Graph Mixing Additive Networks

TL;DR

GMAN addresses learning from sets of sparse temporal graphs by modeling each trajectory as a directed path graph with time-encoded edges, preserving temporal distances and permutation invariance across paths. It combines Extended GNAN encoders (ExtGNAN) with a partitioned subset-mixing scheme to process subsets of graphs, enabling a tunable trade-off between interpretability and expressivity, and can be compactly written as GMAN(S) = $\sum_{c=1}^d \sum_{i=1}^k [\Phi_i(S_i)]_c$. GMAN is strictly more expressive than GNAN, and grouping graphs into non-singleton subsets strictly increases expressivity, with formal proofs provided in the appendix. Empirically, GMAN achieves strong performance on in-hospital mortality prediction from PhysioNet P12 and fake-news propagation on GossipCop while delivering multi-resolution explanations (node-, graph-, and set-level attributions).

Abstract

We introduce GMAN, a flexible, interpretable, and expressive framework that extends Graph Neural Additive Networks (GNANs) to learn from sets of sparse time-series data. GMAN represents each time-dependent trajectory as a directed graph and applies an enriched, more expressive GNAN to each graph. It allows users to control the interpretability-expressivity trade-off by grouping features and graphs to encode priors, and it provides feature, node, and graph-level interpretability. On real-world datasets, including mortality prediction from blood tests and fake-news detection, GMAN outperforms strong non-interpretable black-box baselines while delivering actionable, domain-aligned explanations.

Theorems & Definitions (4)

• theorem 1
• theorem 2
• theorem 3
• theorem 4