Graph kernels for chemoinformatics. A critical discussion · Graph kernels for chemoinformatics. A critical discussion Matthias Rupp Berlin Institute of Technology, Germany 6th German

Graph kernels for chemoinformatics.A critical discussion

Matthias Rupp

Berlin Institute of Technology, Germany

6th German Conference on Chemoinformatics,Goslar, Germany, November 7–9, 2010

Outline

Introduction Kernel-based learning

Graph kernels Idea, taxonomy

Applications Virtual screening, pKa estimation

Discussion Assessment

Matthias Rupp: Graph kernels in chemoinformatics 2

Machine learning: introduction

I Algorithmic search for patterns in data

I Inference from known samples to new ones

Application examples:

I Ligand-based virtual screening

I Quantitative structure-property relationships

I Toxicity mode of action

Method examples:

I Linear regression

I Principle component analysis

I Artificial neural networks

-10 -5 5 10x

-4

-2

2

4

6

8

fHxL


Machine learning: kernel-based learning

Idea:

I Transform samples into higher-dimensional space

I Implicitly do inference there

-2 Π -Π 0 Π 2 Π

x 7→-2Π -Π Π 2Π

x

-1

1sin x

Input space Feature space

<x, x′> =d∑

i=1

xix′i inner product

k(x, x′) = <φ(x), φ(x′)> kernel function

Example: φ(x) = (x , sin x)


Graph kernels: idea

Define kernels directly on graphs!

k(G ,G ′) = <φ(G ), φ(G ′)> kernel function

I Combine graph theory and machine learning

I Complete graph kernels are computationally hard

small moleculemolecular graph

668 HUAN ET AL.

FIG. 9. Large subgraph motif found in more than 90% of the Protein Kinase family members that includes a catalyticresidue. Left: graph representations. All edges are proximity edges. Right: mapping of this motif onto the backboneof Cell Division Kinase 5 (1h4l). The motif includes the invariant catalytic residue Lys128, darkened in the graphrepresentation and in the protein structure, and neighboring hydrophobic residues that contact the ligand.

FIG. 10. Least-squares superposition of the largest fingerprint that contains the whole active site in 30 proteins fromour dataset of 35 eukaryotic and 8 prokaryotic serine proteases. Maximum RMSD is 0.5 Å RMSD in the first fourresidues (Asp-His-Ala-Ser). Only 7 serine proteases (ESP: 1lo6A,1eq4A,1fiwA,1eaxA; PSP: 1qq4A, 1sgpE, 1hpgA)are shown superposed, for clarity. The surrounding conserved C! trace is also shown.

protein kinase motifreduced graph

protein-proteininteraction network

Gartner et al., COLT 2003, 129.


Graph kernels: taxonomy

random walksCCCOCCCOCCCCCCCOCOCCCCCCCCSOSCSOCCCCCCCCCCC

CCCOCCOCCCCOCOCNCCCCCCCCCCCCCCCCNCCOCNCCCOC

CCCOCCCOCCCCCCCOCOCCCCCCCCSOSCSOCCCCCCCCCCC


time O(n3)

patterns

sampling

assignments

Gartner et al., COLT/Kernel 2003, 129; Kashima et al., 155, in Scholkopf et al. (eds.),Kernel methods in computational biology, MIT Press, 2004.



random walks

CCCOCCCOCCCCCCCOCOCCCCCCCCSOSCSOCCCCCCCCCCC


time O(n2c2c) for trees, O(n3) for cyclic patterns

patterns

sampling

assignments

Mahe & Vert, Mach. Learn. 75(1): 3, 2009; Horvath et al., KDD 2004, 158.



random walks

time O(nck−1), k ∈ {3, 4, 5}

patterns

sampling

assignments

Shervashidze et al., AISTATS 2009, 488; Kondor et al., ICML 2009, 529.



random walks

time O(n3)

patterns

sampling

assignments

Frohlich et al, QSAR Comb. Sci 25(4): 317, 2006;Rupp et al, J. Chem. Inf. Model. 47(6): 2280, 2007


Applications: virtual screening

Target:

I Peroxisome proliferator-activated receptor γ (PPARγ)

I Related to type 2 diabetes and dyslipidemia

Methods:

I Gaussian process regression

I Graph kernel + descriptors

I Cellular reporter gene assay

Results:

I 8 out of 15 compounds active

I One selective PPARγ agonist with novel scaffold(derivative of natural product truxillic acid),EC50 = 10.03 ± 0.2µM

Rupp et al., ChemMedChem 5(2): 191, 2010.


Applications: quantitative structure-property relationships

Objective:

I Estimation of acid dissociation constants pKa in water

I HA A− + H+; pKa ≈ pH + log10c(HA)c(A−)

Methods:

I Published data (n = 698)

I Kernel ridge regression

I Only graph kernel

Results:

I Best RMSE = 0.23median RMSE = 0.85

I Same performance as semi-empirical reference modelbased on frontier electron theory

Tehan et al., Quant. Struct. Act. Rel. 21(5): 457, 473; Rupp et al, Mol. Inf., 2010 29: 731.


Discussion: choice of kernel

Problem:

I It’s not clear when to use which graph kernel

Questions to ask:

I Does it consider the position of patterns?

I Does it support domain knowledge, e.g., labels?

I Does it exploit molecular graph properties,e.g., bounded vertex degrees?

I Is it positive definite?


Discussion: assessmentKernel methods:

+ Principled way of non-linear pattern recognition

– Solution in terms of training samples instead of input dimensionsAffects computing time, solution size, interpretation

Graph kernels:

+ Principled use of graph theory in kernel learning

+ Defined directly on the graphs

+ Potential in chemoinformatics

– High computational requirements

I Some aid interpretability, some do not

I Recent development, active area of research

Outlook:

I Theoretical and comparative studies needed

I Graph kernels designed for chemoinformaticsMatthias Rupp: Graph kernels in chemoinformatics 13

Acknowledgments

Prof. Dr. Klaus-Robert MullerInstitute of Technology BerlinGermany

Prof. Dr. Gisbert SchneiderETH ZurichSwitzerland

Prof. Dr. Manfred Schubert-Zsilavecz, Dr. Heiko Zettl, Ramona SteriDr. Petra Schneider, Dr. Ewgenij Proschak, Markus HartenfellerDr. Timon Schroeter, Katja HansenDr. Igor Tetko, Robert Korner


Literature

I Mathematical review:

Vishwanathan et al., Graph kernels,J. Mach. Learn. Res. 11: 1201, 2010.

I Chemoinformatics review:

Rupp & Schneider, Graph kernels for molecular similarity,Mol. Inf. 29(4): 266, 2010.

I Slides:

http://www.mrupp.info


http://www.mrupp.info

Documents

Graph kernels for chemoinformatics. A critical discussion · Graph kernels for chemoinformatics. A critical discussion Matthias Rupp Berlin Institute of Technology, Germany 6th German