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  The Incomplete Rosetta Stone Problem: Identifiability Results for Multi-View Nonlinear ICA

Gresele, L., Rubenstein, P., Mehrjou, A., Locatello, F., & Schölkopf, B. (submitted). The Incomplete Rosetta Stone Problem: Identifiability Results for Multi-View Nonlinear ICA.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0003-A535-7 Version Permalink: http://hdl.handle.net/21.11116/0000-0003-A536-6
Genre: Journal Article

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https://arxiv.org/abs/1905.06642 (Any fulltext)
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 Creators:
Gresele, L1, 2, Author              
Rubenstein, PK, Author
Mehrjou, A, Author
Locatello, F, Author
Schölkopf, B3, Author              
Affiliations:
1Department High-Field Magnetic Resonance, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497796              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              
3Dept. Empirical Inference, Max Planck Institute for Intelligent Systems, Max Planck Society, ou_1497647              

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 Abstract: We consider the problem of recovering a common latent source with independent components from multiple views. This applies to settings in which a variable is measured with multiple experimental modalities, and where the goal is to synthesize the disparate measurements into a single unified representation. We consider the case that the observed views are a nonlinear mixing of component-wise corruptions of the sources. When the views are considered separately, this reduces to nonlinear Independent Component Analysis (ICA) for which it is provably impossible to undo the mixing. We present novel identifiability proofs that this is possible when the multiple views are considered jointly, showing that the mixing can theoretically be undone using function approximators such as deep neural networks. In contrast to known identifiability results for nonlinear ICA, we prove that independent latent sources with arbitrary mixing can be recovered as long as multiple, sufficiently different noisy views are available.

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 Dates: 2019-05
 Publication Status: Submitted
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