Independent component analysis (ICA) decomposes multivariate data into mutually independent components (ICs). The ICA model is subject to a constraint that at most one of these components is Gaussian, which is required for model identifiability. Linear non‐Gaussian component analysis (LNGCA) generalizes the ICA model to a linear latent factor model with any number of both non‐Gaussian components (signals) and Gaussian components (noise), where observations are linear combinations of independent components. Although the individual Gaussian components are not identifiable, the Gaussian subspace is identifiable. We introduce an estimator along with its optimization approach in which non‐Gaussian and Gaussian components are estimated simultaneously, maximizing the discrepancy of each non‐Gaussian component from Gaussianity while minimizing the discrepancy of each Gaussian component from Gaussianity. When the number of non‐Gaussian components is unknown, we develop a statistical test to determine it based on resampling and the discrepancy of estimated components. Through a variety of simulation studies, we demonstrate the improvements of our estimator over competing estimators, and we illustrate the effectiveness of our test to determine the number of non‐Gaussian components. Further, we apply our method to real data examples and show its practical value.
Identification of Linear Latent Variable Model with Arbitrary Distribution
An important problem across multiple disciplines is to infer and understand meaningful latent variables. One strategy commonly used is to model the measured variables in terms of the latent variables under suitable assumptions on the connectivity from the latents to the measured (known as measurement model). Furthermore, it might be even more interesting to discover the causal relations among the latent variables (known as structural model). Recently, some methods have been proposed to estimate the structural model by assuming that the noise terms in the measured and latent variables are nonGaussian. However, they are not suitable when some of the noise terms become Gaussian. To bridge this gap, we investigate the problem of identification of the structural model with arbitrary noise distributions. We provide necessary and sufficient condition under which the structural model is identifiable: it is identifiable iff for each pair of adjacent latent variables Lx, Ly, (1) at least one of Lx and Ly has nonGaussian noise, or (2) at least one of them has a nonGaussian ancestor and is not dseparated from the nonGaussian component of this ancestor by the common causes of Lx and Ly. This identifiability result relaxes the nonGaussianity requirements to only a (hopefully small) subset of variables, and accordingly elegantly extends the application scope of the structural model. Based on the above identifiability result, we further propose a practical algorithm to learn the structural model. We verify the correctness of the identifiability result and the effectiveness of the proposed method through empirical studies.
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 Award ID(s):
 2134901
 NSFPAR ID:
 10380985
 Date Published:
 Journal Name:
 Proceedings of the AAAI Conference on Artificial Intelligence
 Volume:
 36
 Issue:
 6
 ISSN:
 21595399
 Page Range / eLocation ID:
 6350 to 6357
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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