ICML 2019

Learning Discrete Structures for Graph Neural Networks

Luca Franceschi, Mathias Niepert, M. Pontil, Xiaojuan He

Main figure for Learning Discrete Structures for Graph Neural Networks

Abstract

Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such a graph-structure is available. In practice, however, real-world graphs are often noisy and incomplete or might not be available at all. With this work, we propose to jointly learn the graph structure and the parameters of graph convolutional networks (GCNs) by approximately solving a bilevel program that learns a discrete probability distribution on the edges of the graph. This allows one to apply GCNs not only in scenarios where the given graph is incomplete or corrupted but also in those where a graph is not available. We conduct a series of experiments that analyze the behavior of the proposed method and demonstrate that it outperforms related methods by a significant margin.

Benchmark Results

Tested on 2 datasets 1 baseline value reported too low

Tables show presented results in global context (best 3 papers + GCN + MLP).

Classic

#ModelAccuracy ↑Paper
1
GraphSAGE+CNA
0.9418 ±0.0033
2
GCN+CNA
0.9366 ±0.0048
3
TransformerConv
0.9350 ±0.0058
21
GCN
0.9004
300
LDS (Cora)
0.8408 ±0.0040
This paper
656
GCN-RND (Cora)
0.8002 ±0.0060
This paper
669
GCN (Cora)
0.7976 ±0.0050
This paper
724
MLP
0.7768
#ModelAccuracy ↑Paper
1
CNA
0.9575 ±0.0058
2
IS-GIB
0.9390 ±0.0187
3
EERM
0.9112 ±0.0145
44
GCN
0.8033 ±0.0088
350
MLP
0.7289 ±0.0010
677
kNN-GCN
0.6830 ±0.0130
This paper
681
SemiEmb
actual #681 vs paper #681
0.6810 ±0.0010
actual #681 vs paper #681
paper 0.6810 ±0.0010
paper 0.6810 ±0.0010 Δ at pub 0.0850
697
ManiReg
actual #697 vs paper #697
0.6770 ±0.0160
actual #697 vs paper #697
paper 0.6770 ±0.0160
paper 0.6770 ±0.0160 Δ at pub 0.0760
815
LogReg
0.6220
This paper
825
rf
0.6070 ±0.0070
This paper
830
RBF SVM
0.6020
This paper
840
Dense-GCN
0.5840 ±0.0110
This paper
841
Linear SVM
0.5830
This paper
844
RBF-GCN
0.5810 ±0.0120
This paper
851
FFNN
0.5670 ±0.0170
This paper
877
LP
actual #877 vs paper #898 21 places worse
0.4530
best reported
actual #877 vs paper #898 21 places worse
paper 0.2320 ±0.0670
paper 0.2320 ±0.0670 Δ at pub 0.2210 Δ today 0.2210
890
Sparse-GCN
0.3310 ±0.0090
This paper
SOTA performance (not significantly different from the best) Proposed method (this paper) Baseline / comparison (this paper) Global context (other papers) Best at pub — reported result worse than the best known when published (best reported in green) Best at pub — reported value improved over the best known when published