2020 IEEE International Symposium
on Information Theory
21-26 June 2020 • Los Angeles, California, USA
| Paper ID | L.4.4 | ||
| Paper Title | Latent Factor Analysis of Gaussian Distributions under Graphical Constraints | ||
| Authors | Md Mahmudul Hasan, Shuangqing Wei, Ali Moharrer, Louisiana State University, United States | ||
| Session | L.4: Distribution Learning | ||
| Presentation | Lecture | ||
| Track | Statistics and Learning Theory | ||
| Manuscript | Click here to download the manuscript | ||
| Virtual Presentation | Click here to watch in the Virtual Symposium | ||
| 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 $\Sigma_x$ 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 $\Sigma_x$. 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. | ||
Plan Ahead
2021 IEEE International Symposium on Information Theory
11-16 July 2021 | Melbourne, Victoria, Australia
