The growth in the size and scope of modern data sets has presented the field of statistics with a number of challenges, among them is how to deal with various forms of heterogeneity. Mixture models provide a principled approach to modeling heterogeneous collections of data. However, it has been demonstrated that singularities appear very frequently in mixture models. These singularities cause statistical estimation methods, such as maximum likelihood estimator (MLE), or optimization techniques, such as expectation-maximization (EM), to have non-standard statistical rate of convergence. In this talk, we provide various insight into geometric structures of singularities in mixture models under two different perspective: statistical and computational perspective.
This talk features joint work with (alphabetically) Raaz Dwivedi, Michael I. Jordan, Koulik Khamaru, Long Nguyen, Ya’acov Ritov, Martin J. Wainwright, and Bin Yu.