Title: Estimating structural shifts in graph domain adaptation via pairwise likelihood maximization
Primary area: transfer learning, meta learning, and lifelong learning
Keywords: Graph domain adaptation, node classification, graph structure shift, distribution matching, U-statistics

Abstract: Graph domain adaptation (GDA) emerges as an important problem in graph machine learning when the distribution of the source graph data used for training is different from that of the target graph data used for testing. While much of the prior work on GDA has focused on the idea of aligning node representations across source and target domains, recent studies show that such approaches can be suboptimal in the presence of conditional structure shift (CSS), where the distribution of graph edges conditioned on labels changes across domains. In this work, we develop a unified framework to solve CSS and show that existing GDA methods for CSS arise as special cases of our framework. This framework further allows us to develop a new method, Pairwise-Likelihood maximization for graph Structure Alignment (PLSA), which uses rich information from pairwise nodes and edges to improve the estimation of target connection probabilities. We establish conditions under which our method is identifiable and introduce a simple edge reweighting scheme based on importance weights to align the source and target graphs. Theoretically, under the contextual stochastic block model (CSBM), we derive finite-sample guarantees using recent results in matrix concentration inequalities for U-statistics. We complement our theoretical results with empirical studies that demonstrate the effectiveness of our method.