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Paper Detail

Paper IDL.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.

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2021 IEEE International Symposium on Information Theory

11-16 July 2021 | Melbourne, Victoria, Australia

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