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Classification and regression in which the inputs are graphs of arbitrarysize and shape have been paid attention in various fields such as computationalchemistry and bioinformatics. Subgraph indicators are often used as the mostfundamental features, but the number of possible subgraph patterns areintractably large due to the combinatorial explosion. We propose a novelefficient algorithm to jointly learn relevant subgraph patterns and nonlinearmodels of their indicators. Previous methods for such joint learning ofsubgraph features and models are based on search for single best subgraphfeatures with specific pruning and boosting procedures of adding theirindicators one by one, which result in linear models of subgraph indicators. Incontrast, the proposed approach is based on directly learning regression treesfor graph inputs using a newly derived bound of the total sum of squares fordata partitions by a given subgraph feature, and thus can learn nonlinearmodels through standard gradient boosting. An illustrative example we call theGraph-XOR problem to consider nonlinearity, numerical experiments with realdatasets, and scalability comparisons to naive approaches using explicitpattern enumeration are also presented.

Jointly learning relevant subgraph patterns and nonlinear models of their indicators