Learning with Small Data: Subgraph Counting Queries

Deep 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 efficient 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. This problem is NP-hard, and needs large training data to learn by DL in nature. To solve this problem, 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 obtain a generalized meta-model to better encode the information of data and pattern graphs and capture the prior of small tasks. 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 cases. One is there are some with ground-truth (few-shot), and one is there is none with ground-truth (zero-shot). We provide our solutions for both. We conduct substantial experiments to confirm that our approach is robust to model degeneration on small training data, and our meta model can fast adapt to new queries by few/zero-shot learning.