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Conference Paper 2019

The Incomplete Rosetta Stone problem: Identifiability results for Multi-view Nonlinear ICA

{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.}

Author(s): Gresele, L and Rubenstein, PK and Mehrjou, A. and Locatello, F and Schölkopf, B
Book Title: 35th Conference on Uncertainty in Artificial Intelligence (UAI 2019)
Volume: 115
Pages: 217--227
Year: 2019
Series: {Proceedings of Machine Learning Research (PLMR)}
Bibtex Type: Conference Paper (inproceedings)
Address: Tel Aviv, Israel
Electronic Archiving: grant_archive

BibTex 

@inproceedings{item_3151802,
  title = {{The Incomplete Rosetta Stone problem: Identifiability results for Multi-view Nonlinear ICA}},
  booktitle = {{35th Conference on Uncertainty in Artificial Intelligence (UAI 2019)}},
  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.}},
  volume = {115},
  pages = {217--227},
  series = {{Proceedings of Machine Learning Research (PLMR)}},
  address = {Tel Aviv, Israel},
  year = {2019},
  slug = {item_3151802},
  author = {Gresele, L and Rubenstein, PK and Mehrjou, A. and Locatello, F and Sch\"olkopf, B}
}