Correlation-Fusion for Variable Clustering in High-Dimensional G-Models: Theory and Algorithms

• Activity Number: 626
• Type: Invited
• Date/Time: Thursday, August 13, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Statistical and Applied Mathematical Sciences Institute
• Author(s): Florentina Bunea*
• Companies: Cornell University
• Keywords: Latent model ; Block-covariance matrix ; Exchangeable ; Variable clustering ; Partition recovery ; High dimensions

Abstract

The problem of deciding on criteria for partitioning a p-dimensional random vector in groups of similar nature is fundamental in variable clustering, a technique widely used in genetics and neuroscience. We advocate the use of probabilistic models for defining a partition G of a p-dimensional vector. For a given, but unknown, partition G we introduce three models, of increasing complexity: G-latent, G-exchangeable and G-block-covariance models. We show that the G-exchangeable and G-block covariance models are identifiable, irrespective of the distribution of X. Moreover, if X is Gaussian, we give mild conditions under which all three models are identifiable. We develop a computationally efficient new method, called Correlation-Fusion, that is shown to recover the unknown partition G with high probability, when data is generated from a Gaussian copula distribution. A minimax lower bound shows that our conditions for recovery are sharp. An extensive simulation study shows that our new method outperforms existing clustering algorithms, when data is generated from a G-model. We illustrate our procedure by estimating regions of interest from an fMRI data set.