Learning with Small Data: Subgraph Counting Queries

AbstractDeep Learning (DL) has been widely used in many applications, and its success is achieved with large training data. A key issue is how to provide a DL solution when there is no large training data to learn initially. In this paper, we explore a meta-learning approach for a specific problem, subgraph isomorphism counting, which is a fundamental problem in graph analysis to count the number of a given pattern graph, p, in a data graph, g, that matches p. There are various data graphs and pattern graphs. A subgraph isomorphism counting query is specified by a pair, (g, p). This problem is NP-hard and needs large training data to learn by DL in nature. We design a Gaussian Process (GP) model which combines Graph Neural Network with Bayesian nonparametric, and we train the GP by a meta-learning algorithm on a small set of training data. By meta-learning, we can obtain a generalized meta-model to better encode the information of data and pattern graphs and capture the prior of small tasks. With the meta-model learned, we handle a collection of pairs (g, p), as a task, where some pairs may be associated with the ground-truth, and some pairs are the queries to answer. There are two