Graph Pattern Mining and Learning through User-defined Relations (Extended Version)

In this work we propose R-GPM, a parallel computing framework for graph pattern mining (GPM) through a user-defined subgraph relation. More specifically, we enable the computation of statistics of patterns through their subgraph classes, generalizing traditional GPM methods. R-GPM provides efficient estimators for these statistics by employing a MCMC sampling algorithm combined with several optimizations. We provide both theoretical guarantees and empirical evaluations of our estimators in application scenarios such as stochastic optimization of deep high-order graph neural network models and pattern (motif) counting. We also propose and evaluate optimizations that enable improvements of our estimators accuracy, while reducing their computational costs in up to 3-orders-of-magnitude. Finally,we show that R-GPM is scalable, providing near-linear speedups on 44 cores in all of our tests.Comment: Extended version of the paper published in the ICDM 201

Neural Subgraph Isomorphism Counting

In this paper, we study a new graph learning problem: learning to count subgraph isomorphisms. Different from other traditional graph learning problems such as node classification and link prediction, subgraph isomorphism counting is NP-complete and requires more global inference to oversee the whole graph. To make it scalable for large-scale graphs and patterns, we propose a learning framework which augments different representation learning architectures and iteratively attends pattern and target data graphs to memorize subgraph isomorphisms for the global counting. We develop both small graphs (<= 1,024 subgraph isomorphisms in each) and large graphs (<= 4,096 subgraph isomorphisms in each) sets to evaluate different models. A mutagenic compound dataset, MUTAG, is also used to evaluate neural models and demonstrate the success of transfer learning. While the learning based approach is inexact, we are able to generalize to count large patterns and data graphs in linear time compared to the exponential time of the original NP-complete problem. Experimental results show that learning based subgraph isomorphism counting can speed up the traditional algorithm, VF2, 10-1,000 times with acceptable errors. Domain adaptation based on fine-tuning also shows the usefulness of our approach in real-world applications.Comment: Accepted by KDD 202

Sequential Stratified Regeneration: MCMC for Large State Spaces with an Application to Subgraph Count Estimation

This work considers the general task of estimating the sum of a bounded function over the edges of a graph, given neighborhood query access and where access to the entire network is prohibitively expensive. To estimate this sum, prior work proposes Markov chain Monte Carlo (MCMC) methods that use random walks started at some seed vertex and whose equilibrium distribution is the uniform distribution over all edges, eliminating the need to iterate over all edges. Unfortunately, these existing estimators are not scalable to massive real-world graphs. In this paper, we introduce Ripple, an MCMC-based estimator that achieves unprecedented scalability by stratifying the Markov chain state space into ordered strata with a new technique that we denote {\em sequential stratified regenerations}. We show that the Ripple estimator is consistent, highly parallelizable, and scales well. We empirically evaluate our method by applying Ripple to the task of estimating connected, induced subgraph counts given some input graph. Therein, we demonstrate that Ripple is accurate and can estimate counts of up to $12$-node subgraphs, which is a task at a scale that has been considered unreachable, not only by prior MCMC-based methods but also by other sampling approaches. For instance, in this target application, we present results in which the Markov chain state space is as large as $10^{43}$, for which Ripple computes estimates in less than $4$ hours, on average.Comment: Markov Chain Monte Carlo, Random Walk, Regenerative Sampling, Motif Analysis, Subgraph Counting, Graph Minin