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.

翻译：隐变量发现是数据分析中的一个核心问题，在应用科学领域具有广泛的应用。本研究考虑由两个统计独立分量通过可逆混合得到的数据，并假设其中一个分量可观测，另一个分量隐藏。我们的目标是恢复隐藏的分量。为此，我们提出了一种配备判别器的自编码器。与已被证明不可识别的标准非线性ICA问题不同，在我们考虑的这种特殊ICA情形下，我们证明该方法能够恢复目标分量直至熵保持变换。我们通过在图像合成、语音克隆及胎儿心电图提取等多项任务中展示了所提出方法的性能。