基于回归聚类的分子轨道机器学习算法
Regression-clustering for Improved Accuracy and Training Cost with Molecular-Orbital-Based Machine Learning
摘要：
基于分子轨道（MOB）特征的机器学习（ML）已被证明是预测后Hartree-Fock相关能的准确和可转移的方法。MOB-ML以前的应用采用高斯过程回归（GPR），它在小训练集上提供了良好的预测精度;然而，GPR训练的成本与数据量成立方关系，并成为大型训练集的计算瓶颈。在目前的工作中，我们通过引入MOB-ML的聚类/回归/分类实现来解决这个问题。在第一步中，回归聚类（RC）用于划分训练数据以最佳地拟合线性回归（LR）模型的集合;在第二步中，使用LR或GPR独立地对每个聚类进行回归;并且在第三步中，训练随机森林分类器（RFC）以基于MOB特征值预测聚类分配。在检查后，RC被发现概括化学直观的前沿分子轨道的分组，并结合RC/LR/RFC和RC/GPR/RFC的MOB-ML实现被发现提供良好的预测精度，大大减少挂钟训练时间。对于多达7个重原子的7211个有机分子的热化几何形状的数据集，这两种实现仅用300个训练分子就达到了化学精度（1千卡/摩尔误差），同时与没有聚类的MOB-ML相比，分别提供了挂钟训练时间的35000倍和4500倍减少。结果还表明，所得模型仅使用小分子训练数据即可保留预测大分子能量的可移植性。最后，它表明，限制每个集群的训练数据点的数量导致预测精度的进一步提高，而挂钟训练时间的增加可以忽略不计。
英文摘要：
Machine learning (ML) in the representation of molecular-orbital-based (MOB) features has been shown to be an accurate and transferable approach to the prediction of post-Hartree-Fock correlation energies. Previous applications of MOB-ML employed Gaussian Process Regression (GPR), which provides good prediction accuracy with small training sets; however, the cost of GPR training scales cubically with the amount of data and becomes a computational bottleneck for large training sets. In the current work, we address this problem by introducing a clustering/regression/classification implementation of MOB-ML. In a first step, regression clustering (RC) is used to partition the training data to best fit an ensemble of linear regression (LR) models; in a second step, each cluster is regressed independently, using either LR or GPR; and in a third step, a random forest classifier (RFC) is trained for the prediction of cluster assignments based on MOB feature values. Upon inspection, RC is found to recapitulate chemically intuitive groupings of the frontier molecular orbitals, and the combined RC/LR/RFC and RC/GPR/RFC implementations of MOB-ML are found to provide good prediction accuracy with greatly reduced wall-clock training times. For a dataset of thermalized geometries of 7211 organic molecules of up to seven heavy atoms, both implementations reach chemical accuracy (1 kcal/mol error) with only 300 training molecules, while providing 35000-fold and 4500-fold reductions in the wall-clock training time, respectively, compared to MOB-ML without clustering. The resulting models are also demonstrated to retain transferability for the prediction of large-molecule energies with only small-molecule training data. Finally, it is shown that capping the number of training datapoints per cluster leads to further improvements in prediction accuracy with negligible increases in wall-clock training time.
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