/mol using as few as 2000 training samples on the QM7 data set.