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Title: Dynamic mixture of finite mixtures of factor analysers with automatic inference on number of clusters and factors Authors:  Margarita Grushanina - WU Vienna University of Economics and Business (Austria) [presenting]
Sylvia Fruehwirth-Schnatter - WU Vienna University of Economics and Business (Austria)
Abstract: Mixtures of factor analysers represent a popular tool for finding structure in data. While in most applications the number of clusters and latent factors within clusters is fixed in advance, recently models with automatic inference on both the number of clusters and factors have been introduced. The automatic inference is usually done by assigning a nonparametric prior and allowing the number of clusters and factors potentially be infinite. The MCMC estimation is performed via an adaptive algorithm, in which the parameters associated with redundant factors are discarded as the chain moves. Besides its clear advantages, this approach also has drawbacks. Running a separate factor-analytical model for each cluster involves matrices of changing dimensions, which makes the model and programming cumbersome. Also, discarding the parameters associated with the redundant factors could lead to a bias in estimating cluster covariance matrices. The contribution to the MFA literature is to allow automatic inference on the number of clusters and factors while keeping both cluster and factor dimensions finite. Thus, some of the abovementioned drawbacks of infinite models are avoided. For the automatic inference on cluster structure, we employ the dynamic mixture of finite mixtures. Automatic inference on cluster-specific factors is performed via an extension of the cumulative shrinkage process prior to using its representation as an ordered version of the Indian buffet process.