Graph kernels are kernel methods measuring graph similarity and serve as a standard tool for graph classification. However, the use of kernel methods for node classification, which is a related problem to graph representation learning, is still ill-posed and the state-of-the-art methods are heavily based on heuristics. Here, we present a novel theoretical kernel-based framework for node classification that can bridge the gap between these two representation learning problems on graphs. Our approach is motivated by graph kernel methodology but extended to learn the node representations capturing the structural information in a graph. We theoretically show that our formulation is as powerful as any positive semidefinite kernels. To efficiently learn the kernel, we propose a novel mechanism for node feature aggregation and a data-driven similarity metric employed during the training phase. More importantly, our framework is flexible and complementary to other graph-based deep learning models, e.g., Graph Convolutional Networks (GCNs). We empirically evaluate our approach on a number of standard node classification benchmarks, and demonstrate that our model sets the new state of the art.

After rebuttal: thank you for the additional experiments. They strengthen the empirical contribution of the paper, so I've increased my score to a 7. ________________ Originality: The paper is a novel combination of known techniques: by reinterpreting the the iterative node aggregation procedure of Kipf et al's GCN as feature smoothing technique, they develop a novel feature mapping function for learning positive semi-definite (psd) graph kernels. The key difference from the Kipf et al approach is they separate the node aggregation and non-linear representation learning components: node features are the output of a multi-layer perceptron and then aggregated once (rather than at every layer) by a multi-hop aggregation function. They argue theoretically that this approach is universal in the sense that it can approximate any invertible psd kernel. Quality: I thought the empirical results of the paper were interesting because they suggest that decoupling the aggregation and representation learning components of GCN-style models leads to better performance (at least on these datasets).

The reviewers were initially positive about the paper but not confident about their opinions. After the author response, a few of their questions were answered, and the discussion led to a consensus that the paper should be a solid contribution to the NeurIPS program.

Graph kernels are kernel methods measuring graph similarity and serve as a standard tool for graph classification. However, the use of kernel methods for node classification, which is a related problem to graph representation learning, is still ill-posed and the state-of-the-art methods are heavily based on heuristics. Here, we present a novel theoretical kernel-based framework for node classification that can bridge the gap between these two representation learning problems on graphs. Our approach is motivated by graph kernel methodology but extended to learn the node representations capturing the structural information in a graph. We theoretically show that our formulation is as powerful as any positive semidefinite kernels.

Graph kernels are kernel methods measuring graph similarity and serve as a standard tool for graph classification. However, the use of kernel methods for node classification, which is a related problem to graph representation learning, is still ill-posed and the state-of-the-art methods are heavily based on heuristics. Here, we present a novel theoretical kernel-based framework for node classification that can bridge the gap between these two representation learning problems on graphs. Our approach is motivated by graph kernel methodology but extended to learn the node representations capturing the structural information in a graph. We theoretically show that our formulation is as powerful as any positive semidefinite kernels.