Jointly learning relevant subgraph patterns and nonlinear models of their indicators

TL;DR

This paper introduces an efficient method for jointly learning relevant subgraph patterns and nonlinear models for graph classification and regression, overcoming the limitations of linear models and exhaustive pattern search.

Contribution

It proposes a novel algorithm that directly learns regression trees for graphs using bounds on data partitions, enabling nonlinear modeling through gradient boosting.

Findings

Effective in capturing nonlinear relationships in graph data

Outperforms naive enumeration approaches in scalability

Demonstrates strong results on real datasets

Abstract

Classification and regression in which the inputs are graphs of arbitrary size and shape have been paid attention in various fields such as computational chemistry and bioinformatics. Subgraph indicators are often used as the most fundamental features, but the number of possible subgraph patterns are intractably large due to the combinatorial explosion. We propose a novel efficient algorithm to jointly learn relevant subgraph patterns and nonlinear models of their indicators. Previous methods for such joint learning of subgraph features and models are based on search for single best subgraph features with specific pruning and boosting procedures of adding their indicators one by one, which result in linear models of subgraph indicators. In contrast, the proposed approach is based on directly learning regression trees for graph inputs using a newly derived bound of the total sum of squares for data partitions by a given subgraph feature, and thus can learn nonlinear models through standard gradient boosting. An illustrative example we call the Graph-XOR problem to consider nonlinearity, numerical experiments with real datasets, and scalability comparisons to naive approaches using explicit pattern enumeration are also presented.