Graph pooling is a crucial operation for encoding hierarchical structures within graphs. Most existing graph pooling approaches formulate the problem as a node clustering task which effectively captures the graph topology. Conventional methods ask users to specify an appropriate number of clusters as a hyperparameter, then assume that all input graphs share the same number of clusters. In inductive settings where the number of clusters can vary, however, the model should be able to represent this variation in its pooling layers in order to learn suitable clusters. Thus we propose GMPool, a novel differentiable graph pooling architecture that automatically determines the appropriate number of clusters based on the input data. The main intuition involves a grouping matrix defined as a quadratic form of the pooling operator, which induces use of binary classification probabilities of pairwise combinations of nodes. GMPool obtains the pooling operator by first computing the grouping matrix, then decomposing it. Extensive evaluations on molecular property prediction tasks demonstrate that our method outperforms conventional methods.

Across many data domains, co-occurrence statistics about the joint appearance of objects are powerfully informative. By transforming unsupervised learning problems into decompositions of co-occurrence statistics, spectral algorithms provide transparent and efficient algorithms for posterior inference such as latent topic analysis and community detection. As object vocabularies grow, however, it becomes rapidly more expensive to store and run inference algorithms on co-occurrence statistics. Rectifying co-occurrence, the key process to uphold model assumptions, becomes increasingly more vital in the presence of rare terms, but current techniques cannot scale to large vocabularies. We propose novel methods that simultaneously compress and rectify co-occurrence statistics, scaling gracefully with the size of vocabulary and the dimension of latent space. We also present new algorithms learning latent variables from the compressed statistics, and verify that our methods perform comparably to previous approaches on both textual and non-textual data.

Many online communities present user-contributed responses, such as reviews of products and answers to questions. User-provided helpfulness votes can highlight the most useful responses, but voting is a social process that can gain momentum based on the popularity of responses and the polarity of existing votes. We propose the Chinese Voting Process (CVP) which models the evolution of helpfulness votes as a self-reinforcing process dependent on position and presentation biases. We evaluate this model on Amazon product reviews and more than 80 StackExchange forums, measuring the intrinsic quality of individual responses and behavioral coefficients of different communities.

Spectral inference provides fast algorithms and provable optimality for latent topic analysis. But for real data these algorithms require additional ad-hoc heuristics, and even then often produce unusable results. We explain this poor performance by casting the problem of topic inference in the framework of Joint Stochastic Matrix Factorization (JSMF) and showing that previous methods violate the theoretical conditions necessary for a good solution to exist. We then propose a novel rectification method that learns high quality topics and their interactions even on small, noisy data. This method achieves results comparable to probabilistic techniques in several domains while maintaining scalability and provable optimality.