We study the classical problem of recovering a multidimensional source process from observations of nonlinear mixtures of this process. Assuming statistical independence of the coordinate processes of the source, we show that this recovery is possible for many popular models of stochastic processes (up to order and monotone scaling of their coordinates) if the mixture is given by a sufficiently differentiable, invertible function. Key to our approach is the combination of tools from stochastic analysis and recent contrastive learning approaches to nonlinear ICA. This yields a scalable method with widely applicable theoretical guarantees for which our experiments indicate good performance.

翻译：我们研究了从对这一过程的非线性混合物的观测中恢复一个多层面来源过程的典型问题。假设来源的协调过程在统计上独立,我们表明,如果混合过程是由一个足够不同、可垂直的功能提供的,这种恢复对于许多流行的随机过程模型(直至其坐标的顺序和单质缩放)来说是可能的。我们的方法的关键在于将随机分析工具与最近对非线性ICA的对比式学习方法结合起来。这产生了一种可伸缩的方法,具有广泛应用的理论保证,我们的实验表明其表现良好。