Distributional Network of Networks for Modeling Data Heterogeneity

Heterogeneous data widely exists in various high-impact applications. Domain adaptation and out-of-distribution generalization paradigms have been formulated to handle the data heterogeneity across domains. However, most existing domain adaptation and out-of-distribution generalization algorithms do not explicitly explain how the label information can be adaptively propagated from the source domains to the target domain. Furthermore, little effort has been devoted to theoretically understanding the convergence of existing algorithms based on neural networks.To address these problems, in this paper, we propose a generic distributional network of networks (TENON) framework, where each node of the main network represents an individual domain associated with a domain-specific network. In this case, the edges within the main network indicate the domain similarity, and the edges within each network indicate the sample similarity. The crucial idea of TENON is to characterize the within-domain label smoothness and cross-domain parameter smoothness in a unified framework. The convergence and optimality of TENON are theoretically analyzed. Furthermore, we show that based on the TENON framework, domain adaptation and out-of-distribution generalization can be naturally formulated as transductive and inductive distribution learning problems, respectively. This motivates us to develop two instantiated algorithms (TENON-DA and TENON-OOD) of the proposed TENON framework for domain adaptation and out-of-distribution generalization. The effectiveness and efficiency of TENON-DA and TENON-OOD are verified both theoretically and empirically.