A Comparative Study of Marginalized Graph Kernel and Message-Passing Neural Network

Abstract

This work proposes a state-of-the-art hybrid kernel to calculate molecular similarity. Combining with Gaussian process models, the performance of the hybrid kernel in predicting molecular properties is comparable to that of the Directed Message Passing Neural Network (D-MPNN). The hybrid kernel consists of a marginalized graph kernel (MGK) and a radial basis function (RBF) kernel that operates on molecular graphs and global molecular features, respectively. Bayesian optimization was used to get the optimal hyperparameters for both models. The comparisons are performed on 11 publicly available data sets. Our results show that the predictions of both models are correlated with similar performance, and the ensemble prediction of both models performs better than either of them. Through principal component analysis, we found that the features extracted by the hybrid kernel are similar to those extracted by D-MPNN. The advantage of D-MPNN lies in computational efficiency, while the advantage of the graph kernel models lies in the inherent uncertainty quantification and accurate uncertainty quantification.

Interpretable Molecular Property Predictions Using Marginalized Graph Kernels

“…Similarly, κ e (•,•) is the bond kernel that computes the similarity between a pair of bonds, which is defined similarly to the atom kernel. For details on the features of atoms, bonds, and associated kernel functions, we refer the reader to ref .…”

“…Of note, in previous work, , Xiang et al set the starting probability using a graph-size-dependent normalization to enhance model performance in cross validation K̅ ( G , G ′ ) = F K ( G , G ′ ) K ( G , G ) K ( G ′ , G ′ ) exp [ − ( K false( G , G false) − K false( G ′ , G ′ false) ) 2 λ 2 ] where F and λ are hyperparameters to be optimized. However, eq violates the additivity of the graph kernel to graph nodes, which, as demonstrated later, is a prerequisite for atomic attribution calculation.…”

“…This has made MGK a practically feasible machine learning method that can be applied to real-world problems of thousands of drug-like molecules . For example, we and others have recently employed marginalized graph kernels as input to Gaussian Process (GP) models, which shows promising results for predicting quantum mechanical and thermodynamic properties and on a range of benchmark data sets spanning drug discovery and toxicity . Importantly, MGK enables competitive prediction accuracy compared to popular directed message-passing neural networks (D-MPNN), but with improved uncertainty quantification of predictions …”

Uncertainty quantification: Can we trust artificial intelligence in drug discovery?

“… Box Bounding ( Netzeva et al., 2005 ) Convex Hull ( Jaworska et al., 2005 ) DM ( Sheridan et al., 2004 ) SDC score ( Liu et al., 2018 ) NNAS ( Allen et al., 2020 ) Virtual screening ( Berenger and Yamanishi, 2019 ) Anticancer peptide activity prediction ( Chen et al., 2021 ) SARS-CoV 2 inhibitor prediction ( Gawriljuk et al., 2021 ) Toxicity prediction ( Jiang et al., 2021 ) Bayesian Parameters and outputs are treated as random variables and maximum a posteriori (MAP) estimation is adopted according to Bayes’ theorem. VI (MC-dropout) ( Gal and Ghahramani, 2016 ) BNN ( Goan and Fookes, 2020 ) GP-MGK ( Xiang et al., 2021 ) MVE ( Nix and Weigend, 1994 ) Bayesian GCN ( Ryu et al., 2019 ) Molecular property prediction ( Zhang and Lee, 2019 ) Virtual screening ( Ryu et al., 2019 ) Protein-ligand interaction prediction ( Kim et al., 2021 ) Ensemble-based The consistency of the predictions from various base models is an estimate of confidence. Bootstrapping ( Scalia et al., 2020 ) RF ( Sheridan, 2012 ) DeltaDelta ( Jimenez-Luna et al., 2019 ) Deep ensemble ( Lakshminarayanan et al., 2017 ) MC-dropout ( Gal and Ghahramani, 2016 ) Drug-likeness prediction ( Beker et al., 2020 ) Molecular property prediction ( Scalia et al., 2020 ) ...…”

“…Xiang et al. proposed a GP model with a hybrid kernel, GP-MGK, for molecular property prediction ( Xiang et al., 2021 ). They found that GP-MGK outperformed D-MPNN, a kind of graph convolutional neural network, regarding uncertainty quantification.…”