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 on several datasets, including image synthesis, voice cloning, and fetal ECG extraction.

翻译：隐变量发现是数据分析中的核心问题，在应用科学领域具有广泛的应用。本研究考虑数据由两个统计独立的组分通过可逆混合而成，并假设其中一个组分可观测而另一个隐藏。我们的目标是恢复隐藏组分。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独立成分分析（ICA）问题不同，在我们此处考虑的ICA特例中，我们证明该方法能在保留熵的变换下恢复目标组分。我们通过多个数据集（包括图像合成、语音克隆和胎儿心电图提取）验证了所提方法的性能。