Negative Dependence, Stable Polynomials, and All That

This tutorial provides an introduction to a rapidly evolving topic: the theory of negative dependence and its numerous ramifications in machine learning. Indeed, negatively dependent probability measures provide a powerful tool for modeling non-i.i.d. data, and thus can impact all aspects of learning, including supervised, unsupervised, interpretable, interactive, and large-scale setups. The most well-known examples of negatively dependent distributions are perhaps the Determinantal Point Processes (DPPs), which have already found numerous ML applications. But DPPs are just the tip of the iceberg; the class of negatively dependent measures is much broader, and given the vast web of mathematical connections it enjoys, its holds great promise as a tool for machine learning. This tutorial exposes the ML audience to this rich mathematical toolbox, while outlining key theoretical ideas and motivating fundamental applications. Tasks that profit from negative dependence include anomaly detection, information maximization, experimental design, validation of black-box systems, architecture learning, fast MCMC sampling, dataset summarization, interpretable learning.