  Latent variable discovery is a central problem in data analysis with a broad
range of applications in applied science. In this work, we consider data given
as an invertible mixture of two statistically independent components and assume
that one of the components is observed while the other is hidden. Our goal is
to recover the hidden component. For this purpose, we propose an autoencoder
equipped with a discriminator. Unlike the standard nonlinear ICA problem, which
was shown to be non-identifiable, in the special case of ICA we consider here,
we show that our approach can recover the component of interest up to
entropy-preserving transformation. We demonstrate the performance of the
proposed approach in several tasks, including image synthesis, voice cloning,
and fetal ECG extraction.
