Title
Latent Factor Analysis of Gaussian Distributions under Graphical Constraints
Document Type
Conference Proceeding
Publication Date
6-1-2020
Abstract
We explore the algebraic structure of the solution space of convex optimization problem Constrained Minimum Trace Factor Analysis (CMTFA), when the population covariance matrix Σx has an additional latent graphical constraint, namely, a latent star topology. In particular, we have shown that CMTFA can have either a rank 1 or a rank n - 1 solution and nothing in between. The special case of a rank 1 solution, corresponds to the case where just one latent variable captures all the dependencies among the observables, giving rise to a star topology. We found explicit conditions for both rank 1 and rank n - 1 solutions for CMTFA solution of Σx. As a basic attempt towards building a more general Gaussian tree, we have found a necessary and a sufficient condition for multiple clusters each having rank 1 CMTFA solution to satisfy a minimum probability, to combine together to build a Gaussian tree.
Publication Source (Journal or Book title)
IEEE International Symposium on Information Theory - Proceedings
First Page
2580
Last Page
2585
Recommended Citation
Hasan, M., Wei, S., & Moharrer, A. (2020). Latent Factor Analysis of Gaussian Distributions under Graphical Constraints. IEEE International Symposium on Information Theory - Proceedings, 2020-June, 2580-2585. https://doi.org/10.1109/ISIT44484.2020.9174323