Nonlinear ICA of Temporally Dependent Stationary Sources
Nonlinear ICA of Temporally Dependent Stationary Sources
复制标题
DOI：
--
复制
发表时间：
2017-04
期刊：
影响因子：
--
通讯作者：
Aapo Hyvärinen;H. Morioka
中科院分区：
文献类型：
--
作者：
Aapo Hyvärinen;H. Morioka
基于时间相关性(例如自相关)，我们发展了独立分量分析(ICA)或盲源分离的非线性推广。我们引入了一个非线性生成模型，假设独立源是时间依赖的、非高斯的和平稳的，并且我们观察到它们的任意非线性混合。我们开发了一种基于Logistic回归的神经网络模型估计方法(即分离源)，该方法学习区分数据的短时间窗口和时间置换数据的时间窗口。我们证明了在假设源具有足够强的时间相关性，并且这些相关性在某种程度上不同于高斯过程中的相关性的情况下，该方法估计了一般光滑混合非线性的源。对于高斯(和类似)源，该方法估计混合的非线性部分。由此，我们给出了时间依赖源的非线性独立分量分析可辨识性的第一个严格而一般的证明，并给出了一种实用的估计方法。
We develop a nonlinear generalization of independent component analysis (ICA) or blind source separation, based on temporal dependencies (e.g. autocorrelations). We introduce a nonlinear generative model where the independent sources are assumed to be temporally dependent, non-Gaussian, and stationary, and we observe arbitrarily nonlinear mixtures of them. We develop a method for estimating the model (i.e. separating the sources) based on logistic regression in a neural network which learns to discriminate between a short temporal window of the data vs. a temporal window of temporally permuted data. We prove that the method estimates the sources for general smooth mixing nonlinearities, assuming the sources have sufficiently strong temporal dependencies, and these dependencies are in a certain way different from dependencies found in Gaussian processes. For Gaussian (and similar) sources, the method estimates the nonlinear part of the mixing. We thus provide the first rigorous and general proof of identifiability of nonlinear ICA for temporally dependent sources, together with a practical method for its estimation.