Binary Independent Component Analysis via Non-stationarity

• URL: http://arxiv.org/abs/2111.15431v1
• Date: Tue, 30 Nov 2021 14:23:53 GMT
• Title: Binary Independent Component Analysis via Non-stationarity
• Authors: Antti Hyttinen, Vit\'oria Barin-Pacela, Aapo Hyv\"arinen
• Abstract summary: We consider independent component analysis of binary data. We start by assuming a linear mixing model in a continuous-valued latent space, followed by a binary observation model. In stark contrast to the continuous-valued case, we prove non-identifiability of the model with few observed variables.
• Score: 7.283533791778359
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider independent component analysis of binary data. While fundamental in practice, this case has been much less developed than ICA for continuous data. We start by assuming a linear mixing model in a continuous-valued latent space, followed by a binary observation model. Importantly, we assume that the sources are non-stationary; this is necessary since any non-Gaussianity would essentially be destroyed by the binarization. Interestingly, the model allows for closed-form likelihood by employing the cumulative distribution function of the multivariate Gaussian distribution. In stark contrast to the continuous-valued case, we prove non-identifiability of the model with few observed variables; our empirical results imply identifiability when the number of observed variables is higher. We present a practical method for binary ICA that uses only pairwise marginals, which are faster to compute than the full multivariate likelihood.

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