2017/12/06 by Victor Veitch, Ekansh Sharma, Veitch, Victor +5
Computer Science · Mathematics · #Advanced Clustering Algorithms Research #Bayesian Methods and Mixture Models #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #Machine Learning (stat.ML) #stat.ML
paper · pdf · doi:10.48550/arxiv.1712.02311
9 pages, 4 figures
arxiv created 2017/12/06 · openalex publication_date 2017/12/06 · arxiv updated 2017/12/07 · openalex created_date 2017/12/22 · openalex updated_date 2026/07/28
A variety of machine learning tasks---e.g., matrix factorization, topic modelling, and feature allocation---can be viewed as learning the parameters of a probability distribution over bipartite graphs. Recently, a new class of models for networks, the sparse exchangeable graphs, have been introduced to resolve some important pathologies of traditional approaches to statistical network modelling; most notably, the inability to model sparsity (in the asymptotic sense). The present paper explains some practical insights arising from this work. We first show how to check if sparsity is relevant for modelling a given (fixed size) dataset by using network subsampling to identify a simple signature of sparsity. We discuss the implications of the (sparse) exchangeable subsampling theory for test-train dataset splitting; we argue common approaches can lead to biased results, and we propose a principled alternative. Finally, we study sparse exchangeable Poisson matrix factorization as a worked example. In particular, we show how to adapt mean field variational inference to the sparse exchangeable setting, allowing us to scale inference to huge datasets.