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Poster
On the Identifiability of Sparse ICA without Assuming Non-Gaussianity
Ignavier Ng · Yujia Zheng · Xinshuai Dong · Kun Zhang

Thu Dec 14 08:45 AM -- 10:45 AM (PST) @ Great Hall & Hall B1+B2 #1019
in Poster Session 5 »

Independent component analysis (ICA) is a fundamental statistical tool used to reveal hidden generative processes from observed data. However, traditional ICA approaches struggle with the rotational invariance inherent in Gaussian distributions, often necessitating the assumption of non-Gaussianity in the underlying sources. This may limit their applicability in broader contexts. To accommodate Gaussian sources, we develop an identifiability theory that relies on second-order statistics without imposing further preconditions on the distribution of sources, by introducing novel assumptions on the connective structure from sources to observed variables. Different from recent work that focuses on potentially restrictive connective structures, our proposed assumption of structural variability is both considerably less restrictive and provably necessary. Furthermore, we propose two estimation methods based on second-order statistics and sparsity constraint. Experimental results are provided to validate our identifiability theory and estimation methods.

Author Information

Ignavier Ng (Carnegie Mellon University)
Yujia Zheng (Carnegie Mellon University)
Xinshuai Dong (Carnegie Mellon University)
Kun Zhang (CMU & MBZUAI)

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