  Transfer learning refers to the transfer of knowledge or information from a
relevant source domain to a target domain. However, most existing transfer
learning theories and algorithms focus on IID tasks, where the source/target
samples are assumed to be independent and identically distributed. Very little
effort is devoted to theoretically studying the knowledge transferability on
non-IID tasks, e.g., cross-network mining. To bridge the gap, in this paper, we
propose rigorous generalization bounds and algorithms for cross-network
transfer learning from a source graph to a target graph. The crucial idea is to
characterize the cross-network knowledge transferability from the perspective
of the Weisfeiler-Lehman graph isomorphism test. To this end, we propose a
novel Graph Subtree Discrepancy to measure the graph distribution shift between
source and target graphs. Then the generalization error bounds on cross-network
transfer learning, including both cross-network node classification and link
prediction tasks, can be derived in terms of the source knowledge and the Graph
Subtree Discrepancy across domains. This thereby motivates us to propose a
generic graph adaptive network (GRADE) to minimize the distribution shift
between source and target graphs for cross-network transfer learning.
Experimental results verify the effectiveness and efficiency of our GRADE
framework on both cross-network node classification and cross-domain
recommendation tasks.
