  Given a graph where every node has certain attributes associated with it and
some nodes have labels associated with them, Collective Classification (CC) is
the task of assigning labels to every unlabeled node using information from the
node as well as its neighbors. It is often the case that a node is not only
influenced by its immediate neighbors but also by higher order neighbors,
multiple hops away. Recent state-of-the-art models for CC learn end-to-end
differentiable variations of Weisfeiler-Lehman (WL) kernels to aggregate
multi-hop neighborhood information. In this work, we propose a Higher Order
Propagation Framework, HOPF, which provides an iterative inference mechanism
for these powerful differentiable kernels. Such a combination of classical
iterative inference mechanism with recent differentiable kernels allows the
framework to learn graph convolutional filters that simultaneously exploit the
attribute and label information available in the neighborhood. Further, these
iterative differentiable kernels can scale to larger hops beyond the memory
limitations of existing differentiable kernels. We also show that existing WL
kernel-based models suffer from the problem of Node Information Morphing where
the information of the node is morphed or overwhelmed by the information of its
neighbors when considering multiple hops. To address this, we propose a
specific instantiation of HOPF, called the NIP models, which preserves the node
information at every propagation step. The iterative formulation of NIP models
further helps in incorporating distant hop information concisely as summaries
of the inferred labels. We do an extensive evaluation across 11 datasets from
different domains. We show that existing CC models do not provide consistent
performance across datasets, while the proposed NIP model with iterative
inference is more robust.
