  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.
